dropbear: libtommath/bn.tex annotate

annotate libtommath/bn.tex @ 1594:c69df5d5db94

ciphers/hashes/kex algorithms won't have string lengths, also use dictionary for fuzzer-preauth_nomaths

author	Matt Johnston <matt@ucc.asn.au>
date	Mon, 05 Mar 2018 21:02:26 +0800
parents	60fc6476e044
children

rev	line source
389 5ff8218bcee9 propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 2af95f00ebd5bb7a28b3817db1218442c935388e) Matt Johnston <matt@ucc.asn.au> parents: 284 diff changeset	1 \documentclass[synpaper]{book}
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	2 \usepackage{hyperref}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	3 \usepackage{makeidx}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	4 \usepackage{amssymb}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	5 \usepackage{color}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	6 \usepackage{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	7 \usepackage{graphicx}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	8 \usepackage{layout}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	9 \def\union{\cup}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	10 \def\intersect{\cap}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	11 \def\getsrandom{\stackrel{\rm R}{\gets}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	12 \def\cross{\times}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	13 \def\cat{\hspace{0.5em} \\| \hspace{0.5em}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	14 \def\catn{$\\|$}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	15 \def\divides{\hspace{0.3em} \| \hspace{0.3em}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	16 \def\nequiv{\not\equiv}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	17 \def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	18 \def\lcm{{\rm lcm}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	19 \def\gcd{{\rm gcd}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	20 \def\log{{\rm log}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	21 \def\ord{{\rm ord}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	22 \def\abs{{\mathit abs}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	23 \def\rep{{\mathit rep}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	24 \def\mod{{\mathit\ mod\ }}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	25 \renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	26 \newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	27 \newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	28 \def\Or{{\rm\ or\ }}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	29 \def\And{{\rm\ and\ }}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	30 \def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	31 \def\implies{\Rightarrow}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	32 \def\undefined{{\rm ``undefined"}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	33 \def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	34 \let\oldphi\phi
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	35 \def\phi{\varphi}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	36 \def\Pr{{\rm Pr}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	37 \newcommand{\str}[1]{{\mathbf{#1}}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	38 \def\F{{\mathbb F}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	39 \def\N{{\mathbb N}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	40 \def\Z{{\mathbb Z}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	41 \def\R{{\mathbb R}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	42 \def\C{{\mathbb C}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	43 \def\Q{{\mathbb Q}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	44 \definecolor{DGray}{gray}{0.5}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	45 \newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	46 \def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	47 \def\gap{\vspace{0.5ex}}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	48 \makeindex
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	49 \begin{document}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	50 \frontmatter
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	51 \pagestyle{empty}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	52 \title{LibTomMath User Manual \\ v1.0}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	53 \author{Tom St Denis \\ [email protected]}
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	54 \maketitle
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	55 This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	56 formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	57
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	58 \vspace{10cm}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	59
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	60 \begin{flushright}Open Source. Open Academia. Open Minds.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	61
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	62 \mbox{ }
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	63
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	64 Tom St Denis,
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	65
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	66 Ontario, Canada
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	67 \end{flushright}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	68
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	69 \tableofcontents
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	70 \listoffigures
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	71 \mainmatter
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	72 \pagestyle{headings}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	73 \chapter{Introduction}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	74 \section{What is LibTomMath?}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	75 LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	76 large integer numbers. It was written in portable ISO C source code so that it will build on any platform with a conforming
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	77 C compiler.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	78
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	79 In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	80 to implement ``bignum'' math. However, the resulting code has proven to be very useful. It has been used by numerous
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	81 universities, commercial and open source software developers. It has been used on a variety of platforms ranging from
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	82 Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	83
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	84 \section{License}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	85 As of the v0.25 the library source code has been placed in the public domain with every new release. As of the v0.28
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	86 release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	87 release as well. This textbook is meant to compliment the project by providing a more solid walkthrough of the development
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	88 algorithms used in the library.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	89
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	90 Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger. They are not required to use LibTomMath.} are in the
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	91 public domain everyone is entitled to do with them as they see fit.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	92
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	93 \section{Building LibTomMath}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	94
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	95 LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC. However, the library will
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	96 also build in MSVC, Borland C out of the box. For any other ISO C compiler a makefile will have to be made by the end
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	97 developer.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	98
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	99 \subsection{Static Libraries}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	100 To build as a static library for GCC issue the following
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	101 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	102 make
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	103 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	104
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	105 command. This will build the library and archive the object files in ``libtommath.a''. Now you link against
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	106 that and include ``tommath.h'' within your programs. Alternatively to build with MSVC issue the following
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	107 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	108 nmake -f makefile.msvc
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	109 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	110
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	111 This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	112 version 6.00 with service pack 5.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	113
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	114 \subsection{Shared Libraries}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	115 To build as a shared library for GCC issue the following
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	116 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	117 make -f makefile.shared
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	118 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	119 This requires the ``libtool'' package (common on most Linux/BSD systems). It will build LibTomMath as both shared
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	120 and static then install (by default) into /usr/lib as well as install the header files in /usr/include. The shared
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	121 library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''. Generally
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	122 you use libtool to link your application against the shared object.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	123
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	124 There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	125 Cygwin to work with since it requires the auto-export/import functionality. The resulting DLL and import library
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	126 ``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	127
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	128 \subsection{Testing}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	129 To build the library and the test harness type
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	130
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	131 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	132 make test
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	133 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	134
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	135 This will build the library, ``test'' and ``mtest/mtest''. The ``test'' program will accept test vectors and verify the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	136 results. ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	137 is included in the package}. Simply pipe mtest into test using
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	138
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	139 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	140 mtest/mtest \| test
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	141 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	142
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	143 If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	144 mtest. For example, if your PRNG program is called ``myprng'' simply invoke
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	145
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	146 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	147 myprng \| mtest/mtest \| test
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	148 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	149
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	150 This will output a row of numbers that are increasing. Each column is a different test (such as addition, multiplication, etc)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	151 that is being performed. The numbers represent how many times the test was invoked. If an error is detected the program
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	152 will exit with a dump of the relevent numbers it was working with.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	153
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	154 \section{Build Configuration}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	155 LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	156 Each phase changes how the library is built and they are applied one after another respectively.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	157
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	158 To make the system more powerful you can tweak the build process. Classes are defined in the file
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	159 ``tommath\_superclass.h''. By default, the symbol ``LTM\_ALL'' shall be defined which simply
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	160 instructs the system to build all of the functions. This is how LibTomMath used to be packaged. This will give you
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	161 access to every function LibTomMath offers.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	162
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	163 However, there are cases where such a build is not optional. For instance, you want to perform RSA operations. You
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	164 don't need the vast majority of the library to perform these operations. Aside from LTM\_ALL there is
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	165 another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt. Additional
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	166 classes can be defined base on the need of the user.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	167
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	168 \subsection{Build Depends}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	169 In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	170 which further define symbols. All of the symbols (technically they're macros $\ldots$) represent a given C source
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	171 file. For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''. When a define has been enabled the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	172 function in the respective file will be compiled and linked into the library. Accordingly when the define
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	173 is absent the file will not be compiled and not contribute any size to the library.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	174
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	175 You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	176 This is to help resolve as many dependencies as possible. In the last pass the symbol LTM\_LAST will be defined.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	177 This is useful for ``trims''.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	178
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	179 \subsection{Build Tweaks}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	180 A tweak is an algorithm ``alternative''. For example, to provide tradeoffs (usually between size and space).
