зеркало из https://github.com/mozilla/pjs.git
Reduced the number of temporary variables allocated and freed during a
modular exponentiation by over 99%. Modified mp_mul and mp_sqr to only allocate temporary variables when absolutely needed. Changed mp_copy and mp_init_copy to allocate space according to the amount allocated in the source, reducing the need to grow the variable later.
This commit is contained in:
nelsonb%netscape.com
Родитель
9d98b785c7
Коммит
c095d3c281
|
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@ -35,7 +35,7 @@
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* the GPL. If you do not delete the provisions above, a recipient
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* may use your version of this file under either the MPL or the GPL.
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*
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* $Id: mpi.c,v 1.11 2000-08-01 01:38:29 nelsonb%netscape.com Exp $
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* $Id: mpi.c,v 1.12 2000-08-02 01:03:14 nelsonb%netscape.com Exp $
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*/
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#include "mpi-priv.h"
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@ -79,6 +79,9 @@ static const char *s_dmap_1 =
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/* }}} */
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unsigned long mp_allocs;
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unsigned long mp_frees;
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/* {{{ Default precision manipulation */
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/* Default precision for newly created mp_int's */
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@ -132,6 +135,7 @@ mp_err mp_init(mp_int *mp)
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mp_err mp_init_size(mp_int *mp, mp_size prec)
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{
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ARGCHK(mp != NULL && prec > 0, MP_BADARG);
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/*if (prec < 128) prec = 128; /* XXX HACK */
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if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL)
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return MP_MEM;
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@ -163,12 +167,12 @@ mp_err mp_init_copy(mp_int *mp, const mp_int *from)
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if(mp == from)
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return MP_OKAY;
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if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
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if((DIGITS(mp) = s_mp_alloc(ALLOC(from), sizeof(mp_digit))) == NULL)
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return MP_MEM;
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s_mp_copy(DIGITS(from), DIGITS(mp), USED(from));
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USED(mp) = USED(from);
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ALLOC(mp) = USED(from);
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ALLOC(mp) = ALLOC(from);
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SIGN(mp) = SIGN(from);
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return MP_OKAY;
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@ -209,7 +213,7 @@ mp_err mp_copy(const mp_int *from, mp_int *to)
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s_mp_copy(DIGITS(from), DIGITS(to), USED(from));
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} else {
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if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
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if((tmp = s_mp_alloc(ALLOC(from), sizeof(mp_digit))) == NULL)
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return MP_MEM;
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s_mp_copy(DIGITS(from), tmp, USED(from));
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@ -222,7 +226,7 @@ mp_err mp_copy(const mp_int *from, mp_int *to)
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}
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DIGITS(to) = tmp;
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ALLOC(to) = USED(from);
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ALLOC(to) = ALLOC(from);
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}
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/* Copy the precision and sign from the original */
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@ -795,48 +799,184 @@ CLEANUP:
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Compute c = a * b. All parameters may be identical.
