mp_montgomery_setup.c

   1 #include "tommath_private.h"
   2 #ifdef MP_MONTGOMERY_SETUP_C
   3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
   4 /* SPDX-License-Identifier: Unlicense */
   5
   6 /* setups the montgomery reduction stuff */
   7 mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho)
   8 {
   9    mp_digit x, b;
  10
  11    /* fast inversion mod 2**k
  12     *
  13     * Based on the fact that
  14     *
  15     * XA = 1 (mod 2**n)  =>  (X(2-XA)) A = 1 (mod 2**2n)
  16     *                    =>  2*X*A - X*X*A*A = 1
  17     *                    =>  2*(1) - (1)     = 1
  18     */
  19    b = n->dp[0];
  20
  21    if ((b & 1u) == 0u) {
  22       return MP_VAL;
  23    }
  24
  25    x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */
  26    x *= 2u - (b * x);              /* here x*a==1 mod 2**8 */
  27    x *= 2u - (b * x);              /* here x*a==1 mod 2**16 */
  28 #if defined(MP_64BIT) || !(defined(MP_16BIT))
  29    x *= 2u - (b * x);              /* here x*a==1 mod 2**32 */
  30 #endif
  31 #ifdef MP_64BIT
  32    x *= 2u - (b * x);              /* here x*a==1 mod 2**64 */
  33 #endif
  34
  35    /* rho = -1/m mod b */
  36    *rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK;
  37
  38    return MP_OKAY;
  39 }
  40 #endif