/* -*-c-*-
*
- * $Id: mpbarrett.c,v 1.5 2000/07/29 17:04:33 mdw Exp $
+ * $Id: mpbarrett.c,v 1.9 2004/04/01 12:50:09 mdw Exp $
*
* Barrett modular reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpbarrett.c,v $
+ * Revision 1.9 2004/04/01 12:50:09 mdw
+ * Add cyclic group abstraction, with test code. Separate off exponentation
+ * functions for better static linking. Fix a buttload of bugs on the way.
+ * Generally ensure that negative exponents do inversion correctly. Add
+ * table of standard prime-field subgroups. (Binary field subgroups are
+ * currently unimplemented but easy to add if anyone ever finds a good one.)
+ *
+ * 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.
* 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);
- MP_SHRINK(d);
- return (d);
-}
+ /* --- Fix up the sign --- */
-/* --- @mpbarrett_exp@ --- *
- *
- * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
- * @mp *d@ = fake destination
- * @mp *a@ = base
- * @mp *e@ = exponent
- *
- * Returns: Result, %$a^e \bmod m$%.
- */
-
-mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
-{
- mpscan sc;
- mp *x = MP_ONE;
- mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
- unsigned sq = 0;
-
- a = MP_COPY(a);
- 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 (;;) {
- if (!MP_RSTEP(&sc))
- goto done;
- if (MP_RBIT(&sc))
- break;
- sq++;
- }
+ 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;
}
- /* --- 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);
- if (d != MP_NEW)
- MP_DROP(d);
- return (x);
+ MP_SHRINK(d);
+ return (d);
}
/*----- 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);
return (ok);
}
-static int vexp(dstr *v)
-{
- mp *m = *(mp **)v[0].buf;
- mp *a = *(mp **)v[1].buf;
- mp *b = *(mp **)v[2].buf;
- mp *r = *(mp **)v[3].buf;
- mp *mr;
- int ok = 1;
-
- mpbarrett mb;
- mpbarrett_create(&mb, m);
-
- mr = mpbarrett_exp(&mb, MP_NEW, a, b);
-
- if (MP_CMP(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);
- fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
- fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- mp_drop(m);
- mp_drop(a);
- mp_drop(b);
- mp_drop(r);
- mp_drop(mr);
- mpbarrett_destroy(&mb);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return ok;
-}
-
static test_chunk tests[] = {
{ "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
- { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
{ 0, 0, { 0 } }
};