tommath/bn_mp_montgomery_reduce.c

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/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
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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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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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*/
#include <tommath.h>
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/* computes xR**-1 == x (mod N) via Montgomery Reduction */
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int
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mp_montgomery_reduce (mp_int * x, 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?
*
* Note that unlike in mp_mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
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digs = n->used * 2 + 1;
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if ((digs < MP_WARRAY) &&
n->used <
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(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
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) {
if ((res = mp_grow (x, digs)) != MP_OKAY) {
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return res;
}
}
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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
*
* The value of rho must be precalculated via
* bn_mp_montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
*/
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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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{
register int iy;
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register mp_digit *tmpn, *tmpx, u;
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register 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 */
u = 0;
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/* Multiply and add in place */
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 */
/* propagate carries upwards as required*/
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while (u) {
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*tmpx += u;
u = *tmpx >> DIGIT_BIT;
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*tmpx++ &= MP_MASK;
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}
}
}
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/* at this point the n.used'th least
* significant digits of x are all zero
* which means we can shift x to the
* right by n.used digits and the
* residue is unchanged.
*/
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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) {
return s_mp_sub (x, n, x);
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}
return MP_OKAY;
}