/* -*-c-*-
*
- * $Id: mpbarrett.c,v 1.1 1999/12/10 23:21:59 mdw Exp $
+ * $Id: mpbarrett.c,v 1.8 2001/06/16 13:00:20 mdw Exp $
*
* Barrett modular reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpbarrett.c,v $
+ * Revision 1.8 2001/06/16 13:00:20 mdw
+ * Use the generic exponentiation functions.
+ *
+ * Revision 1.7 2001/04/19 18:25:26 mdw
+ * Use sliding-window exponentiation.
+ *
+ * Revision 1.6 2000/10/08 12:03:44 mdw
+ * (mpbarrett_reduce): Cope with negative numbers.
+ *
+ * Revision 1.5 2000/07/29 17:04:33 mdw
+ * Change to use left-to-right bitwise exponentiation. This will improve
+ * performance when the base is small.
+ *
+ * Revision 1.4 2000/06/17 11:45:09 mdw
+ * Major memory management overhaul. Added arena support. Use the secure
+ * arena for secret integers. Replace and improve the MP management macros
+ * (e.g., replace MP_MODIFY by MP_DEST).
+ *
+ * Revision 1.3 1999/12/12 15:08:52 mdw
+ * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
+ * significant digits.
+ *
+ * Revision 1.2 1999/12/11 01:50:56 mdw
+ * Improve initialization slightly.
+ *
* Revision 1.1 1999/12/10 23:21:59 mdw
* Barrett reduction support: works with even moduli.
*
#include "mp.h"
#include "mpbarrett.h"
+#include "mpbarrett-exp.h"
/*----- Main code ---------------------------------------------------------*/
mp_shrink(m);
mb->k = MP_LEN(m);
mb->m = MP_COPY(m);
- b = mp_lsl(MP_NEW, MP_ONE, 2 * MPW_BITS * mb->k);
+ b = mp_new(2 * mb->k + 1, 0);
+ MPX_ZERO(b->v, b->vl - 1);
+ b->vl[-1] = 1;
mp_div(&b, 0, b, m);
mb->mu = b;
}
* Returns: The residue of @m@ modulo the number in the reduction
* context.
*
- * Use: Performs an efficient modular reduction. The argument is
- * assumed to be positive.
+ * Use: Performs an efficient modular reduction.
*/
mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
if (MP_LEN(m) < k) {
m = MP_COPY(m);
- MP_DROP(d);
+ if (d)
+ MP_DROP(d);
return (m);
}
mp qq;
mp_build(&qq, m->v + (k - 1), m->vl);
q = mp_mul(MP_NEW, &qq, mb->mu);
- q = mp_lsr(q, q, MPW_BITS * (k + 1));
+ if (MP_LEN(q) <= k) {
+ m = MP_COPY(m);
+ if (d)
+ MP_DROP(d);
+ return (m);
+ }
}
/* --- Second stage --- */
mvl = m->vl;
else
mvl = m->v + k + 1;
- r = mp_create(k + 1);
- mpx_umul(r->v, r->vl, q->v, q->vl, mb->m->v, mb->m->vl);
- r->f = (q->f | mb->m->f) & MP_BURN;
- MP_MODIFY(d, k + 1);
+ r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
+ mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
+ MP_DEST(d, k + 1, r->f);
mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
- d->f = (m->f | r->f) & MP_BURN;
+ d->f = (m->f | r->f) & (MP_BURN | MP_NEG);
MP_DROP(r);
MP_DROP(q);
MP_DROP(m);
while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
+ /* --- Fix up the sign --- */
+
+ if (d->f & MP_NEG) {
+ mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl);
+ d->f &= ~MP_NEG;
+ }
+
MP_SHRINK(d);
return (d);
}
mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
{
- mpscan sc;
mp *x = MP_ONE;
- mp *spare = MP_NEW;
-
- a = MP_COPY(a);
- mp_scan(&sc, e);
- if (MP_STEP(&sc)) {
- size_t sq = 0;
- for (;;) {
- mp *dd;
- if (MP_BIT(&sc)) {
- while (sq) {
- dd = mp_sqr(spare, a);
- dd = mpbarrett_reduce(mb, dd, dd);
- spare = a; a = dd;
- sq--;
- }
- dd = mp_mul(spare, x, a);
- dd = mpbarrett_reduce(mb, dd, dd);
- spare = x; x = dd;
- }
- sq++;
- if (!MP_STEP(&sc))
- break;
- }
- }
-
- MP_DROP(a);
- if (spare != MP_NEW)
- MP_DROP(spare);
- if (d != MP_NEW)
- MP_DROP(d);
+ mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
+
+ MP_SHRINK(e);
+ if (!MP_LEN(e))
+ ;
+ else if (MP_LEN(e) < EXP_THRESH)
+ EXP_SIMPLE(x, a, e);
+ else
+ EXP_WINDOW(x, a, e);
+ mp_drop(d);
+ mp_drop(spare);
return (x);
}
mpbarrett_create(&mb, n);
s = mpbarrett_reduce(&mb, MP_NEW, x);
- if (MP_CMP(s, !=, r)) {
+ if (!MP_EQ(s, r)) {
fputs("\n*** barrett reduction failure\n", stderr);
fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
mr = mpbarrett_exp(&mb, MP_NEW, a, b);
- if (MP_CMP(mr, !=, r)) {
+ if (!MP_EQ(mr, r)) {
fputs("\n*** barrett modexp failed", stderr);
fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);