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	181 They can be enabled at any pass of the configuration phase.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	182
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	183 \begin{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	184 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	185 \begin{tabular}{\|l\|l\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	186 \hline \textbf{Define} & \textbf{Purpose} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	187 \hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	188 & functional mp\_div() function \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	189 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	190 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	191 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	192 \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	193
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	194 \subsection{Build Trims}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	195 A trim is a manner of removing functionality from a function that is not required. For instance, to perform
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	196 RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	197 Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	198 only if LTM\_LAST has been defined.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	199
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	200 \subsubsection{Moduli Related}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	201 \begin{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	202 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	203 \begin{tabular}{\|l\|l\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	204 \hline \textbf{Restriction} & \textbf{Undefine} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	205 \hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	206 & BN\_MP\_REDUCE\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	207 & BN\_MP\_REDUCE\_SETUP\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	208 & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	209 & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	210 \hline Exponentiation with random odd moduli & (The above plus the following) \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	211 & BN\_MP\_REDUCE\_2K\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	212 & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	213 & BN\_MP\_REDUCE\_IS\_2K\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	214 & BN\_MP\_DR\_IS\_MODULUS\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	215 & BN\_MP\_DR\_REDUCE\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	216 & BN\_MP\_DR\_SETUP\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	217 \hline Modular inverse odd moduli only & BN\_MP\_INVMOD\_SLOW\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	218 \hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	219 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	220 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	221 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	222 \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	223
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	224 \subsubsection{Operand Size Related}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	225 \begin{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	226 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	227 \begin{tabular}{\|l\|l\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	228 \hline \textbf{Restriction} & \textbf{Undefine} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	229 \hline Moduli $\le 2560$ bits & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	230 & BN\_S\_MP\_MUL\_DIGS\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	231 & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	232 & BN\_S\_MP\_SQR\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	233 \hline Polynomial Schmolynomial & BN\_MP\_KARATSUBA\_MUL\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	234 & BN\_MP\_KARATSUBA\_SQR\_C \\
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	235 & BN\_MP\_TOOM\_MUL\_C \\
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	236 & BN\_MP\_TOOM\_SQR\_C \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	237
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	238 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	239 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	240 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	241 \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	242
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	243
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	244 \section{Purpose of LibTomMath}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	245 Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	246 bleeding edge performance in mind. First and foremost LibTomMath was written to be entirely open. Not only is the
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	247 source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	248 source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	249 arithmetic techniques.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	250
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	251 LibTomMath was written to be an instructive collection of source code. This is why there are many comments, only one
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	252 function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	253 increase.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	254
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	255 Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	256 the library (beat that!).
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	257
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	258 So you may be thinking ``should I use LibTomMath?'' and the answer is a definite maybe. Let me tabulate what I think
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	259 are the pros and cons of LibTomMath by comparing it to the math routines from GnuPG\footnote{GnuPG v1.2.3 versus LibTomMath v0.28}.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	260
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	261 \newpage\begin{figure}[here]
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	262 \begin{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	263 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	264 \begin{tabular}{\|l\|c\|c\|l\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	265 \hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	266 \hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath $ = 71.97$ \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	267 \hline Commented function prototypes & X && GnuPG function names are cryptic. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	268 \hline Speed && X & LibTomMath is slower. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	269 \hline Totally free & X & & GPL has unfavourable restrictions.\\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	270 \hline Large function base & X & & GnuPG is barebones. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	271 \hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	272 \hline Portable & X & & GnuPG requires configuration to build. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	273 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	274 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	275 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	276 \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	277 \caption{LibTomMath Valuation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	278 \end{figure}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	279
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	280 It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	281 However, LibTomMath was written with cryptography in mind. It provides essentially all of the functions a cryptosystem
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	282 would require when working with large integers.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	283
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	284 So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	285 own application but I think there are reasons not to. While LibTomMath is slower than libraries such as GnuMP it is
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	286 not normally significantly slower. On x86 machines the difference is normally a factor of two when performing modular
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	287 exponentiations. It depends largely on the processor, compiler and the moduli being used.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	288
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	289 Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern. However,
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	290 on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	291 that is very flexible, complete and performs well in resource contrained environments. Fast RSA for example can
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	292 be performed with as little as 8KB of ram for data (again depending on build options).
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	293
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	294 \chapter{Getting Started with LibTomMath}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	295 \section{Building Programs}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	296 In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	297 libtommath.a). There is no library initialization required and the entire library is thread safe.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	298
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	299 \section{Return Codes}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	300 There are three possible return codes a function may return.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	301
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	302 \index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	303 \begin{figure}[here!]
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	304 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	305 \begin{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	306 \begin{tabular}{\|l\|l\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	307 \hline \textbf{Code} & \textbf{Meaning} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	308 \hline MP\_OKAY & The function succeeded. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	309 \hline MP\_VAL & The function input was invalid. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	310 \hline MP\_MEM & Heap memory exhausted. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	311 \hline &\\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	312 \hline MP\_YES & Response is yes. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	313 \hline MP\_NO & Response is no. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	314 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	315 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	316 \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	317 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	318 \caption{Return Codes}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	319 \end{figure}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	320
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	321 The last two codes listed are not actually ``return'ed'' by a function. They are placed in an integer (the caller must
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	322 provide the address of an integer it can store to) which the caller can access. To convert one of the three return codes
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	323 to a string use the following function.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	324
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	325 \index{mp\_error\_to\_string}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	326 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	327 char *mp_error_to_string(int code);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	328 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	329
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	330 This will return a pointer to a string which describes the given error code. It will not work for the return codes
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	331 MP\_YES and MP\_NO.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	332
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	333 \section{Data Types}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	334 The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath. This data type is used to
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	335 organize all of the data required to manipulate the integer it represents. Within LibTomMath it has been prototyped
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	336 as the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	337
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	338 \index{mp\_int}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	339 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	340 typedef struct \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	341 int used, alloc, sign;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	342 mp_digit *dp;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	343 \} mp_int;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	344 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	345
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	346 Where ``mp\_digit'' is a data type that represents individual digits of the integer. By default, an mp\_digit is the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	347 ISO C ``unsigned long'' data type and each digit is $28-$bits long. The mp\_digit type can be configured to suit other
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	348 platforms by defining the appropriate macros.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	349
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	350 All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure. You must allocate memory to
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	351 hold the structure itself by yourself (whether off stack or heap it doesn't matter). The very first thing that must be
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	352 done to use an mp\_int is that it must be initialized.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	353
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	354 \section{Function Organization}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	355
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	356 The arithmetic functions of the library are all organized to have the same style prototype. That is source operands
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	357 are passed on the left and the destination is on the right. For instance,
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	358
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	359 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	360 mp_add(&a, &b, &c); /* c = a + b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	361 mp_mul(&a, &a, &c); /* c = a * a */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	362 mp_div(&a, &b, &c, &d); /* c = [a/b], d = a mod b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	363 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	364
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	365 Another feature of the way the functions have been implemented is that source operands can be destination operands as well.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	366 For instance,
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	367
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	368 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	369 mp_add(&a, &b, &b); /* b = a + b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	370 mp_div(&a, &b, &a, &c); /* a = [a/b], c = a mod b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	371 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	372
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	373 This allows operands to be re-used which can make programming simpler.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	374
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	375 \section{Initialization}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	376 \subsection{Single Initialization}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	377 A single mp\_int can be initialized with the ``mp\_init'' function.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	378
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	379 \index{mp\_init}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	380 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	381 int mp_init (mp_int * a);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	382 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	383
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	384 This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	385 represents the default integer which is zero. If the functions returns MP\_OKAY then the mp\_int is ready to be used
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	386 by the other LibTomMath functions.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	387
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	388 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	389 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	390 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	391 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	392 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	393
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	394 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	395 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	396 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	397 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	398 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	399
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	400 /* use the number */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	401
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	402 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	403 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	404 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	405
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	406 \subsection{Single Free}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	407 When you are finished with an mp\_int it is ideal to return the heap it used back to the system. The following function
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	408 provides this functionality.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	409
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	410 \index{mp\_clear}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	411 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	412 void mp_clear (mp_int * a);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	413 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	414
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	415 The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses. It sets the
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	416 pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	417 Is is legal to call mp\_clear() twice on the same mp\_int in a row.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	418
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	419 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	420 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	421 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	422 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	423 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	424
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	425 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	426 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	427 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	428 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	429 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	430
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	431 /* use the number */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	432
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	433 /* We're done with it. */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	434 mp_clear(&number);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	435
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	436 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	437 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	438 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	439
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	440 \subsection{Multiple Initializations}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	441 Certain algorithms require more than one large integer. In these instances it is ideal to initialize all of the mp\_int
