/* -*-c-*-
*
- * $Id: mpmont.c,v 1.8 1999/12/22 15:55:00 mdw Exp $
+ * $Id: mpmont.c,v 1.15 2001/06/16 13:00:20 mdw Exp $
*
* Montgomery reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpmont.c,v $
+ * Revision 1.15 2001/06/16 13:00:20 mdw
+ * Use the generic exponentiation functions.
+ *
+ * Revision 1.14 2001/02/22 09:04:26 mdw
+ * Cosmetic fix.
+ *
+ * Revision 1.13 2001/02/03 12:00:29 mdw
+ * Now @mp_drop@ checks its argument is non-NULL before attempting to free
+ * it. Note that the macro version @MP_DROP@ doesn't do this.
+ *
+ * Revision 1.12 2000/10/08 15:48:35 mdw
+ * Rename Karatsuba constants now that we have @gfx_kmul@ too.
+ *
+ * Revision 1.11 2000/10/08 12:04:27 mdw
+ * (mpmont_reduce, mpmont_mul): Cope with negative numbers.
+ *
+ * Revision 1.10 2000/07/29 17:05:43 mdw
+ * (mpmont_expr): Use sliding window exponentiation, with a drop-through
+ * for small exponents to use a simple left-to-right bitwise routine. This
+ * can reduce modexp times by up to a quarter.
+ *
+ * Revision 1.9 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 1.8 1999/12/22 15:55:00 mdw
* Adjust Karatsuba parameters.
*
#include "mp.h"
#include "mpmont.h"
+#include "mpmont-exp.h"
/*----- Tweakables --------------------------------------------------------*/
/* #define MPMONT_DISABLE */
-/*----- Main code ---------------------------------------------------------*/
+/*----- Reduction and multiplication --------------------------------------*/
/* --- @mpmont_create@ --- *
*
void mpmont_create(mpmont *mm, mp *m)
{
size_t n = MP_LEN(m);
- mp *r2 = mp_create(2 * n + 1);
+ mp *r2 = mp_new(2 * n + 1, 0);
mp r;
/* --- Validate the arguments --- */
/* --- Check for serious Karatsuba reduction --- */
- if (n > KARATSUBA_CUTOFF * 3) {
+ if (n > MPK_THRESH * 3) {
mp al;
mpw *vl;
mp *u;
/* --- Initial conditioning of the arguments --- */
- if (d == a)
- MP_MODIFY(d, 2 * n + 1);
- else {
- MP_MODIFY(d, 2 * n + 1);
- MPX_COPY(d->v, d->vl, a->v, a->vl);
- }
-
+ a = MP_COPY(a);
+ if (d)
+ MP_DROP(d);
+ d = a;
+ MP_DEST(d, 2 * n + 1, a->f);
+
dv = d->v; dvl = d->vl;
mv = mm->m->v; mvl = mm->m->vl;
/* --- Wrap everything up --- */
- d->f = a->f & MP_BURN;
memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
d->vl -= n;
- if (MP_CMP(d, >=, mm->m))
- d = mp_sub(d, d, mm->m);
+ if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
+ mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
+ if (d->f & MP_NEG) {
+ mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
+ d->f &= ~MP_NEG;
+ }
MP_SHRINK(d);
return (d);
}
mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
{
- if (mm->n > KARATSUBA_CUTOFF * 3) {
+ if (mm->n > MPK_THRESH * 3) {
d = mp_mul(d, a, b);
d = mpmont_reduce(mm, d, d);
} else {
a = MP_COPY(a);
b = MP_COPY(b);
- MP_MODIFY(d, 2 * n + 1);
+ MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
dv = d->v; dvl = d->vl;
MPX_ZERO(dv, dvl);
av = a->v; avl = a->vl;
memmove(d->v, dv, MPWS(dvl - dv));
d->vl -= dv - d->v;
+ if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
+ mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
+ if ((a->f ^ b->f) & MP_NEG)
+ mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
MP_SHRINK(d);
d->f = (a->f | b->f) & MP_BURN;
- if (MP_CMP(d, >=, mm->m))
- d = mp_sub(d, d, mm->m);
MP_DROP(a);
MP_DROP(b);
}
#endif
+/*----- Exponentiation ----------------------------------------------------*/
+
/* --- @mpmont_expr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *a@ = base
* @mp *e@ = exponent
*
- * Returns: Result, %$a^e R \bmod m$%.
+ * Returns: Result, %$(a R^{-1})^e R \bmod m$%.
*/
mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
{
- mpscan sc;
- mp *ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
mp *x = MP_COPY(mm->r);
- mp *spare = MP_NEW;
-
- 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, ar);
- dd = mpmont_reduce(mm, dd, dd);
- spare = ar; ar = dd;
- sq--;
- }
- dd = mpmont_mul(mm, spare, x, ar);
- spare = x; x = dd;
- }
- sq++;
- if (!MP_STEP(&sc))
- break;
- }
- }
- MP_DROP(ar);
- 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) == 0)
+ ;
+ 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);
}
mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e)
{
- d = mpmont_expr(mm, d, a, e);
+ d = mpmont_mul(mm, d, a, mm->r2);
+ d = mpmont_expr(mm, d, d, e);
d = mpmont_reduce(mm, d, d);
return (d);
}
ok = 0;
}
- if (MP_CMP(mm.r, !=, r)) {
+ if (!MP_EQ(mm.r, r)) {
fputs("\n*** bad r", stderr);
fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
ok = 0;
}
- if (MP_CMP(mm.r2, !=, r2)) {
+ if (!MP_EQ(mm.r2, r2)) {
fputs("\n*** bad r2", stderr);
fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
mp *qr = mp_mul(MP_NEW, a, b);
mp_div(0, &qr, qr, m);
- if (MP_CMP(qr, !=, r)) {
+ if (!MP_EQ(qr, r)) {
fputs("\n*** classical modmul failed", stderr);
fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
mr = mpmont_reduce(&mm, mr, mr);
- if (MP_CMP(mr, !=, r)) {
+ if (!MP_EQ(mr, r)) {
fputs("\n*** montgomery modmul failed", stderr);
fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
mr = mpmont_exp(&mm, MP_NEW, a, b);
- if (MP_CMP(mr, !=, r)) {
+ if (!MP_EQ(mr, r)) {
fputs("\n*** montgomery 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