Mercurial > dropbear

annotate libtommath/bn_mp_montgomery_reduce.c @ 1453:336cae2238ca

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test close < 0, from Marco Wenzel
author Matt Johnston <matt@ucc.asn.au>
date Wed, 18 Oct 2017 22:41:27 +0800
parents 60fc6476e044
children 8bba51a55704
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 #include <tommath_private.h>
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2 #ifdef BN_MP_MONTGOMERY_REDUCE_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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4 *
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5 * LibTomMath is a library that provides multiple-precision
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6 * integer arithmetic as well as number theoretic functionality.
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7 *
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8 * The library was designed directly after the MPI library by
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9 * Michael Fromberger but has been written from scratch with
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10 * additional optimizations in place.
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11 *
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12 * The library is free for all purposes without any express
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13 * guarantee it works.
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14 *
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15 * Tom St Denis, [email protected], http://libtom.org
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16 */
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17
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18 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
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19 int
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20 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
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21 {
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22 int ix, res, digs;
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23 mp_digit mu;
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24
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25 /* can the fast reduction [comba] method be used?
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26 *
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27 * Note that unlike in mul you're safely allowed *less*
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28 * than the available columns [255 per default] since carries
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29 * are fixed up in the inner loop.
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30 */
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31 digs = (n->used * 2) + 1;
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32 if ((digs < MP_WARRAY) &&
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33 (n->used <
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34 (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
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35 return fast_mp_montgomery_reduce (x, n, rho);
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36 }
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37
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38 /* grow the input as required */
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39 if (x->alloc < digs) {
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40 if ((res = mp_grow (x, digs)) != MP_OKAY) {
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41 return res;
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42 }
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43 }
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44 x->used = digs;
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45
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46 for (ix = 0; ix < n->used; ix++) {
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47 /* mu = ai * rho mod b
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48 *
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49 * The value of rho must be precalculated via
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50 * montgomery_setup() such that
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51 * it equals -1/n0 mod b this allows the
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52 * following inner loop to reduce the
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53 * input one digit at a time
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54 */
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55 mu = (mp_digit) (((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
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56
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57 /* a = a + mu * m * b**i */
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58 {
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59 int iy;
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60 mp_digit *tmpn, *tmpx, u;
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61 mp_word r;
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62
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63 /* alias for digits of the modulus */
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64 tmpn = n->dp;
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65
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66 /* alias for the digits of x [the input] */
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67 tmpx = x->dp + ix;
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68
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69 /* set the carry to zero */
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70 u = 0;
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71
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72 /* Multiply and add in place */
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73 for (iy = 0; iy < n->used; iy++) {
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74 /* compute product and sum */
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75 r = ((mp_word)mu * (mp_word)*tmpn++) +
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76 (mp_word) u + (mp_word) *tmpx;
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77
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78 /* get carry */
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79 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
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80
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81 /* fix digit */
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82 *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
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83 }
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84 /* At this point the ix'th digit of x should be zero */
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85
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86
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87 /* propagate carries upwards as required*/
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88 while (u != 0) {
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89 *tmpx += u;
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90 u = *tmpx >> DIGIT_BIT;
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91 *tmpx++ &= MP_MASK;
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92 }
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93 }
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94 }
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95
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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96 /* at this point the n.used'th least
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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97 * significant digits of x are all zero
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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98 * which means we can shift x to the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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99 * right by n.used digits and the
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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100 * residue is unchanged.
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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101 */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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102
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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103 /* x = x/b**n.used */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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104 mp_clamp(x);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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105 mp_rshd (x, n->used);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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106
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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107 /* if x >= n then x = x - n */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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108 if (mp_cmp_mag (x, n) != MP_LT) {
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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109 return s_mp_sub (x, n, x);
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Matt Johnston <matt@ucc.asn.au>
parents:
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110 }
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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111
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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112 return MP_OKAY;
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Matt Johnston <matt@ucc.asn.au>
parents:
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113 }
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
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114 #endif
389
5ff8218bcee9 propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 2af95f00ebd5bb7a28b3817db1218442c935388e)
Matt Johnston <matt@ucc.asn.au>
parents: 284
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115
1436
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents: 389
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116 /* $Source$ */
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Matt Johnston <matt@ucc.asn.au>
parents: 389
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117 /* $Revision$ */
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parents: 389
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118 /* $Date$ */