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	442 variables in an ``all or nothing'' fashion. That is, they are either all initialized successfully or they are all
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	443 not initialized.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	444
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	445 The mp\_init\_multi() function provides this functionality.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	446
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	447 \index{mp\_init\_multi} \index{mp\_clear\_multi}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	448 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	449 int mp_init_multi(mp_int *mp, ...);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	450 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	451
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	452 It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures. It will attempt to initialize them all
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	453 at once. If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	454 are available for use. A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	455 from the heap at the same time.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	456
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	457 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	458 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	459 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	460 mp_int num1, num2, num3;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	461 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	462
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	463 if ((result = mp_init_multi(&num1,
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	464 &num2,
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	465 &num3, NULL)) != MP\_OKAY) \{
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	466 printf("Error initializing the numbers. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	467 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	468 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	469 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	470
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	471 /* use the numbers */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	472
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	473 /* We're done with them. */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	474 mp_clear_multi(&num1, &num2, &num3, NULL);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	475
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	476 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	477 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	478 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	479
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	480 \subsection{Other Initializers}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	481 To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	482
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	483 \index{mp\_init\_copy}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	484 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	485 int mp_init_copy (mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	486 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	487
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	488 This function will initialize $a$ and make it a copy of $b$ if all goes well.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	489
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	490 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	491 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	492 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	493 mp_int num1, num2;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	494 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	495
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	496 /* initialize and do work on num1 ... */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	497
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	498 /* We want a copy of num1 in num2 now */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	499 if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	500 printf("Error initializing the copy. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	501 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	502 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	503 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	504
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	505 /* now num2 is ready and contains a copy of num1 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	506
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	507 /* We're done with them. */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	508 mp_clear_multi(&num1, &num2, NULL);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	509
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	510 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	511 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	512 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	513
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	514 Another less common initializer is mp\_init\_size() which allows the user to initialize an mp\_int with a given
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	515 default number of digits. By default, all initializers allocate \textbf{MP\_PREC} digits. This function lets
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	516 you override this behaviour.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	517
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	518 \index{mp\_init\_size}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	519 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	520 int mp_init_size (mp_int * a, int size);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	521 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	522
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	523 The $size$ parameter must be greater than zero. If the function succeeds the mp\_int $a$ will be initialized
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	524 to have $size$ digits (which are all initially zero).
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	525
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	526 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	527 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	528 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	529 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	530 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	531
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	532 /* we need a 60-digit number */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	533 if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	534 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	535 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	536 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	537 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	538
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	539 /* use the number */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	540
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	541 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	542 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	543 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	544
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	545 \section{Maintenance Functions}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	546
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	547 \subsection{Reducing Memory Usage}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	548 When an mp\_int is in a state where it won't be changed again\footnote{A Diffie-Hellman modulus for instance.} excess
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	549 digits can be removed to return memory to the heap with the mp\_shrink() function.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	550
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	551 \index{mp\_shrink}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	552 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	553 int mp_shrink (mp_int * a);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	554 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	555
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	556 This will remove excess digits of the mp\_int $a$. If the operation fails the mp\_int should be intact without the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	557 excess digits being removed. Note that you can use a shrunk mp\_int in further computations, however, such operations
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	558 will require heap operations which can be slow. It is not ideal to shrink mp\_int variables that you will further
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	559 modify in the system (unless you are seriously low on memory).
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	560
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	561 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	562 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	563 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	564 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	565 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	566
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	567 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	568 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	569 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	570 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	571 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	572
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	573 /* use the number [e.g. pre-computation] */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	574
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	575 /* We're done with it for now. */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	576 if ((result = mp_shrink(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	577 printf("Error shrinking the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	578 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	579 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	580 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	581
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	582 /* use it .... */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	583
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	584
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	585 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	586 mp_clear(&number);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	587
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	588 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	589 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	590 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	591
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	592 \subsection{Adding additional digits}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	593
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	594 Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	595 the integer the mp\_int is meant to equal. The \textit{used} parameter dictates how many digits are significant, that is,
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	596 contribute to the value of the mp\_int. The \textit{alloc} parameter dictates how many digits are currently available in
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	597 the array. If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	598 your desired size.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	599
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	600 \index{mp\_grow}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	601 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	602 int mp_grow (mp_int * a, int size);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	603 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	604
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	605 This will grow the array of digits of $a$ to $size$. If the \textit{alloc} parameter is already bigger than
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	606 $size$ the function will not do anything.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	607
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	608 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	609 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	610 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	611 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	612 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	613
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	614 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	615 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	616 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	617 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	618 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	619
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	620 /* use the number */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	621
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	622 /* We need to add 20 digits to the number */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	623 if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	624 printf("Error growing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	625 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	626 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	627 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	628
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	629
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	630 /* use the number */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	631
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	632 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	633 mp_clear(&number);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	634
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	635 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	636 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	637 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	638
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	639 \chapter{Basic Operations}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	640 \section{Small Constants}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	641 Setting mp\_ints to small constants is a relatively common operation. To accomodate these instances there are two
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	642 small constant assignment functions. The first function is used to set a single digit constant while the second sets
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	643 an ISO C style ``unsigned long'' constant. The reason for both functions is efficiency. Setting a single digit is quick but the
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	644 domain of a digit can change (it's always at least $0 \ldots 127$).
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	645
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	646 \subsection{Single Digit}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	647
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	648 Setting a single digit can be accomplished with the following function.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	649
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	650 \index{mp\_set}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	651 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	652 void mp_set (mp_int * a, mp_digit b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	653 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	654
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	655 This will zero the contents of $a$ and make it represent an integer equal to the value of $b$. Note that this
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	656 function has a return type of \textbf{void}. It cannot cause an error so it is safe to assume the function
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	657 succeeded.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	658
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	659 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	660 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	661 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	662 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	663 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	664
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	665 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	666 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	667 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	668 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	669 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	670
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	671 /* set the number to 5 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	672 mp_set(&number, 5);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	673
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	674 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	675 mp_clear(&number);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	676
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	677 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	678 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	679 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	680
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	681 \subsection{Long Constants}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	682
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	683 To set a constant that is the size of an ISO C ``unsigned long'' and larger than a single digit the following function
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	684 can be used.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	685
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	686 \index{mp\_set\_int}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	687 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	688 int mp_set_int (mp_int * a, unsigned long b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	689 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	690
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	691 This will assign the value of the 32-bit variable $b$ to the mp\_int $a$. Unlike mp\_set() this function will always
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	692 accept a 32-bit input regardless of the size of a single digit. However, since the value may span several digits
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	693 this function can fail if it runs out of heap memory.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	694
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	695 To get the ``unsigned long'' copy of an mp\_int the following function can be used.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	696
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	697 \index{mp\_get\_int}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	698 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	699 unsigned long mp_get_int (mp_int * a);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	700 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	701
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	702 This will return the 32 least significant bits of the mp\_int $a$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	703
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	704 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	705 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	706 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	707 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	708 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	709
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	710 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	711 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	712 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	713 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	714 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	715
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	716 /* set the number to 654321 (note this is bigger than 127) */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	717 if ((result = mp_set_int(&number, 654321)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	718 printf("Error setting the value of the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	719 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	720 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	721 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	722
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	723 printf("number == \%lu", mp_get_int(&number));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	724
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	725 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	726 mp_clear(&number);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	727