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*/
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mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c)
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mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int * c)
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{
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mp_digit *pb = MP_DIGITS(b);
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mp_word w;
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mp_int tmp;
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mp_err res;
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mp_size ib;
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ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
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if((res = mp_copy(a, c)) != MP_OKAY)
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return res;
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if (a == c) {
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if ((res = mp_init_copy(&tmp, a)) != MP_OKAY)
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return res;
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if (a == b)
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b = &tmp;
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a = &tmp;
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} else if (b == c) {
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if ((res = mp_init_copy(&tmp, b)) != MP_OKAY)
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return res;
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b = &tmp;
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} else {
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MP_DIGITS(&tmp) = 0;
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}
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if((res = s_mp_mul(c, b)) != MP_OKAY)
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return res;
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/* This has the effect of left-padding with zeroes... */
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mp_zero(c);
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if((res = s_mp_pad(c, USED(a) + USED(b))) != MP_OKAY)
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goto CLEANUP;
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/* Outer loop: Digits of b */
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for(ib = 0; ib < USED(b); ib++) {
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mp_digit b_i = *pb++;
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mp_digit *pc = DIGITS(c) + ib;
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mp_digit *pa = DIGITS(a);
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mp_digit *palim = DIGITS(a) + USED(a);
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if(b_i == 0)
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continue;
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w = 0;
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/* Inner product: Digits of a */
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while (pa < palim) {
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w += ((mp_word)b_i * *pa++) + *pc;
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*pc++ = ACCUM(w);
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w = CARRYOUT(w);
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}
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*pc = (mp_digit)w;
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}
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s_mp_clamp(c);
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if(SIGN(a) == SIGN(b) || s_mp_cmp_d(c, 0) == MP_EQ)
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SIGN(c) = ZPOS;
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else
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SIGN(c) = NEG;
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return MP_OKAY;
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CLEANUP:
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mp_clear(&tmp);
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return res;
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} /* end mp_mul() */
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/* }}} */
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/* {{{ mp_sqr(a, b) */
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/* {{{ mp_sqr(a, sqr) */
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#if MP_SQUARE
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mp_err mp_sqr(const mp_int *a, mp_int *b)
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/*
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Computes the square of a. This can be done more
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efficiently than a general multiplication, because many of the
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computation steps are redundant when squaring. The inner product
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step is a bit more complicated, but we save a fair number of
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iterations of the multiplication loop.
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*/
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/* sqr = a^2; Caller provides both a and tmp; */
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mp_err mp_sqr(const mp_int *a, mp_int *sqr)
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{
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mp_word w, k = 0;
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mp_err res;
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mp_size ix, jx, kx;
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mp_int tmp;
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ARGCHK(a != NULL && b != NULL, MP_BADARG);
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ARGCHK(a != NULL && sqr != NULL, MP_BADARG);
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if((res = mp_copy(a, b)) != MP_OKAY)
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return res;
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if (a == sqr) {
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if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
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return res;
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a = &tmp;
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} else {
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DIGITS(&tmp) = 0;
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}
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if((res = s_mp_sqr(b)) != MP_OKAY)
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return res;
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/* Left-pad with zeroes */
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mp_zero(sqr);
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if((res = s_mp_pad(sqr, 2 * USED(a))) != MP_OKAY)
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goto CLEANUP;
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SIGN(b) = ZPOS;
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for(ix = 0; ix < USED(a); ix++) {
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if(DIGIT(a, ix) == 0)
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continue;
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return MP_OKAY;
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w = DIGIT(sqr, ix + ix) + (DIGIT(a, ix) * (mp_word)DIGIT(a, ix));
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DIGIT(sqr, ix + ix) = ACCUM(w);
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k = CARRYOUT(w);
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/*
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The inner product is computed as:
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(C, S) = t[i,j] + 2 a[i] a[j] + C
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This can overflow what can be represented in an mp_word, and
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since C arithmetic does not provide any way to check for
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overflow, we have to check explicitly for overflow conditions
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before they happen.
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*/
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for(jx = ix + 1; jx < USED(a); jx++) {
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mp_word u = 0, v;
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/* Compute the multiplicative step */
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w = (mp_word)DIGIT(a, ix) * DIGIT(a, jx);
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/* If w is more than half MP_WORD_MAX, the doubling will
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overflow, and we need to record a carry out into the next
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word */
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u = (w >> (MP_WORD_BIT - 1)) & 1;
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/* Double what we've got, overflow will be ignored as defined
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for C arithmetic (we've already noted if it is to occur)
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*/
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w *= 2;
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/* Compute the additive step */
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v = (mp_word)DIGIT(sqr, ix + jx) + k;
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/* If we do not already have an overflow carry, check to see
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if the addition will cause one, and set the carry out if so
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*/
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u |= ((MP_WORD_MAX - v) < w);
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/* Add in the rest, again ignoring overflow */
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w += v;
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/* Set the i,j digit of the output */
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DIGIT(sqr, ix + jx) = ACCUM(w);
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/* Save carry information for the next iteration of the loop.
