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 *
15 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
16 */
17
18/* setups the montgomery reduction stuff */
19int
20mp_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 = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
52
53  return MP_OKAY;
54}
55#endif
56
57/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */
58/* $Revision: 1.5 $ */
59/* $Date: 2006/12/28 01:25:13 $ */
60