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	728 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	729 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	730 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	731
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	732 This should output the following if the program succeeds.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	733
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	734 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	735 number == 654321
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	736 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	737
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	738 \subsection{Long Constants - platform dependant}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	739
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	740 \index{mp\_set\_long}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	741 \begin{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	742 int mp_set_long (mp_int * a, unsigned long b);
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	743 \end{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	744
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	745 This will assign the value of the platform-dependant sized variable $b$ to the mp\_int $a$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	746
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	747 To get the ``unsigned long'' copy of an mp\_int the following function can be used.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	748
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	749 \index{mp\_get\_long}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	750 \begin{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	751 unsigned long mp_get_long (mp_int * a);
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	752 \end{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	753
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	754 This will return the least significant bits of the mp\_int $a$ that fit into an ``unsigned long''.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	755
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	756 \subsection{Long Long Constants}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	757
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	758 \index{mp\_set\_long\_long}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	759 \begin{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	760 int mp_set_long_long (mp_int * a, unsigned long long b);
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	761 \end{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	762
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	763 This will assign the value of the 64-bit variable $b$ to the mp\_int $a$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	764
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	765 To get the ``unsigned long long'' copy of an mp\_int the following function can be used.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	766
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	767 \index{mp\_get\_long\_long}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	768 \begin{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	769 unsigned long long mp_get_long_long (mp_int * a);
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	770 \end{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	771
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	772 This will return the 64 least significant bits of the mp\_int $a$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	773
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	774 \subsection{Initialize and Setting Constants}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	775 To both initialize and set small constants the following two functions are available.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	776 \index{mp\_init\_set} \index{mp\_init\_set\_int}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	777 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	778 int mp_init_set (mp_int * a, mp_digit b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	779 int mp_init_set_int (mp_int * a, unsigned long b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	780 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	781
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	782 Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	783
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	784 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	785 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	786 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	787 mp_int number1, number2;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	788 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	789
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	790 /* initialize and set a single digit */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	791 if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	792 printf("Error setting number1: \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	793 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	794 return EXIT_FAILURE;
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	795 \}
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	796
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	797 /* initialize and set a long */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	798 if ((result = mp_init_set_int(&number2, 1023)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	799 printf("Error setting number2: \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	800 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	801 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	802 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	803
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	804 /* display */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	805 printf("Number1, Number2 == \%lu, \%lu",
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	806 mp_get_int(&number1), mp_get_int(&number2));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	807
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	808 /* clear */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	809 mp_clear_multi(&number1, &number2, NULL);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	810
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	811 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	812 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	813 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	814
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	815 If this program succeeds it shall output.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	816 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	817 Number1, Number2 == 100, 1023
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	818 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	819
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	820 \section{Comparisons}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	821
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	822 Comparisons in LibTomMath are always performed in a ``left to right'' fashion. There are three possible return codes
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	823 for any comparison.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	824
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	825 \index{MP\_GT} \index{MP\_EQ} \index{MP\_LT}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	826 \begin{figure}[here]
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	827 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	828 \begin{tabular}{\|c\|c\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	829 \hline \textbf{Result Code} & \textbf{Meaning} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	830 \hline MP\_GT & $a > b$ \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	831 \hline MP\_EQ & $a = b$ \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	832 \hline MP\_LT & $a < b$ \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	833 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	834 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	835 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	836 \caption{Comparison Codes for $a, b$}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	837 \label{fig:CMP}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	838 \end{figure}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	839
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	840 In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared. In this case $a$ is said to be ``to the left'' of
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	841 $b$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	842
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	843 \subsection{Unsigned comparison}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	844
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	845 An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	846 mp\_int structures. This is analogous to an absolute comparison. The function mp\_cmp\_mag() will compare two
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	847 mp\_int variables based on their digits only.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	848
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	849 \index{mp\_cmp\_mag}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	850 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	851 int mp_cmp_mag(mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	852 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	853 This will compare $a$ to $b$ placing $a$ to the left of $b$. This function cannot fail and will return one of the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	854 three compare codes listed in figure \ref{fig:CMP}.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	855
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	856 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	857 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	858 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	859 mp_int number1, number2;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	860 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	861
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	862 if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	863 printf("Error initializing the numbers. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	864 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	865 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	866 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	867
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	868 /* set the number1 to 5 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	869 mp_set(&number1, 5);
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	870
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	871 /* set the number2 to -6 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	872 mp_set(&number2, 6);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	873 if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	874 printf("Error negating number2. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	875 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	876 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	877 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	878
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	879 switch(mp_cmp_mag(&number1, &number2)) \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	880 case MP_GT: printf("\|number1\| > \|number2\|"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	881 case MP_EQ: printf("\|number1\| = \|number2\|"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	882 case MP_LT: printf("\|number1\| < \|number2\|"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	883 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	884
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	885 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	886 mp_clear_multi(&number1, &number2, NULL);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	887
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	888 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	889 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	890 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	891
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	892 If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	893 successfully it should print the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	894
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	895 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	896 \|number1\| < \|number2\|
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	897 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	898
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	899 This is because $\vert -6 \vert = 6$ and obviously $5 < 6$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	900
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	901 \subsection{Signed comparison}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	902
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	903 To compare two mp\_int variables based on their signed value the mp\_cmp() function is provided.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	904
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	905 \index{mp\_cmp}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	906 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	907 int mp_cmp(mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	908 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	909
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	910 This will compare $a$ to the left of $b$. It will first compare the signs of the two mp\_int variables. If they
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	911 differ it will return immediately based on their signs. If the signs are equal then it will compare the digits
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	912 individually. This function will return one of the compare conditions codes listed in figure \ref{fig:CMP}.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	913
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	914 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	915 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	916 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	917 mp_int number1, number2;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	918 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	919
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	920 if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	921 printf("Error initializing the numbers. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	922 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	923 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	924 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	925
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	926 /* set the number1 to 5 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	927 mp_set(&number1, 5);
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	928
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	929 /* set the number2 to -6 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	930 mp_set(&number2, 6);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	931 if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	932 printf("Error negating number2. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	933 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	934 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	935 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	936
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	937 switch(mp_cmp(&number1, &number2)) \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	938 case MP_GT: printf("number1 > number2"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	939 case MP_EQ: printf("number1 = number2"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	940 case MP_LT: printf("number1 < number2"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	941 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	942
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	943 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	944 mp_clear_multi(&number1, &number2, NULL);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	945
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	946 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	947 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	948 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	949
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	950 If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	951 successfully it should print the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	952
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	953 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	954 number1 > number2
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	955 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	956
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	957 \subsection{Single Digit}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	958
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	959 To compare a single digit against an mp\_int the following function has been provided.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	960
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	961 \index{mp\_cmp\_d}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	962 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	963 int mp_cmp_d(mp_int * a, mp_digit b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	964 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	965
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	966 This will compare $a$ to the left of $b$ using a signed comparison. Note that it will always treat $b$ as
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	967 positive. This function is rather handy when you have to compare against small values such as $1$ (which often
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	968 comes up in cryptography). The function cannot fail and will return one of the tree compare condition codes
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	969 listed in figure \ref{fig:CMP}.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	970
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	971
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	972 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	973 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	974 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	975 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	976 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	977
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	978 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	979 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	980 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	981 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	982 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	983
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	984 /* set the number to 5 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	985 mp_set(&number, 5);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	986
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	987 switch(mp_cmp_d(&number, 7)) \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	988 case MP_GT: printf("number > 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	989 case MP_EQ: printf("number = 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	990 case MP_LT: printf("number < 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	991 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	992
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	993 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	994 mp_clear(&number);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	995
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	996 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	997 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	998 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	999
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1000 If this program functions properly it will print out the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1001
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1002 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1003 number < 7
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1004 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1005
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1006 \section{Logical Operations}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1007
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1008 Logical operations are operations that can be performed either with simple shifts or boolean operators such as
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1009 AND, XOR and OR directly. These operations are very quick.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1010