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This is why k must be an mp_word, instead of an mp_digit */
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k = CARRYOUT(w) | (u << DIGIT_BIT);
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} /* for(jx ...) */
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/* Set the last digit in the cycle and reset the carry */
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k = DIGIT(sqr, ix + jx) + k;
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DIGIT(sqr, ix + jx) = ACCUM(k);
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k = CARRYOUT(k);
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/* If we are carrying out, propagate the carry to the next digit
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in the output. This may cascade, so we have to be somewhat
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circumspect -- but we will have enough precision in the output
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that we won't overflow
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*/
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kx = 1;
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while(k) {
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k = (mp_word)DIGIT(sqr, ix + jx + kx) + 1;
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DIGIT(sqr, ix + jx + kx) = ACCUM(k);
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k = CARRYOUT(k);
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++kx;
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}
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} /* for(ix ...) */
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SIGN(sqr) = ZPOS;
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s_mp_clamp(sqr);
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CLEANUP:
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mp_clear(&tmp);
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return res;
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} /* end mp_sqr() */
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#endif
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@ -858,6 +998,7 @@ mp_err mp_sqr(const mp_int *a, mp_int *b)
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mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r)
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{
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mp_err res;
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mp_int *pQ, *pR;
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mp_int qtmp, rtmp;
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int cmp;
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@ -866,46 +1007,61 @@ mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r)
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if(mp_cmp_z(b) == MP_EQ)
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return MP_RANGE;
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DIGITS(&qtmp) = 0;
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DIGITS(&rtmp) = 0;
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/* Set up some temporaries... */
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if((res = mp_init_copy(&qtmp, a)) != MP_OKAY)
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return res;
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if((res = mp_init_copy(&rtmp, b)) != MP_OKAY)
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goto CLEANUP;
