/* -*-c-*-
*
- * $Id: mpbarrett.c,v 1.3 1999/12/12 15:08:52 mdw Exp $
+ * $Id: mpbarrett.c,v 1.7 2001/04/19 18:25:26 mdw Exp $
*
* Barrett modular reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpbarrett.c,v $
+ * 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.
mp_shrink(m);
mb->k = MP_LEN(m);
mb->m = MP_COPY(m);
- b = mp_create(2 * mb->k + 1);
+ 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);
* 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);
}
q = mp_mul(MP_NEW, &qq, mb->mu);
if (MP_LEN(q) <= k) {
m = MP_COPY(m);
- MP_DROP(d);
+ if (d)
+ MP_DROP(d);
return (m);
}
}
mvl = m->vl;
else
mvl = m->v + k + 1;
- r = mp_create(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);
- r->f = (q->f | mb->m->f) & MP_BURN;
- MP_MODIFY(d, k + 1);
+ 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);
}
* Returns: Result, %$a^e \bmod m$%.
*/
-mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
+#define WINSZ 5
+#define TABSZ (1 << (WINSZ - 1))
+
+#define THRESH (((MPW_BITS / WINSZ) << 2) + 1)
+
+static mp *exp_simple(mpbarrett *mb, mp *d, mp *a, mp *e)
{
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 (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);
return (x);
}
+mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
+{
+ mp **tab;
+ mp *a2;
+ mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
+ mp *x = MP_ONE;
+ unsigned i, sq = 0;
+ mpscan sc;
+
+ /* --- Do we bother? --- */
+
+ MP_SHRINK(e);
+ if (MP_LEN(e) == 0)
+ goto exit;
+ if (MP_LEN(e) < THRESH) {
+ x->ref--;
+ return (exp_simple(mb, d, a, e));
+ }
+
+ /* --- Do the precomputation --- */
+
+ a2 = mp_sqr(MP_NEW, a);
+ a2 = mpbarrett_reduce(mb, a2, a2);
+ tab = xmalloc(TABSZ * sizeof(mp *));
+ tab[0] = MP_COPY(a);
+ for (i = 1; i < TABSZ; i++) {
+ mp *x = mp_mul(MP_NEW, tab[i - 1], a2);
+ tab[i] = mpbarrett_reduce(mb, x, x);
+ }
+ mp_drop(a2);
+ mp_rscan(&sc, e);
+
+ /* --- Skip top-end zero bits --- *
+ *
+ * If the initial step worked, there must be a set bit somewhere, so keep
+ * stepping until I find it.
+ */
+
+ MP_RSTEP(&sc);
+ while (!MP_RBIT(&sc))
+ MP_RSTEP(&sc);
+
+ /* --- Now for the main work --- */
+
+ for (;;) {
+ unsigned l = 0;
+ unsigned z = 0;
+
+ /* --- The next bit is set, so read a window index --- *
+ *
+ * Reset @i@ to zero and increment @sq@. Then, until either I read
+ * @WINSZ@ bits or I run out of bits, scan in a bit: if it's clear, bump
+ * the @z@ counter; if it's set, push a set bit into @i@, shift it over
+ * by @z@ bits, bump @sq@ by @z + 1@ and clear @z@. By the end of this
+ * palaver, @i@ is an index to the precomputed value in @tab@.
+ */
+
+ i = 0;
+ sq++;
+ for (;;) {
+ l++;
+ if (l >= WINSZ || !MP_RSTEP(&sc))
+ break;
+ if (!MP_RBIT(&sc))
+ z++;
+ else {
+ i = ((i << 1) | 1) << z;
+ sq += z + 1;
+ z = 0;
+ }
+ }
+
+ /* --- Do the squaring --- *
+ *
+ * Remember that @sq@ carries over from the zero-skipping stuff below.
+ */
+
+ while (sq) {
+ mp *y;
+ y = mp_sqr(spare, x);
+ y = mpbarrett_reduce(mb, y, y);
+ spare = x; x = y;
+ sq--;
+ }
+
+ /* --- Do the multiply --- */
+
+ { mp *y = mp_mul(spare, x, tab[i]); spare = x;
+ x = mpbarrett_reduce(mb, y, y); }
+
+ /* --- Now grind along through the rest of the bits --- */
+
+ sq = z;
+ for (;;) {
+ if (!MP_RSTEP(&sc))
+ goto done;
+ if (MP_RBIT(&sc))
+ break;
+ sq++;
+ }
+ }
+
+ /* --- 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--;
+ }
+
+ /* --- Done --- */
+
+ for (i = 0; i < TABSZ; i++)
+ mp_drop(tab[i]);
+ xfree(tab);
+exit:
+ mp_drop(d);
+ mp_drop(spare);
+ return (x);
+}
+
/*----- Test rig ----------------------------------------------------------*/
#ifdef TEST_RIG
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);
projects / u / mdw / catacomb / blobdiff