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1011 \subsection{Multiplication by two}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1012
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1013 Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1014 right depending on the operation.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1015
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1016 When multiplying or dividing by two a special case routine can be used which are as follows.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1017 \index{mp\_mul\_2} \index{mp\_div\_2}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1018 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1019 int mp_mul_2(mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1020 int mp_div_2(mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1021 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1022
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1023 The former will assign twice $a$ to $b$ while the latter will assign half $a$ to $b$. These functions are fast
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1024 since the shift counts and maskes are hardcoded into the routines.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1025
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1026 \begin{small} \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1027 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1028 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1029 mp_int number;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1030 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1031
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1032 if ((result = mp_init(&number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1033 printf("Error initializing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1034 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1035 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1036 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1037
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1038 /* set the number to 5 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1039 mp_set(&number, 5);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1040
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1041 /* multiply by two */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1042 if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1043 printf("Error multiplying the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1044 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1045 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1046 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1047 switch(mp_cmp_d(&number, 7)) \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1048 case MP_GT: printf("2*number > 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1049 case MP_EQ: printf("2*number = 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1050 case MP_LT: printf("2*number < 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1051 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1052
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1053 /* now divide by two */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1054 if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1055 printf("Error dividing the number. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1056 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1057 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1058 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1059 switch(mp_cmp_d(&number, 7)) \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1060 case MP_GT: printf("2*number/2 > 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1061 case MP_EQ: printf("2*number/2 = 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1062 case MP_LT: printf("2*number/2 < 7"); break;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1063 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1064
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1065 /* we're done with it. */
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1066 mp_clear(&number);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1067
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1068 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1069 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1070 \end{alltt} \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1071
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1072 If this program is successful it will print out the following text.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1073
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1074 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1075 2*number > 7
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1076 2*number/2 < 7
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1077 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1078
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1079 Since $10 > 7$ and $5 < 7$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1080
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1081 To multiply by a power of two the following function can be used.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1082
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1083 \index{mp\_mul\_2d}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1084 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1085 int mp_mul_2d(mp_int * a, int b, mp_int * c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1086 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1087
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1088 This will multiply $a$ by $2^b$ and store the result in ``c''. If the value of $b$ is less than or equal to
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1089 zero the function will copy $a$ to ``c'' without performing any further actions. The multiplication itself
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1090 is implemented as a right-shift operation of $a$ by $b$ bits.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1091
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1092 To divide by a power of two use the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1093
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1094 \index{mp\_div\_2d}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1095 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1096 int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1097 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1098 Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'. If $b \le 0$ then the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1099 function simply copies $a$ over to ``c'' and zeroes $d$. The variable $d$ may be passed as a \textbf{NULL}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1100 value to signal that the remainder is not desired. The division itself is implemented as a left-shift
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1101 operation of $a$ by $b$ bits.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1102
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1103 \subsection{Polynomial Basis Operations}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1104
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1105 Strictly speaking the organization of the integers within the mp\_int structures is what is known as a
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1106 ``polynomial basis''. This simply means a field element is stored by divisions of a radix. For example, if
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1107 $f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1108 the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1109
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1110 To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place. The
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1111 following function provides this operation.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1112
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1113 \index{mp\_lshd}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1114 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1115 int mp_lshd (mp_int * a, int b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1116 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1117
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1118 This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1119 in the least significant digits. Similarly to divide by a power of $x$ the following function is provided.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1120
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1121 \index{mp\_rshd}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1122 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1123 void mp_rshd (mp_int * a, int b)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1124 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1125 This will divide $a$ in place by $x^b$ and discard the remainder. This function cannot fail as it performs the operations
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1126 in place and no new digits are required to complete it.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1127
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1128 \subsection{AND, OR and XOR Operations}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1129
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1130 While AND, OR and XOR operations are not typical ``bignum functions'' they can be useful in several instances. The
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1131 three functions are prototyped as follows.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1132
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1133 \index{mp\_or} \index{mp\_and} \index{mp\_xor}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1134 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1135 int mp_or (mp_int * a, mp_int * b, mp_int * c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1136 int mp_and (mp_int * a, mp_int * b, mp_int * c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1137 int mp_xor (mp_int * a, mp_int * b, mp_int * c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1138 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1139
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1140 Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1141
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1142 \section{Addition and Subtraction}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1143
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1144 To compute an addition or subtraction the following two functions can be used.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1145
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1146 \index{mp\_add} \index{mp\_sub}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1147 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1148 int mp_add (mp_int * a, mp_int * b, mp_int * c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1149 int mp_sub (mp_int * a, mp_int * b, mp_int * c)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1150 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1151
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1152 Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction. The operations are fully sign
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1153 aware.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1154
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1155 \section{Sign Manipulation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1156 \subsection{Negation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1157 \label{sec:NEG}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1158 Simple integer negation can be performed with the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1159
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1160 \index{mp\_neg}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1161 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1162 int mp_neg (mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1163 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1164
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1165 Which assigns $-a$ to $b$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1166
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1167 \subsection{Absolute}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1168 Simple integer absolutes can be performed with the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1169
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1170 \index{mp\_neg}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1171 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1172 int mp_abs (mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1173 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1174
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1175 Which assigns $\vert a \vert$ to $b$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1176
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1177 \section{Integer Division and Remainder}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1178 To perform a complete and general integer division with remainder use the following function.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1179
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1180 \index{mp\_div}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1181 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1182 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1183 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1184
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1185 This divides $a$ by $b$ and stores the quotient in $c$ and $d$. The signed quotient is computed such that
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1186 $bc + d = a$. Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required. If
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1187 $b$ is zero the function returns \textbf{MP\_VAL}.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1188
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1189
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1190 \chapter{Multiplication and Squaring}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1191 \section{Multiplication}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1192 A full signed integer multiplication can be performed with the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1193 \index{mp\_mul}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1194 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1195 int mp_mul (mp_int * a, mp_int * b, mp_int * c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1196 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1197 Which assigns the full signed product $ab$ to $c$. This function actually breaks into one of four cases which are
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1198 specific multiplication routines optimized for given parameters. First there are the Toom-Cook multiplications which
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1199 should only be used with very large inputs. This is followed by the Karatsuba multiplications which are for moderate
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1200 sized inputs. Then followed by the Comba and baseline multipliers.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1201
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1202 Fortunately for the developer you don't really need to know this unless you really want to fine tune the system. mp\_mul()
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1203 will determine on its own\footnote{Some tweaking may be required.} what routine to use automatically when it is called.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1204
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1205 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1206 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1207 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1208 mp_int number1, number2;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1209 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1210
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1211 /* Initialize the numbers */
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1212 if ((result = mp_init_multi(&number1,
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1213 &number2, NULL)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1214 printf("Error initializing the numbers. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1215 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1216 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1217 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1218
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1219 /* set the terms */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1220 if ((result = mp_set_int(&number, 257)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1221 printf("Error setting number1. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1222 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1223 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1224 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1225
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1226 if ((result = mp_set_int(&number2, 1023)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1227 printf("Error setting number2. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1228 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1229 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1230 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1231
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1232 /* multiply them */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1233 if ((result = mp_mul(&number1, &number2,
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1234 &number1)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1235 printf("Error multiplying terms. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1236 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1237 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1238 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1239
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1240 /* display */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1241 printf("number1 * number2 == \%lu", mp_get_int(&number1));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1242
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1243 /* free terms and return */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1244 mp_clear_multi(&number1, &number2, NULL);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1245
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1246 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1247 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1248 \end{alltt}
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1249
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1250 If this program succeeds it shall output the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1251
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1252 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1253 number1 * number2 == 262911
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1254 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1255
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1256 \section{Squaring}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1257 Since squaring can be performed faster than multiplication it is performed it's own function instead of just using
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1258 mp\_mul().
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1259
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1260 \index{mp\_sqr}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1261 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1262 int mp_sqr (mp_int * a, mp_int * b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1263 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1264
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1265 Will square $a$ and store it in $b$. Like the case of multiplication there are four different squaring
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1266 algorithms all which can be called from mp\_sqr(). It is ideal to use mp\_sqr over mp\_mul when squaring terms because
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1267 of the speed difference.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1268
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1269 \section{Tuning Polynomial Basis Routines}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1270
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1271 Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1272 the Comba and baseline algorithms use. At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1273 considerably less work. For example, a 10000-digit multiplication would take roughly 724,000 single precision
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1274 multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1275 of 138).