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if (!q || q == a || q == b) {
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if((res = mp_init_copy(&qtmp, a)) != MP_OKAY)
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return res;
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pQ = &qtmp;
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} else {
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if((res = mp_copy(a, q)) != MP_OKAY)
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return res;
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pQ = q;
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}
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if (!r || r == a || r == b) {
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if((res = mp_init_copy(&rtmp, b)) != MP_OKAY)
|
||||
goto CLEANUP;
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||||
pR = &rtmp;
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||||
} else {
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||||
if((res = mp_copy(b, r)) != MP_OKAY)
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goto CLEANUP;
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||||
pR = r;
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||||
}
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||||
|
||||
/*
|
||||
If a <= b, we can compute the solution without division;
|
||||
otherwise, we actually do the work required.
|
||||
*/
|
||||
if((cmp = s_mp_cmp(&qtmp, &rtmp)) < 0) {
|
||||
s_mp_exch(&qtmp, &rtmp);
|
||||
mp_zero(&qtmp);
|
||||
if((cmp = s_mp_cmp(pQ, pR)) < 0) {
|
||||
s_mp_exch(pQ, pR);
|
||||
mp_zero(pQ);
|
||||
} else if(cmp == 0) {
|
||||
mp_zero(&qtmp);
|
||||
DIGIT(&qtmp, 0) = 1;
|
||||
mp_zero(&rtmp);
|
||||
mp_set(pQ, 1);
|
||||
mp_zero(pR);
|
||||
} else {
|
||||
if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY)
|
||||
if((res = s_mp_div(pQ, pR)) != MP_OKAY)
|
||||
goto CLEANUP;
|
||||
}
|
||||
|
||||
/* Compute the signs for the output */
|
||||
SIGN(&rtmp) = SIGN(a); /* Sr = Sa */
|
||||
SIGN(pR) = SIGN(a); /* Sr = Sa */
|
||||
if(SIGN(a) == SIGN(b))
|
||||
SIGN(&qtmp) = ZPOS; /* Sq = ZPOS if Sa = Sb */
|
||||
SIGN(pQ) = ZPOS; /* Sq = ZPOS if Sa = Sb */
|
||||
else
|
||||
SIGN(&qtmp) = NEG; /* Sq = NEG if Sa != Sb */
|
||||
SIGN(pQ) = NEG; /* Sq = NEG if Sa != Sb */
|
||||
|
||||
if(s_mp_cmp_d(&qtmp, 0) == MP_EQ)
|
||||
SIGN(&qtmp) = ZPOS;
|
||||
if(s_mp_cmp_d(&rtmp, 0) == MP_EQ)
|
||||
SIGN(&rtmp) = ZPOS;
|
||||
if(s_mp_cmp_d(pQ, 0) == MP_EQ)
|
||||
SIGN(pQ) = ZPOS;
|
||||
if(s_mp_cmp_d(pR, 0) == MP_EQ)
|
||||
SIGN(pR) = ZPOS;
|
||||
|
||||
/* Copy output, if it is needed */
|
||||
if(q)
|
||||
s_mp_exch(&qtmp, q);
|
||||
if(q && q != pQ)
|
||||
s_mp_exch(pQ, q);
|
||||
|
||||
if(r)
|
||||
s_mp_exch(&rtmp, r);
|
||||
if(r && r != pR)
|
||||
s_mp_exch(pR, r);
|
||||
|
||||
CLEANUP:
|
||||
mp_clear(&rtmp);
|
||||
|
|
@ -2219,6 +2375,7 @@ mp_err s_mp_grow(mp_int *mp, mp_size min)
|
|||
|
||||
/* Set min to next nearest default precision block size */
|
||||
min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec;
|
||||
/* if (min < 128) min = 128; /* XXX HACK */
|
||||
|
||||
if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL)
|
||||
return MP_MEM;
|
||||
|
|
@ -2248,8 +2405,12 @@ mp_err s_mp_pad(mp_int *mp, mp_size min)
|
|||
mp_err res;
|
||||
|
||||
/* Make sure there is room to increase precision */
|
||||
if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY)
|
||||
return res;
|
||||
if (min > ALLOC(mp)) {
|
||||
