119 lines
3.2 KiB
C
119 lines
3.2 KiB
C
#include <tommath_private.h>
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#ifdef BN_MP_MONTGOMERY_REDUCE_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
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/* computes xR**-1 == x (mod N) via Montgomery Reduction */
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int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
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{
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int ix, res, digs;
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mp_digit mu;
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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 < (int)MP_WARRAY) &&
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(x->used <= (int)MP_WARRAY) &&
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(n->used <
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(int)(1u << (((size_t)CHAR_BIT * sizeof(mp_word)) - (2u * (size_t)DIGIT_BIT))))) {
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return fast_mp_montgomery_reduce(x, n, rho);
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}
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/* grow the input as required */
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if (x->alloc < digs) {
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if ((res = mp_grow(x, digs)) != MP_OKAY) {
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return res;
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}
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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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/* 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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{
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int iy;
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mp_digit *tmpn, *tmpx, u;
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mp_word r;
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/* alias for digits of the modulus */
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tmpn = n->dp;
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/* alias for the digits of x [the input] */
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tmpx = x->dp + ix;
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/* set the carry to zero */
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u = 0;
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/* Multiply and add in place */
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for (iy = 0; iy < n->used; iy++) {
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/* compute product and sum */
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r = ((mp_word)mu * (mp_word)*tmpn++) +
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(mp_word)u + (mp_word)*tmpx;
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/* get carry */
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u = (mp_digit)(r >> (mp_word)DIGIT_BIT);
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/* fix digit */
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*tmpx++ = (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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*tmpx += u;
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u = *tmpx >> DIGIT_BIT;
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*tmpx++ &= MP_MASK;
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}
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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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/* ref: $Format:%D$ */
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/* git commit: $Format:%H$ */
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/* commit time: $Format:%ai$ */
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