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1276
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1277 So why not always use Karatsuba or Toom-Cook? The simple answer is that they have so much overhead that they're not
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1278 actually faster than Comba until you hit distinct ``cutoff'' points. For Karatsuba with the default configuration,
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1279 GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4). That is, at
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1280 110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1281
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1282 Toom-Cook has incredible overhead and is probably only useful for very large inputs. So far no known cutoff points
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1283 exist and for the most part I just set the cutoff points very high to make sure they're not called.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1284
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1285 A demo program in the ``etc/'' directory of the project called ``tune.c'' can be used to find the cutoff points. This
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1286 can be built with GCC as follows
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1287
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1288 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1289 make XXX
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1290 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1291 Where ``XXX'' is one of the following entries from the table \ref{fig:tuning}.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1292
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1293 \begin{figure}[here]
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1294 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1295 \begin{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1296 \begin{tabular}{\|l\|l\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1297 \hline \textbf{Value of XXX} & \textbf{Meaning} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1298 \hline tune & Builds portable tuning application \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1299 \hline tune86 & Builds x86 (pentium and up) program for COFF \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1300 \hline tune86c & Builds x86 program for Cygwin \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1301 \hline tune86l & Builds x86 program for Linux (ELF format) \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1302 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1303 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1304 \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1305 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1306 \caption{Build Names for Tuning Programs}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1307 \label{fig:tuning}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1308 \end{figure}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1309
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1310 When the program is running it will output a series of measurements for different cutoff points. It will first find
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1311 good Karatsuba squaring and multiplication points. Then it proceeds to find Toom-Cook points. Note that the Toom-Cook
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1312 tuning takes a very long time as the cutoff points are likely to be very high.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1313
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1314 \chapter{Modular Reduction}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1315
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1316 Modular reduction is process of taking the remainder of one quantity divided by another. Expressed
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1317 as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1318
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1319 \begin{equation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1320 a \equiv b \mbox{ (mod }c\mbox{)}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1321 \label{eqn:mod}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1322 \end{equation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1323
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1324 Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1325 fast reduction algorithms can be written for the limited range.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1326
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1327 Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1328 algorithm mp\_exptmod when an appropriate modulus is detected.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1329
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1330 \section{Straight Division}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1331 In order to effect an arbitrary modular reduction the following algorithm is provided.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1332
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1333 \index{mp\_mod}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1334 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1335 int mp_mod(mp_int a, mp_int b, mp_int *c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1336 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1337
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1338 This reduces $a$ modulo $b$ and stores the result in $c$. The sign of $c$ shall agree with the sign
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1339 of $b$. This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1340
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1341 \section{Barrett Reduction}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1342
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1343 Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1344 a decent speedup over straight division. First a $\mu$ value must be precomputed with the following function.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1345
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1346 \index{mp\_reduce\_setup}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1347 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1348 int mp_reduce_setup(mp_int a, mp_int b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1349 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1350
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1351 Given a modulus in $b$ this produces the required $\mu$ value in $a$. For any given modulus this only has to
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1352 be computed once. Modular reduction can now be performed with the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1353
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1354 \index{mp\_reduce}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1355 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1356 int mp_reduce(mp_int a, mp_int b, mp_int *c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1357 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1358
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1359 This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$. $a$ must be in the range
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1360 $0 \le a < b^2$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1361
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1362 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1363 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1364 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1365 mp_int a, b, c, mu;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1366 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1367
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1368 /* initialize a,b to desired values, mp_init mu,
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1369 * c and set c to 1...we want to compute a^3 mod b
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1370 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1371
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1372 /* get mu value */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1373 if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1374 printf("Error getting mu. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1375 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1376 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1377 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1378
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1379 /* square a to get c = a^2 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1380 if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1381 printf("Error squaring. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1382 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1383 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1384 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1385
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1386 /* now reduce `c' modulo b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1387 if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1388 printf("Error reducing. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1389 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1390 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1391 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1392
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1393 /* multiply a to get c = a^3 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1394 if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1395 printf("Error reducing. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1396 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1397 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1398 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1399
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1400 /* now reduce `c' modulo b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1401 if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1402 printf("Error reducing. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1403 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1404 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1405 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1406
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1407 /* c now equals a^3 mod b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1408
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1409 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1410 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1411 \end{alltt}
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1412
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1413 This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1414
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1415 \section{Montgomery Reduction}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1416
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1417 Montgomery is a specialized reduction algorithm for any odd moduli. Like Barrett reduction a pre--computation
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1418 step is required. This is accomplished with the following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1419
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1420 \index{mp\_montgomery\_setup}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1421 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1422 int mp_montgomery_setup(mp_int a, mp_digit mp);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1423 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1424
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1425 For the given odd moduli $a$ the precomputation value is placed in $mp$. The reduction is computed with the
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1426 following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1427
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1428 \index{mp\_montgomery\_reduce}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1429 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1430 int mp_montgomery_reduce(mp_int a, mp_int m, mp_digit mp);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1431 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1432 This reduces $a$ in place modulo $m$ with the pre--computed value $mp$. $a$ must be in the range
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1433 $0 \le a < b^2$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1434
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1435 Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit. With the default
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1436 setup for instance, the limit is $127$ digits ($3556$--bits). Note that this function is not limited to
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1437 $127$ digits just that it falls back to a baseline algorithm after that point.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1438
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1439 An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1440 where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1441
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1442 To quickly calculate $R$ the following function was provided.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1443
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1444 \index{mp\_montgomery\_calc\_normalization}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1445 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1446 int mp_montgomery_calc_normalization(mp_int a, mp_int b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1447 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1448 Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1449
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1450 The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system. For
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1451 example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1452 multiplying it by $R$. Consider the following code snippet.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1453
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1454 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1455 int main(void)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1456 \{
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1457 mp_int a, b, c, R;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1458 mp_digit mp;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1459 int result;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1460
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1461 /* initialize a,b to desired values,
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1462 * mp_init R, c and set c to 1....
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1463 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1464
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1465 /* get normalization */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1466 if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1467 printf("Error getting norm. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1468 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1469 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1470 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1471
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1472 /* get mp value */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1473 if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1474 printf("Error setting up montgomery. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1475 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1476 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1477 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1478
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1479 /* normalize `a' so now a is equal to aR */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1480 if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1481 printf("Error computing aR. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1482 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1483 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1484 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1485
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1486 /* square a to get c = a^2R^2 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1487 if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1488 printf("Error squaring. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1489 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1490 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1491 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1492
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1493 /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1494 if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1495 printf("Error reducing. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1496 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1497 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1498 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1499
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1500 /* multiply a to get c = a^3R^2 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1501 if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1502 printf("Error reducing. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1503 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1504 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1505 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1506
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1507 /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1508 if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1509 printf("Error reducing. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1510 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1511 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1512 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1513
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1514 /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1515 if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1516 printf("Error reducing. \%s",
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1517 mp_error_to_string(result));
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1518 return EXIT_FAILURE;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1519 \}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1520
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1521 /* c now equals a^3 mod b */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1522
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1523 return EXIT_SUCCESS;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1524 \}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1525 \end{alltt}
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1526
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1527 This particular example does not look too efficient but it demonstrates the point of the algorithm. By
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1528 normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$. This allows
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1529 a single final reduction to correct for the normalization and the fast reduction used within the algorithm.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1530
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1531 For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1532
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1533 \section{Restricted Dimminished Radix}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1534
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1535 ``Dimminished Radix'' reduction refers to reduction with respect to moduli that are ameniable to simple
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1536 digit shifting and small multiplications. In this case the ``restricted'' variant refers to moduli of the
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1537 form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$).