if ((res = s_mp_grow(mp, min)) != MP_OKAY)
|
||||
return res;
|
||||
} else {
|
||||
s_mp_setz(DIGITS(mp) + USED(mp), min - USED(mp));
|
||||
}
|
||||
|
||||
/* Increase precision; should already be 0-filled */
|
||||
USED(mp) = min;
|
||||
|
|
@ -2307,6 +2468,7 @@ void s_mp_copy(const mp_digit *sp, mp_digit *dp, mp_size count)
|
|||
/* Allocate ni records of nb bytes each, and return a pointer to that */
|
||||
void *s_mp_alloc(size_t nb, size_t ni)
|
||||
{
|
||||
++mp_allocs;
|
||||
return calloc(nb, ni);
|
||||
|
||||
} /* end s_mp_alloc() */
|
||||
|
|
@ -2320,9 +2482,10 @@ void *s_mp_alloc(size_t nb, size_t ni)
|
|||
/* Free the memory pointed to by ptr */
|
||||
void s_mp_free(void *ptr)
|
||||
{
|
||||
if(ptr)
|
||||
if(ptr) {
|
||||
++mp_frees;
|
||||
free(ptr);
|
||||
|
||||
}
|
||||
} /* end s_mp_free() */
|
||||
#endif
|
||||
|
||||
|
|
@ -2938,46 +3101,7 @@ mp_err s_mp_sub(mp_int *a, const mp_int *b) /* magnitude subtract */
|
|||
/* Compute a = |a| * |b| */
|
||||
mp_err s_mp_mul(mp_int *a, const mp_int *b)
|
||||
{
|
||||
mp_digit *pb = MP_DIGITS(b);
|
||||
mp_word w;
|
||||
mp_int tmp;
|
||||
mp_err res;
|
||||
mp_size ib;
|
||||
|
||||
if((res = mp_init_size(&tmp, USED(a) + USED(b))) != MP_OKAY)
|
||||
return res;
|
||||
|
||||
/* This has the effect of left-padding with zeroes... */
|
||||
USED(&tmp) = USED(a) + USED(b);
|
||||
|
||||
/* Outer loop: Digits of b */
|
||||
for(ib = 0; ib < USED(b); ib++) {
|
||||
mp_digit b_i = *pb++;
|
||||
mp_digit *pt = DIGITS(&tmp) + ib;
|
||||
mp_digit *pa = DIGITS(a);
|
||||
mp_digit *palim = DIGITS(a) + USED(a);
|
||||
|
||||
if(b_i == 0)
|
||||
continue;
|
||||
|
||||
w = 0;
|
||||
/* Inner product: Digits of a */
|
||||
while (pa < palim) {
|
||||
w += ((mp_word)b_i * *pa++) + *pt;
|
||||
*pt++ = ACCUM(w);
|
||||
w = CARRYOUT(w);
|
||||
}
|
||||
|
||||
*pt = (mp_digit)w;
|
||||
}
|
||||
|
||||
s_mp_clamp(&tmp);
|
||||
s_mp_exch(&tmp, a);
|
||||
|
||||
mp_clear(&tmp);
|
||||
|
||||
return MP_OKAY;
|
||||
|
||||
return mp_mul(a, b, a);
|
||||
} /* end s_mp_mul() */
|
||||
|
||||
/* }}} */
|
||||
|
|
@ -3016,114 +3140,26 @@ mp_err s_mp_mul_d_add_offset(mp_int *a, mp_digit b, mp_int *c, mp_size offset)
|
|||
return MP_OKAY;
|
||||
}
|
||||
|
||||
#if MP_SQUARE
|
||||
/* {{{ s_mp_sqr(a) */
|
||||
|
||||
/*
|
||||
Computes the square of a, in place. This can be done more
|
||||
efficiently than a general multiplication, because many of the
|
||||
computation steps are redundant when squaring. The inner product
|
||||
step is a bit more complicated, but we save a fair number of
|
||||
iterations of the multiplication loop.
|
||||
*/
|
||||
#if MP_SQUARE
|
||||
mp_err s_mp_sqr(mp_int *a)
|
||||
{
|
||||
mp_word w, k = 0;
|
||||
mp_int tmp;
|
||||
mp_err res;
|
||||
mp_size ix, jx, kx;
|
||||
mp_int tmp;
|
||||
|
||||
if((res = mp_init_size(&tmp, 2 * USED(a))) != MP_OKAY)
|
||||
return res;
|
||||
|
||||
/* Left-pad with zeroes */
|
||||
USED(&tmp) = 2 * USED(a);
|
||||
|
||||
for(ix = 0; ix < USED(a); ix++) {
|
||||
if(DIGIT(a, ix) == 0)
|
||||
continue;
|
||||
|
||||
w = DIGIT(&tmp, ix + ix) + (DIGIT(a, ix) * (mp_word)DIGIT(a, ix));
|
||||
|
||||
DIGIT(&tmp, ix + ix) = ACCUM(w);
|
||||
k = CARRYOUT(w);
|
||||
|
||||
/*
|
||||
The inner product is computed as:
|
||||
|
||||
(C, S) = t[i,j] + 2 a[i] a[j] + C
|
||||
|
||||
This can overflow what can be represented in an mp_word, and
|
||||
since C arithmetic does not provide any way to check for
|
||||
overflow, we have to check explicitly for overflow conditions
|
||||
before they happen.
