|
282
|
1 #include <tommath.h> |
|
|
2 #ifdef BN_MP_MONTGOMERY_SETUP_C |
|
|
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
|
|
4 * |
|
|
5 * LibTomMath is a library that provides multiple-precision |
|
|
6 * integer arithmetic as well as number theoretic functionality. |
|
|
7 * |
|
|
8 * The library was designed directly after the MPI library by |
|
|
9 * Michael Fromberger but has been written from scratch with |
|
|
10 * additional optimizations in place. |
|
|
11 * |
|
|
12 * The library is free for all purposes without any express |
|
|
13 * guarantee it works. |
|
|
14 * |
|
386
|
15 * Tom St Denis, [email protected], http://math.libtomcrypt.com |
|
282
|
16 */ |
|
|
17 |
|
|
18 /* setups the montgomery reduction stuff */ |
|
|
19 int |
|
|
20 mp_montgomery_setup (mp_int * n, mp_digit * rho) |
|
|
21 { |
|
|
22 mp_digit x, b; |
|
|
23 |
|
|
24 /* fast inversion mod 2**k |
|
|
25 * |
|
|
26 * Based on the fact that |
|
|
27 * |
|
|
28 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) |
|
|
29 * => 2*X*A - X*X*A*A = 1 |
|
|
30 * => 2*(1) - (1) = 1 |
|
|
31 */ |
|
|
32 b = n->dp[0]; |
|
|
33 |
|
|
34 if ((b & 1) == 0) { |
|
|
35 return MP_VAL; |
|
|
36 } |
|
|
37 |
|
|
38 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */ |
|
|
39 x *= 2 - b * x; /* here x*a==1 mod 2**8 */ |
|
|
40 #if !defined(MP_8BIT) |
|
|
41 x *= 2 - b * x; /* here x*a==1 mod 2**16 */ |
|
|
42 #endif |
|
|
43 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) |
|
|
44 x *= 2 - b * x; /* here x*a==1 mod 2**32 */ |
|
|
45 #endif |
|
|
46 #ifdef MP_64BIT |
|
|
47 x *= 2 - b * x; /* here x*a==1 mod 2**64 */ |
|
|
48 #endif |
|
|
49 |
|
|
50 /* rho = -1/m mod b */ |
|
386
|
51 *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; |
|
282
|
52 |
|
|
53 return MP_OKAY; |
|
|
54 } |
|
|
55 #endif |
|
386
|
56 |
|
|
57 /* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */ |
|
|
58 /* $Revision: 1.4 $ */ |
|
|
59 /* $Date: 2006/12/04 21:34:03 $ */ |
