mp_montgomery_reduce.c

   1 #include "tommath_private.h"
   2 #ifdef MP_MONTGOMERY_REDUCE_C
   3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
   4 /* SPDX-License-Identifier: Unlicense */
   5
   6 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
   7 mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
   8 {
   9    mp_err err;
  10    int ix, digs;
  11
  12    /* can the fast reduction [comba] method be used?
  13     *
  14     * Note that unlike in mul you're safely allowed *less*
  15     * than the available columns [255 per default] since carries
  16     * are fixed up in the inner loop.
  17     */
  18    digs = (n->used * 2) + 1;
  19    if ((digs < MP_WARRAY) &&
  20        (x->used <= MP_WARRAY) &&
  21        (n->used < MP_MAX_COMBA)) {
  22       return s_mp_montgomery_reduce_comba(x, n, rho);
  23    }
  24
  25    /* grow the input as required */
  26    if ((err = mp_grow(x, digs)) != MP_OKAY) {
  27       return err;
  28    }
  29    x->used = digs;
  30
  31    for (ix = 0; ix < n->used; ix++) {
  32       int iy;
  33       mp_digit u, mu;
  34
  35       /* mu = ai * rho mod b
  36        *
  37        * The value of rho must be precalculated via
  38        * montgomery_setup() such that
  39        * it equals -1/n0 mod b this allows the
  40        * following inner loop to reduce the
  41        * input one digit at a time
  42        */
  43       mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
  44
  45       /* a = a + mu * m * b**i */
  46
  47       /* Multiply and add in place */
  48       u = 0;
  49       for (iy = 0; iy < n->used; iy++) {
  50          /* compute product and sum */
  51          mp_word r = ((mp_word)mu * (mp_word)n->dp[iy]) +
  52                      (mp_word)u + (mp_word)x->dp[ix + iy];
  53
  54          /* get carry */
  55          u       = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
  56
  57          /* fix digit */
  58          x->dp[ix + iy] = (mp_digit)(r & (mp_word)MP_MASK);
  59       }
  60       /* At this point the ix'th digit of x should be zero */
  61
  62       /* propagate carries upwards as required*/
  63       while (u != 0u) {
  64          x->dp[ix + iy]   += u;
  65          u        = x->dp[ix + iy] >> MP_DIGIT_BIT;
  66          x->dp[ix + iy] &= MP_MASK;
  67          ++iy;
  68       }
  69    }
  70
  71    /* at this point the n.used'th least
  72     * significant digits of x are all zero
  73     * which means we can shift x to the
  74     * right by n.used digits and the
  75     * residue is unchanged.
  76     */
  77
  78    /* x = x/b**n.used */
  79    mp_clamp(x);
  80    mp_rshd(x, n->used);
  81
  82    /* if x >= n then x = x - n */
  83    if (mp_cmp_mag(x, n) != MP_LT) {
  84       return s_mp_sub(x, n, x);
  85    }
  86
  87    return MP_OKAY;
  88 }
  89 #endif