|
||||
*/
|
||||
for(jx = ix + 1; jx < USED(a); jx++) {
|
||||
mp_word u = 0, v;
|
||||
|
||||
/* Compute the multiplicative step */
|
||||
w = (mp_word)DIGIT(a, ix) * DIGIT(a, jx);
|
||||
|
||||
/* If w is more than half MP_WORD_MAX, the doubling will
|
||||
overflow, and we need to record a carry out into the next
|
||||
word */
|
||||
u = (w >> (MP_WORD_BIT - 1)) & 1;
|
||||
|
||||
/* Double what we've got, overflow will be ignored as defined
|
||||
for C arithmetic (we've already noted if it is to occur)
|
||||
*/
|
||||
w *= 2;
|
||||
|
||||
/* Compute the additive step */
|
||||
v = (mp_word)DIGIT(&tmp, ix + jx) + k;
|
||||
|
||||
/* If we do not already have an overflow carry, check to see
|
||||
if the addition will cause one, and set the carry out if so
|
||||
*/
|
||||
u |= ((MP_WORD_MAX - v) < w);
|
||||
|
||||
/* Add in the rest, again ignoring overflow */
|
||||
w += v;
|
||||
|
||||
/* Set the i,j digit of the output */
|
||||
DIGIT(&tmp, ix + jx) = ACCUM(w);
|
||||
|
||||
/* Save carry information for the next iteration of the loop.
|
||||
This is why k must be an mp_word, instead of an mp_digit */
|
||||
k = CARRYOUT(w) | (u << DIGIT_BIT);
|
||||
|
||||
} /* for(jx ...) */
|
||||
|
||||
/* Set the last digit in the cycle and reset the carry */
|
||||
k = DIGIT(&tmp, ix + jx) + k;
|
||||
DIGIT(&tmp, ix + jx) = ACCUM(k);
|
||||
k = CARRYOUT(k);
|
||||
|
||||
/* If we are carrying out, propagate the carry to the next digit
|
||||
in the output. This may cascade, so we have to be somewhat
|
||||
circumspect -- but we will have enough precision in the output
|
||||
that we won't overflow
|
||||
*/
|
||||
kx = 1;
|
||||
while(k) {
|
||||
k = (mp_word)DIGIT(&tmp, ix + jx + kx) + 1;
|
||||
DIGIT(&tmp, ix + jx + kx) = ACCUM(k);
|
||||
k = CARRYOUT(k);
|
||||
++kx;
|
||||
}
|
||||
} /* for(ix ...) */
|
||||
|
||||
s_mp_clamp(&tmp);
|
||||
s_mp_exch(&tmp, a);
|
||||
|
||||
res = mp_sqr(a, &tmp);
|
||||
if (res == MP_OKAY) {
|
||||
s_mp_exch(&tmp, a);
|
||||
}
|
||||
mp_clear(&tmp);
|
||||
|
||||
return MP_OKAY;
|
||||
|
||||
} /* end s_mp_sqr() */
|
||||
#endif
|
||||
return res;
|
||||
}
|
||||
|
||||
/* }}} */
|
||||
#endif
|
||||
|
||||
/* {{{ s_mp_div(a, b) */
|
||||
|
||||
|
|
@ -3155,15 +3191,15 @@ mp_err s_mp_div(mp_int *a, mp_int *b)
|
|||
}
|
||||
|
||||
/* Allocate space to store the quotient */
|
||||
if((res = mp_init_size(", USED(a))) != MP_OKAY)
|
||||
if((res = mp_init_size(", MP_ALLOC(a))) != MP_OKAY)
|
||||
return res;
|
||||
|
||||
/* A working temporary for division */
|
||||
if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
|
||||
if((res = mp_init_size(&t, MP_ALLOC(a))) != MP_OKAY)
|
||||
goto T;
|
||||
|
||||
/* Allocate space for the remainder */
|
||||
if((res = mp_init_size(&rem, USED(a))) != MP_OKAY)
|
||||
if((res = mp_init_size(&rem, MP_ALLOC(a))) != MP_OKAY)
|
||||
goto REM;
|
||||
|
||||
/* Normalize to optimize guessing */
|
||||
|
|
|
|||
|
|
@ -29,7 +29,7 @@
|
|||
* the GPL. If you do not delete the provisions above, a recipient
|
||||
* may use your version of this file under either the MPL or the
|
||||
* GPL.
