90 lines
2.4 KiB
C
90 lines
2.4 KiB
C
#include "tommath_private.h"
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#ifdef MP_MONTGOMERY_REDUCE_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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/* computes xR**-1 == x (mod N) via Montgomery Reduction */
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mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
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{
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mp_err err;
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int ix, digs;
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/* can the fast reduction [comba] method be used?
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*
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* Note that unlike in mul you're safely allowed *less*
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* than the available columns [255 per default] since carries
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* are fixed up in the inner loop.
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*/
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digs = (n->used * 2) + 1;
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if ((digs < MP_WARRAY) &&
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(x->used <= MP_WARRAY) &&
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(n->used < MP_MAX_COMBA)) {
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return s_mp_montgomery_reduce_comba(x, n, rho);
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}
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/* grow the input as required */
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if ((err = mp_grow(x, digs)) != MP_OKAY) {
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return err;
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}
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x->used = digs;
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for (ix = 0; ix < n->used; ix++) {
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int iy;
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mp_digit u, mu;
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/* mu = ai * rho mod b
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*
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* The value of rho must be precalculated via
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* montgomery_setup() such that
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* it equals -1/n0 mod b this allows the
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* following inner loop to reduce the
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* input one digit at a time
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*/
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mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
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/* a = a + mu * m * b**i */
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/* Multiply and add in place */
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u = 0;
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for (iy = 0; iy < n->used; iy++) {
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/* compute product and sum */
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mp_word r = ((mp_word)mu * (mp_word)n->dp[iy]) +
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(mp_word)u + (mp_word)x->dp[ix + iy];
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/* get carry */
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u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
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/* fix digit */
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x->dp[ix + iy] = (mp_digit)(r & (mp_word)MP_MASK);
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}
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/* At this point the ix'th digit of x should be zero */
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/* propagate carries upwards as required*/
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while (u != 0u) {
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x->dp[ix + iy] += u;
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u = x->dp[ix + iy] >> MP_DIGIT_BIT;
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x->dp[ix + iy] &= MP_MASK;
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++iy;
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}
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}
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/* at this point the n.used'th least
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* significant digits of x are all zero
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* which means we can shift x to the
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* right by n.used digits and the
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* residue is unchanged.
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*/
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/* x = x/b**n.used */
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mp_clamp(x);
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mp_rshd(x, n->used);
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/* if x >= n then x = x - n */
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if (mp_cmp_mag(x, n) != MP_LT) {
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return s_mp_sub(x, n, x);
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}
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return MP_OKAY;
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}
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#endif
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