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comparison 3rdparty/libtommath/bn_mp_montgomery_setup.c @ 0:2cf249471370

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author Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
date Tue, 08 May 2018 16:09:12 +0900
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-1:000000000000 0:2cf249471370
1 #include <tommath_private.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 *
15 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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 */
51 *rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
52
53 return MP_OKAY;
54 }
55 #endif
56
57 /* $Source$ */
58 /* $Revision$ */
59 /* $Date$ */