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      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 (at) gmail.com, http://libtom.org
     18  */
     19 
     20 /* setups the montgomery reduction stuff */
     21 int
     22 mp_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