|
||||
* $Id: mpmontg.c,v 1.3 2000-08-01 01:38:30 nelsonb%netscape.com Exp $
|
||||
* $Id: mpmontg.c,v 1.4 2000-08-02 01:03:14 nelsonb%netscape.com Exp $
|
||||
*/
|
||||
|
||||
/* This file implements moduluar exponentiation using Montgomery's
|
||||
|
|
@ -55,9 +55,9 @@
|
|||
#define ODD_INTS 16 /* 2 ** (WINDOW_BITS - 1) */
|
||||
|
||||
typedef struct {
|
||||
mp_int N; /* modulus N */
|
||||
mp_digit n0prime; /* n0' = - (n0 ** -1) mod MP_RADIX */
|
||||
mp_size b; /* R == 2 ** b, also b = # significant bits in N */
|
||||
mp_int N; /* modulus N */
|
||||
} mp_mont_modulus;
|
||||
|
||||
/* computes T = REDC(T), 2^b == R */
|
||||
|
|
@ -70,17 +70,17 @@ mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
|
|||
int i;
|
||||
int n = MP_USED(&mmm->N);
|
||||
|
||||
mp_init(&m);
|
||||
|
||||
MP_CHECKOK( s_mp_grow(T, 2 * n + 2) );
|
||||
MP_CHECKOK( s_mp_pad(T, MP_USED(T) + n + 2) );
|
||||
for (i = 0; i < n; ++i ) {
|
||||
mp_digit m_i = MP_DIGIT(T, i) * n0prime;
|
||||
/* T += N * m_i * (MP_RADIX ** i); */
|
||||
MP_CHECKOK( s_mp_mul_d_add_offset(&mmm->N, m_i, T, i) );
|
||||
}
|
||||
s_mp_clamp(T);
|
||||
|
||||
/* T /= R */
|
||||
#ifdef DEBUG
|
||||
MP_CHECKOK( mp_init(&m) );
|
||||
MP_CHECKOK( mp_div_2d(T, mmm->b, T, &m));
|
||||
/* here, remainder m should be equal to zero */
|
||||
if (mp_cmp_z(&m) != 0) {
|
||||
|
|
@ -102,7 +102,9 @@ mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
|
|||
}
|
||||
rv = MP_OKAY;
|
||||
loser:
|
||||
#ifdef DEBUG
|
||||
mp_clear(&m);
|
||||
#endif
|
||||
return rv;
|
||||
}
|
||||
|
||||
|
|
@ -112,7 +114,7 @@ mp_err mp_to_mont(const mp_int *x, mp_mont_modulus *mmm, mp_int *xMont)
|
|||
|
||||
/* xMont = x * R mod N where N is modulus */
|
||||
MP_CHECKOK( mpl_lsh(x, xMont, mmm->b) ); /* xMont = x << b */
|
||||
MP_CHECKOK( mp_mod(xMont, &mmm->N, xMont) ); /* mod N */
|
||||
MP_CHECKOK( mp_div(xMont, &mmm->N, 0, xMont) ); /* mod N */
|
||||
loser:
|
||||
return rv;
|
||||
}
|
||||
|
|
@ -150,23 +152,25 @@ mp_err mp_exptmod(const mp_int *inBase, const mp_int *exponent,
|
|||
mp_size bits_in_exponent;
|
||||
mp_size i;
|
||||
mp_err rv;
|
||||
mp_int square, accum, goodBase;
|
||||
mp_int square, accum, goodBase, tmp;
|
||||
mp_mont_modulus mmm;
|
||||
|
||||
/* function for computing n0prime only works if n0 is odd */
|
||||
if (!mp_isodd(modulus))
|
||||
return s_mp_exptmod(inBase, exponent, modulus, result);
|
||||
|
||||
mp_init(&goodBase);