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1538
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1539 As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1540
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1541 \index{mp\_dr\_setup}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1542 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1543 void mp_dr_setup(mp_int a, mp_digit d);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1544 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1545
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1546 This computes the value required for the modulus $a$ and stores it in $d$. This function cannot fail
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1547 and does not return any error codes. After the pre--computation a reduction can be performed with the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1548 following.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1549
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1550 \index{mp\_dr\_reduce}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1551 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1552 int mp_dr_reduce(mp_int a, mp_int b, mp_digit mp);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1553 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1554
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1555 This reduces $a$ in place modulo $b$ with the pre--computed value $mp$. $b$ must be of a restricted
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1556 dimminished radix form and $a$ must be in the range $0 \le a < b^2$. Dimminished radix reductions are
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1557 much faster than both Barrett and Montgomery reductions as they have a much lower asymtotic running time.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1558
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1559 Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1560 BBS cryptographic purposes. This reduction algorithm is useful for Diffie-Hellman and ECC where fixed
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1561 primes are acceptable.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1562
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1563 Note that unlike Montgomery reduction there is no normalization process. The result of this function is
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1564 equal to the correct residue.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1565
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1566 \section{Unrestricted Dimminshed Radix}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1567
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1568 Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1569 form $2^k - p$ for $0 < p < \beta$. In this sense the unrestricted reductions are more flexible as they
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1570 can be applied to a wider range of numbers.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1571
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1572 \index{mp\_reduce\_2k\_setup}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1573 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1574 int mp_reduce_2k_setup(mp_int a, mp_digit d);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1575 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1576
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1577 This will compute the required $d$ value for the given moduli $a$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1578
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1579 \index{mp\_reduce\_2k}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1580 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1581 int mp_reduce_2k(mp_int a, mp_int n, mp_digit d);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1582 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1583
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1584 This will reduce $a$ in place modulo $n$ with the pre--computed value $d$. From my experience this routine is
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1585 slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1586
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1587 \chapter{Exponentiation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1588 \section{Single Digit Exponentiation}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1589 \index{mp\_expt\_d\_ex}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1590 \begin{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1591 int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1592 \end{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1593 This function computes $c = a^b$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1594
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1595 With parameter \textit{fast} set to $0$ the old version of the algorithm is used,
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1596 when \textit{fast} is $1$, a faster but not statically timed version of the algorithm is used.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1597
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1598 The old version uses a simple binary left-to-right algorithm.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1599 It is faster than repeated multiplications by $a$ for all values of $b$ greater than three.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1600
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1601 The new version uses a binary right-to-left algorithm.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1602
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1603 The difference between the old and the new version is that the old version always
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1604 executes $DIGIT\_BIT$ iterations. The new algorithm executes only $n$ iterations
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1605 where $n$ is equal to the position of the highest bit that is set in $b$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1606
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1607 \index{mp\_expt\_d}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1608 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1609 int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1610 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1611 mp\_expt\_d(a, b, c) is a wrapper function to mp\_expt\_d\_ex(a, b, c, 0).
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1612
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1613 \section{Modular Exponentiation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1614 \index{mp\_exptmod}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1615 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1616 int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1617 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1618 This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm. This function
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1619 will automatically detect the fastest modular reduction technique to use during the operation. For negative values of
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1620 $X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1621 $gcd(G, P) = 1$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1622
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1623 This function is actually a shell around the two internal exponentiation functions. This routine will automatically
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1624 detect when Barrett, Montgomery, Restricted and Unrestricted Dimminished Radix based exponentiation can be used. Generally
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1625 moduli of the a ``restricted dimminished radix'' form lead to the fastest modular exponentiations. Followed by Montgomery
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1626 and the other two algorithms.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1627
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1628 \section{Root Finding}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1629 \index{mp\_n\_root}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1630 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1631 int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1632 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1633 This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$. The implementation of this function is not
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1634 ideal for values of $b$ greater than three. It will work but become very slow. So unless you are working with very small
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1635 numbers (less than 1000 bits) I'd avoid $b > 3$ situations. Will return a positive root only for even roots and return
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1636 a root with the sign of the input for odd roots. For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1637 will return $-2$.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1638
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1639 This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly. Since
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1640 the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1641 values of $b$. If particularly large roots are required then a factor method could be used instead. For example,
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1642 $a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1643 $\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1644
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1645 \chapter{Prime Numbers}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1646 \section{Trial Division}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1647 \index{mp\_prime\_is\_divisible}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1648 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1649 int mp_prime_is_divisible (mp_int * a, int *result)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1650 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1651 This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1652 outcome in ``result''. That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is. Note that
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1653 if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1654 the default is to set it to zero first.}.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1655
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1656 \section{Fermat Test}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1657 \index{mp\_prime\_fermat}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1658 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1659 int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1660 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1661 Performs a Fermat primality test to the base $b$. That is it computes $b^a \mbox{ mod }a$ and tests whether the value is
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1662 equal to $b$ or not. If the values are equal then $a$ is probably prime and $result$ is set to one. Otherwise $result$
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1663 is set to zero.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1664
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1665 \section{Miller-Rabin Test}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1666 \index{mp\_prime\_miller\_rabin}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1667 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1668 int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1669 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1670 Performs a Miller-Rabin test to the base $b$ of $a$. This test is much stronger than the Fermat test and is very hard to
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1671 fool (besides with Carmichael numbers). If $a$ passes the test (therefore is probably prime) $result$ is set to one.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1672 Otherwise $result$ is set to zero.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1673
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1674 Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1675 Miller-Rabin are a subset of the failures of the Fermat test.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1676
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1677 \subsection{Required Number of Tests}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1678 Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1679 or so unique bases. However, it has been proven that the probability of failure goes down as the size of the input goes up.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1680 This is why a simple function has been provided to help out.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1681
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1682 \index{mp\_prime\_rabin\_miller\_trials}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1683 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1684 int mp_prime_rabin_miller_trials(int size)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1685 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1686 This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1687 in bits. This comes in handy specially since larger numbers are slower to test. For example, a 512-bit number would
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1688 require ten tests whereas a 1024-bit number would only require four tests.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1689
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1690 You should always still perform a trial division before a Miller-Rabin test though.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1691
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1692 \section{Primality Testing}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1693 \index{mp\_prime\_is\_prime}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1694 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1695 int mp_prime_is_prime (mp_int * a, int t, int *result)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1696 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1697 This will perform a trial division followed by $t$ rounds of Miller-Rabin tests on $a$ and store the result in $result$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1698 If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero. Note that $t$ is bounded by
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1699 $1 \le t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number of primes in the prime number table (by default this is $256$).
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1700
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1701 \section{Next Prime}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1702 \index{mp\_prime\_next\_prime}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1703 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1704 int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1705 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1706 This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests. Set $bbs\_style$ to one if you
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1707 want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1708
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1709 \section{Random Primes}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1710 \index{mp\_prime\_random}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1711 \begin{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1712 int mp_prime_random(mp_int *a, int t, int size, int bbs,
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1713 ltm_prime_callback cb, void *dat)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1714 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1715 This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1716 $t$ rounds of tests. The ``ltm\_prime\_callback'' is a typedef for
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1717
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1718 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1719 typedef int ltm_prime_callback(unsigned char dst, int len, void dat);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1720 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1721
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1722 Which is a function that must read $len$ bytes (and return the amount stored) into $dst$. The $dat$ variable is simply
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1723 copied from the original input. It can be used to pass RNG context data to the callback. The function
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1724 mp\_prime\_random() is more suitable for generating primes which must be secret (as in the case of RSA) since there
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1725 is no skew on the least significant bits.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1726
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1727 \textit{Note:} As of v0.30 of the LibTomMath library this function has been deprecated. It is still available
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1728 but users are encouraged to use the new mp\_prime\_random\_ex() function instead.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1729
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1730 \subsection{Extended Generation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1731 \index{mp\_prime\_random\_ex}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1732 \begin{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1733 int mp_prime_random_ex(mp_int *a, int t,
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1734 int size, int flags,
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1735 ltm_prime_callback cb, void *dat);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1736 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1737 This will generate a prime in $a$ using $t$ tests of the primality testing algorithms. The variable $size$
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1738 specifies the bit length of the prime desired. The variable $flags$ specifies one of several options available
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1739 (see fig. \ref{fig:primeopts}) which can be OR'ed together. The callback parameters are used as in
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1740 mp\_prime\_random().
