/* -*-c-*-
*
- * $Id: mpbarrett.c,v 1.4 2000/06/17 11:45:09 mdw Exp $
+ * $Id: mpbarrett.c,v 1.6 2000/10/08 12:03:44 mdw Exp $
*
* Barrett modular reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpbarrett.c,v $
+ * 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
* 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)
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);
}
{
mpscan sc;
mp *x = MP_ONE;
- mp *spare = MP_NEW;
+ mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
+ unsigned sq = 0;
a = MP_COPY(a);
- mp_scan(&sc, e);
- if (e->f & MP_BURN)
- spare = MP_NEWSEC;
- if (MP_STEP(&sc)) {
- size_t sq = 0;
+ mp_rscan(&sc, e);
+ if (!MP_RSTEP(&sc))
+ goto exit;
+ while (!MP_RBIT(&sc))
+ MP_RSTEP(&sc);
+
+ /* --- Do the main body of the work --- */
+
+ for (;;) {
+ sq++;
+ while (sq) {
+ mp *y;
+ y = mp_sqr(spare, x);
+ y = mpbarrett_reduce(mb, y, y);
+ spare = x; x = y;
+ sq--;
+ }
+ {
+ mp *y = mp_mul(spare, x, a);
+ y = mpbarrett_reduce(mb, y, y);
+ spare = x; x = y;
+ }
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;
- }
+ if (!MP_RSTEP(&sc))
+ goto done;
+ if (MP_RBIT(&sc))
+ break;
sq++;
- if (!MP_STEP(&sc))
- break;
}
}
+ /* --- Do a final round of squaring --- */
+
+done:
+ while (sq) {
+ mp *y;
+ y = mp_sqr(spare, x);
+ y = mpbarrett_reduce(mb, y, y);
+ spare = x; x = y;
+ sq--;
+ }
+
+exit:
MP_DROP(a);
if (spare != MP_NEW)
MP_DROP(spare);
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);