mp_reduce.c

   1 #include "tommath_private.h"
   2 #ifdef MP_REDUCE_C
   3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
   4 /* SPDX-License-Identifier: Unlicense */
   5
   6 /* reduces x mod m, assumes 0 < x < m**2, mu is
   7  * precomputed via mp_reduce_setup.
   8  * From HAC pp.604 Algorithm 14.42
   9  */
  10 mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu)
  11 {
  12    mp_int  q;
  13    mp_err  err;
  14    int     um = m->used;
  15
  16    /* q = x */
  17    if ((err = mp_init_copy(&q, x)) != MP_OKAY) {
  18       return err;
  19    }
  20
  21    /* q1 = x / b**(k-1)  */
  22    mp_rshd(&q, um - 1);
  23
  24    /* according to HAC this optimization is ok */
  25    if ((mp_digit)um > ((mp_digit)1 << (MP_DIGIT_BIT - 1))) {
  26       if ((err = mp_mul(&q, mu, &q)) != MP_OKAY) {
  27          goto LBL_ERR;
  28       }
  29    } else if (MP_HAS(S_MP_MUL_HIGH)) {
  30       if ((err = s_mp_mul_high(&q, mu, &q, um)) != MP_OKAY) {
  31          goto LBL_ERR;
  32       }
  33    } else if (MP_HAS(S_MP_MUL_HIGH_COMBA)) {
  34       if ((err = s_mp_mul_high_comba(&q, mu, &q, um)) != MP_OKAY) {
  35          goto LBL_ERR;
  36       }
  37    } else {
  38       err = MP_VAL;
  39       goto LBL_ERR;
  40    }
  41
  42    /* q3 = q2 / b**(k+1) */
  43    mp_rshd(&q, um + 1);
  44
  45    /* x = x mod b**(k+1), quick (no division) */
  46    if ((err = mp_mod_2d(x, MP_DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
  47       goto LBL_ERR;
  48    }
  49
  50    /* q = q * m mod b**(k+1), quick (no division) */
  51    if ((err = s_mp_mul(&q, m, &q, um + 1)) != MP_OKAY) {
  52       goto LBL_ERR;
  53    }
  54
  55    /* x = x - q */
  56    if ((err = mp_sub(x, &q, x)) != MP_OKAY) {
  57       goto LBL_ERR;
  58    }
  59
  60    /* If x < 0, add b**(k+1) to it */
  61    if (mp_cmp_d(x, 0uL) == MP_LT) {
  62       mp_set(&q, 1uL);
  63       if ((err = mp_lshd(&q, um + 1)) != MP_OKAY) {
  64          goto LBL_ERR;
  65       }
  66       if ((err = mp_add(x, &q, x)) != MP_OKAY) {
  67          goto LBL_ERR;
  68       }
  69    }
  70
  71    /* Back off if it's too big */
  72    while (mp_cmp(x, m) != MP_LT) {
  73       if ((err = s_mp_sub(x, m, x)) != MP_OKAY) {
  74          goto LBL_ERR;
  75       }
  76    }
  77
  78 LBL_ERR:
  79    mp_clear(&q);
  80
  81    return err;
  82 }
  83 #endif