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1741
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1742 \begin{figure}[here]
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1743 \begin{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1744 \begin{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1745 \begin{tabular}{\|r\|l\|}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1746 \hline \textbf{Flag} & \textbf{Meaning} \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1747 \hline LTM\_PRIME\_BBS & Make the prime congruent to $3$ modulo $4$ \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1748 \hline LTM\_PRIME\_SAFE & Make a prime $p$ such that $(p - 1)/2$ is also prime. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1749 & This option implies LTM\_PRIME\_BBS as well. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1750 \hline LTM\_PRIME\_2MSB\_OFF & Makes sure that the bit adjacent to the most significant bit \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1751 & Is forced to zero. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1752 \hline LTM\_PRIME\_2MSB\_ON & Makes sure that the bit adjacent to the most significant bit \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1753 & Is forced to one. \\
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1754 \hline
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1755 \end{tabular}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1756 \end{small}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1757 \end{center}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1758 \caption{Primality Generation Options}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1759 \label{fig:primeopts}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1760 \end{figure}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1761
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1762 \chapter{Input and Output}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1763 \section{ASCII Conversions}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1764 \subsection{To ASCII}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1765 \index{mp\_toradix}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1766 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1767 int mp_toradix (mp_int * a, char *str, int radix);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1768 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1769 This still store $a$ in ``str'' as a base-``radix'' string of ASCII chars. This function appends a NUL character
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1770 to terminate the string. Valid values of ``radix'' line in the range $[2, 64]$. To determine the size (exact) required
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1771 by the conversion before storing any data use the following function.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1772
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1773 \index{mp\_radix\_size}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1774 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1775 int mp_radix_size (mp_int * a, int radix, int *size)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1776 \end{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1777 This stores in ``size'' the number of characters (including space for the NUL terminator) required. Upon error this
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1778 function returns an error code and ``size'' will be zero.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1779
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1780 \subsection{From ASCII}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1781 \index{mp\_read\_radix}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1782 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1783 int mp_read_radix (mp_int * a, char *str, int radix);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1784 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1785 This will read the base-``radix'' NUL terminated string from ``str'' into $a$. It will stop reading when it reads a
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1786 character it does not recognize (which happens to include th NUL char... imagine that...). A single leading $-$ sign
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1787 can be used to denote a negative number.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1788
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1789 \section{Binary Conversions}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1790
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1791 Converting an mp\_int to and from binary is another keen idea.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1792
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1793 \index{mp\_unsigned\_bin\_size}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1794 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1795 int mp_unsigned_bin_size(mp_int *a);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1796 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1797
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1798 This will return the number of bytes (octets) required to store the unsigned copy of the integer $a$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1799
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1800 \index{mp\_to\_unsigned\_bin}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1801 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1802 int mp_to_unsigned_bin(mp_int a, unsigned char b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1803 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1804 This will store $a$ into the buffer $b$ in big--endian format. Fortunately this is exactly what DER (or is it ASN?)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1805 requires. It does not store the sign of the integer.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1806
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1807 \index{mp\_read\_unsigned\_bin}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1808 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1809 int mp_read_unsigned_bin(mp_int a, unsigned char b, int c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1810 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1811 This will read in an unsigned big--endian array of bytes (octets) from $b$ of length $c$ into $a$. The resulting
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1812 integer $a$ will always be positive.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1813
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1814 For those who acknowledge the existence of negative numbers (heretic!) there are ``signed'' versions of the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1815 previous functions.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1816
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1817 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1818 int mp_signed_bin_size(mp_int *a);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1819 int mp_read_signed_bin(mp_int a, unsigned char b, int c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1820 int mp_to_signed_bin(mp_int a, unsigned char b);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1821 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1822 They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1823 byte depending on the sign. If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1824 is non--zero.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1825
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1826 \chapter{Algebraic Functions}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1827 \section{Extended Euclidean Algorithm}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1828 \index{mp\_exteuclid}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1829 \begin{alltt}
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1830 int mp_exteuclid(mp_int a, mp_int b,
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1831 mp_int U1, mp_int U2, mp_int *U3);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1832 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1833
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1834 This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1835
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1836 \begin{equation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1837 a \cdot U1 + b \cdot U2 = U3
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1838 \end{equation}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1839
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1840 Any of the U1/U2/U3 paramters can be set to \textbf{NULL} if they are not desired.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1841
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1842 \section{Greatest Common Divisor}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1843 \index{mp\_gcd}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1844 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1845 int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1846 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1847 This will compute the greatest common divisor of $a$ and $b$ and store it in $c$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1848
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1849 \section{Least Common Multiple}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1850 \index{mp\_lcm}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1851 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1852 int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1853 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1854 This will compute the least common multiple of $a$ and $b$ and store it in $c$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1855
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1856 \section{Jacobi Symbol}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1857 \index{mp\_jacobi}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1858 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1859 int mp_jacobi (mp_int * a, mp_int * p, int *c)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1860 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1861 This will compute the Jacobi symbol for $a$ with respect to $p$. If $p$ is prime this essentially computes the Legendre
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1862 symbol. The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$. If $p$ is prime
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1863 then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$. The result will be $0$ if $a$ divides $p$
1436 60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1864 and the result will be $1$ if $a$ is a quadratic residue modulo $p$.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1865
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1866 \section{Modular square root}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1867 \index{mp\_sqrtmod\_prime}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1868 \begin{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1869 int mp_sqrtmod_prime(mp_int n, mp_int p, mp_int *r)
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1870 \end{alltt}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1871
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1872 This will solve the modular equatioon $r^2 = n \mod p$ where $p$ is a prime number greater than 2 (odd prime).
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1873 The result is returned in the third argument $r$, the function returns \textbf{MP\_OKAY} on success,
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1874 other return values indicate failure.
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1875
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1876 The implementation is split for two different cases:
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1877
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1878 1. if $p \mod 4 == 3$ we apply \href{http://cacr.uwaterloo.ca/hac/}{Handbook of Applied Cryptography algorithm 3.36} and compute $r$ directly as
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1879 $r = n^{(p+1)/4} \mod p$
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1880
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1881 2. otherwise we use \href{https://en.wikipedia.org/wiki/Tonelli-Shanks_algorithm}{Tonelli-Shanks algorithm}
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1882
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1883 The function does not check the primality of parameter $p$ thus it is up to the caller to assure that this parameter
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1884 is a prime number. When $p$ is a composite the function behaviour is undefined, it may even return a false-positive
60fc6476e044 Update to libtommath v1.0 Matt Johnston <matt@ucc.asn.au> parents: 389 diff changeset	1885 \textbf{MP\_OKAY}.
284 eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1886
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1887 \section{Modular Inverse}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1888 \index{mp\_invmod}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1889 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1890 int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1891 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1892 Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1893
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1894 \section{Single Digit Functions}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1895
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1896 For those using small numbers (\textit{snicker snicker}) there are several ``helper'' functions
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1897
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1898 \index{mp\_add\_d} \index{mp\_sub\_d} \index{mp\_mul\_d} \index{mp\_div\_d} \index{mp\_mod\_d}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1899 \begin{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1900 int mp_add_d(mp_int a, mp_digit b, mp_int c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1901 int mp_sub_d(mp_int a, mp_digit b, mp_int c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1902 int mp_mul_d(mp_int a, mp_digit b, mp_int c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1903 int mp_div_d(mp_int a, mp_digit b, mp_int c, mp_digit *d);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1904 int mp_mod_d(mp_int a, mp_digit b, mp_digit c);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1905 \end{alltt}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1906
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1907 These work like the full mp\_int capable variants except the second parameter $b$ is a mp\_digit. These
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1908 functions fairly handy if you have to work with relatively small numbers since you will not have to allocate
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1909 an entire mp\_int to store a number like $1$ or $2$.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1910
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1911 \input{bn.ind}
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1912
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583) Matt Johnston <matt@ucc.asn.au> parents: diff changeset	1913 \end{document}

Mercurial > dropbear

annotate libtommath/bn.tex @ 1594:c69df5d5db94