|
||||
if (mp_cmp(inBase, modulus) < 0) {
|
||||
base = inBase;
|
||||
MP_DIGITS(&goodBase) = 0;
|
||||
} else {
|
||||
mp_init(&goodBase);
|
||||
base = &goodBase;
|
||||
MP_CHECKOK( mp_mod(inBase, modulus, &goodBase) );
|
||||
}
|
||||
|
||||
mp_init_size(&square, 2 * MP_USED(modulus) + 2);
|
||||
mp_init_size(&accum, 2 * MP_USED(modulus) + 2);
|
||||
mp_init_size(&accum, 3 * MP_USED(modulus) + 2);
|
||||
mp_init_size(&tmp, 3 * MP_USED(modulus) + 2);
|
||||
|
||||
mmm.N = *modulus; /* a copy of the mp_int struct */
|
||||
i = mpl_significant_bits(modulus);
|
||||
|
|
@ -187,15 +191,14 @@ mp_err mp_exptmod(const mp_int *inBase, const mp_int *exponent,
|
|||
int expOff;
|
||||
mp_int power2, oddPowers[ODD_INTS];
|
||||
|
||||
mp_init(oddPowers);
|
||||
MP_CHECKOK( mp_copy(&square, oddPowers));
|
||||
MP_CHECKOK( mp_init_copy(oddPowers, &square) );
|
||||
|
||||
mp_init(&power2);
|
||||
mp_init_size(&power2, MP_USED(modulus) + 2 * MP_USED(&square) + 2);
|
||||
MP_CHECKOK( mp_sqr(&square, &power2) ); /* square = square ** 2 */
|
||||
MP_CHECKOK( s_mp_redc(&power2, &mmm) );
|
||||
|
||||
for (i = 1; i < ODD_INTS; ++i) {
|
||||
mp_init(oddPowers + i);
|
||||
mp_init_size(oddPowers + i, MP_USED(modulus) + 2 * MP_USED(&power2) + 2);
|
||||
MP_CHECKOK( mp_mul(oddPowers + (i - 1), &power2, oddPowers + i) );
|
||||
MP_CHECKOK( s_mp_redc(oddPowers + i, &mmm) );
|
||||
}
|
||||
|
|
@ -203,10 +206,13 @@ mp_err mp_exptmod(const mp_int *inBase, const mp_int *exponent,
|
|||
MP_CHECKOK( mp_to_mont(&accum, &mmm, &accum) );
|
||||
|
||||
#define SQUARE \
|
||||
MP_CHECKOK( s_mp_sqr(&accum) );\
|
||||
memset(tmp.dp, 0, tmp.alloc * sizeof(mp_digit)); \
|
||||
MP_CHECKOK( mp_sqr(&accum, &tmp) );\
|
||||
mp_exch(&accum, &tmp); \
|
||||
MP_CHECKOK( s_mp_redc(&accum, &mmm) )
|
||||
#define MUL(x) \
|
||||
MP_CHECKOK( s_mp_mul(&accum, oddPowers + (x)) ); \
|
||||
MP_CHECKOK( mp_mul(&accum, oddPowers + (x), &tmp) ); \
|
||||
mp_exch(&accum, &tmp); \
|
||||
MP_CHECKOK( s_mp_redc(&accum, &mmm))
|
||||
|
||||
for (expOff = bits_in_exponent - WINDOW_BITS; expOff >= 0; expOff -= WINDOW_BITS) {
|
||||
|
|
@ -278,6 +284,7 @@ loser:
|
|||
mp_clear(&square);
|
||||
mp_clear(&accum);
|
||||
mp_clear(&goodBase);
|
||||
mp_clear(&tmp);
|
||||
/* Don't mp_clear mmm.N because it is merely a copy of modulus.
|
||||
** Just zap it.
|
||||
*/
|
||||
|
|
|
|||
Загрузка…
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