1/*	$NetBSD: bn_mp_montgomery_setup.c,v 1.2 2017/01/28 21:31:47 christos Exp $	*/
2
3#include <tommath.h>
4#ifdef BN_MP_MONTGOMERY_SETUP_C
5/* LibTomMath, multiple-precision integer library -- Tom St Denis
6 *
7 * LibTomMath is a library that provides multiple-precision
8 * integer arithmetic as well as number theoretic functionality.
9 *
10 * The library was designed directly after the MPI library by
11 * Michael Fromberger but has been written from scratch with
12 * additional optimizations in place.
13 *
14 * The library is free for all purposes without any express
15 * guarantee it works.
16 *
17 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
18 */
19
20/* setups the montgomery reduction stuff */
21int
22mp_montgomery_setup (mp_int * n, mp_digit * rho)
23{
24  mp_digit x, b;
25
26/* fast inversion mod 2**k
27 *
28 * Based on the fact that
29 *
30 * XA = 1 (mod 2**n)  =>  (X(2-XA)) A = 1 (mod 2**2n)
31 *                    =>  2*X*A - X*X*A*A = 1
32 *                    =>  2*(1) - (1)     = 1
33 */
34  b = n->dp[0];
35
36  if ((b & 1) == 0) {
37    return MP_VAL;
38  }
39
40  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
41  x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
42#if !defined(MP_8BIT)
43  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
44#endif
45#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
46  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
47#endif
48#ifdef MP_64BIT
49  x *= 2 - b * x;               /* here x*a==1 mod 2**64 */
50#endif
51
52  /* rho = -1/m mod b */
53  *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
54
55  return MP_OKAY;
56}
57#endif
58
59/* Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v  */
60/* Revision: 1.5  */
61/* Date: 2006/12/28 01:25:13  */
62