/* -*-c-*-
*
- * $Id: mpmont.c,v 1.2 1999/11/19 13:17:26 mdw Exp $
+ * $Id: mpmont.c,v 1.6 1999/12/10 23:18:39 mdw Exp $
*
* Montgomery reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpmont.c,v $
+ * Revision 1.6 1999/12/10 23:18:39 mdw
+ * Change interface for suggested destinations.
+ *
+ * Revision 1.5 1999/11/22 13:58:40 mdw
+ * Add an option to disable Montgomery reduction, so that performance
+ * comparisons can be done.
+ *
+ * Revision 1.4 1999/11/21 12:27:06 mdw
+ * Remove a division from the Montgomery setup by calculating
+ * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
+ * %$R^2$%.
+ *
+ * Revision 1.3 1999/11/21 11:35:10 mdw
+ * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
+ * @mpmont_mul@ for squaring in exponentiation.
+ *
* Revision 1.2 1999/11/19 13:17:26 mdw
* Add extra interface to exponentiation which returns a Montgomerized
* result.
#include "mp.h"
#include "mpmont.h"
+/*----- Tweakables --------------------------------------------------------*/
+
+/* --- @MPMONT_DISABLE@ --- *
+ *
+ * Replace all the clever Montgomery reduction with good old-fashioned long
+ * division.
+ */
+
+/* #define MPMONT_DISABLE */
+
/*----- Main code ---------------------------------------------------------*/
/* --- @mpmont_create@ --- *
* Returns: ---
*
* Use: Initializes a Montgomery reduction context ready for use.
+ * The argument @m@ must be a positive odd integer.
*/
+#ifdef MPMONT_DISABLE
+
void mpmont_create(mpmont *mm, mp *m)
{
+ mp_shrink(m);
+ mm->m = MP_COPY(m);
+ mm->r = MP_ONE;
+ mm->r2 = MP_ONE;
+}
+
+#else
+
+void mpmont_create(mpmont *mm, mp *m)
+{
+ /* --- Validate the arguments --- */
+
+ assert(((void)"Montgomery modulus must be positive",
+ (m->f & MP_NEG) == 0));
+ assert(((void)"Montgomery modulus must be odd", m->v[0] & 1));
+
/* --- Take a copy of the modulus --- */
mp_shrink(m);
{
mpw av[2] = { 0, 1 };
mp a, b;
- mp *i;
+ mp *i = MP_NEW;
mpw mi;
mp_build(&a, av, av + 2);
{
size_t l = MP_LEN(m);
- mp *r = mp_create(l + 1);
+ mp *r = mp_create(2 * l + 1);
mm->shift = l * MPW_BITS;
MPX_ZERO(r->v, r->vl - 1);
r->vl[-1] = 1;
- mm->r = mm->r2 = MP_NEW;
- mp_div(0, &mm->r, r, m);
- r = mp_sqr(r, mm->r);
+ mm->r2 = MP_NEW;
mp_div(0, &mm->r2, r, m);
+ mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
MP_DROP(r);
}
}
+#endif
+
/* --- @mpmont_destroy@ --- *
*
* Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
- * @const mp *a@ = source, assumed positive
+ * @mp *a@ = source, assumed positive
*
* Returns: Result, %$a R^{-1} \bmod m$%.
*/
-mp *mpmont_reduce(mpmont *mm, mp *d, const mp *a)
+#ifdef MPMONT_DISABLE
+
+mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
+{
+ mp_div(0, &d, a, mm->m);
+ return (d);
+}
+
+#else
+
+mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
{
mpw *dv, *dvl;
- const mpw *mv, *mvl;
+ mpw *mv, *mvl;
size_t n;
/* --- Initial conditioning of the arguments --- */
n = MP_LEN(mm->m);
if (d == a)
- MP_MODIFY(d, 2 * n);
+ MP_MODIFY(d, 2 * n + 1);
else {
- MP_MODIFY(d, 2 * n);
+ MP_MODIFY(d, 2 * n + 1);
memcpy(d->v, a->v, MPWS(MP_LEN(a)));
memset(d->v + MP_LEN(a), 0, MPWS(MP_LEN(d) - MP_LEN(a)));
}
return (d);
}
+#endif
+
/* --- @mpmont_mul@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
- * @const mp *a, *b@ = sources, assumed positive
+ * @mp *a, *b@ = sources, assumed positive
*
* Returns: Result, %$a b R^{-1} \bmod m$%.
*/
-mp *mpmont_mul(mpmont *mm, mp *d, const mp *a, const mp *b)
+#ifdef MPMONT_DISABLE
+
+mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
{
- mpw *dv, *dvl;
- const mpw *av, *avl;
- const mpw *bv, *bvl;
- const mpw *mv, *mvl;
- mpw y;
- size_t n, i;
+ d = mp_mul(d, a, b);
+ mp_div(0, &d, d, mm->m);
+ return (d);
+}
- /* --- Initial conditioning of the arguments --- */
+#else
- if (MP_LEN(a) > MP_LEN(b)) {
- const mp *t = a; a = b; b = t;
- }
- n = MP_LEN(mm->m);
-
- MP_MODIFY(d, 2 * n + 1);
- dv = d->v; dvl = d->vl;
- MPX_ZERO(dv, dvl);
- av = a->v; avl = a->vl;
- bv = b->v; bvl = b->vl;
- mv = mm->m->v; mvl = mm->m->vl;
- y = *bv;
+mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
+{
+ if (MP_LEN(a) > KARATSUBA_CUTOFF && MP_LEN(b) > KARATSUBA_CUTOFF) {
+ d = mp_mul(d, a, b);
+ d = mpmont_reduce(mm, d, d);
+ } else {
+ mpw *dv, *dvl;
+ mpw *av, *avl;
+ mpw *bv, *bvl;
+ mpw *mv, *mvl;
+ mpw y;
+ size_t n, i;
+
+ /* --- Initial conditioning of the arguments --- */
+
+ if (MP_LEN(a) > MP_LEN(b)) {
+ mp *t = a; a = b; b = t;
+ }
+ n = MP_LEN(mm->m);
+
+ a = MP_COPY(a);
+ b = MP_COPY(b);
+ MP_MODIFY(d, 2 * n + 1);
+ dv = d->v; dvl = d->vl;
+ MPX_ZERO(dv, dvl);
+ av = a->v; avl = a->vl;
+ bv = b->v; bvl = b->vl;
+ mv = mm->m->v; mvl = mm->m->vl;
+ y = *bv;
+
+ /* --- Montgomery multiplication phase --- */
+
+ i = 0;
+ while (i < n && av < avl) {
+ mpw x = *av++;
+ mpw u = MPW((*dv + x * y) * mm->mi);
+ MPX_UMLAN(dv, dvl, bv, bvl, x);
+ MPX_UMLAN(dv, dvl, mv, mvl, u);
+ dv++;
+ i++;
+ }
- /* --- Montgomery multiplication phase --- */
+ /* --- Simpler Montgomery reduction phase --- */
- i = 0;
- while (i < n && av < avl) {
- mpw x = *av++;
- mpw u = MPW((*dv + x * y) * mm->mi);
- MPX_UMLAN(dv, dvl, bv, bvl, x);
- MPX_UMLAN(dv, dvl, mv, mvl, u);
- dv++;
- i++;
- }
+ while (i < n) {
+ mpw u = MPW(*dv * mm->mi);
+ MPX_UMLAN(dv, dvl, mv, mvl, u);
+ dv++;
+ i++;
+ }
- /* --- Simpler Montgomery reduction phase --- */
+ /* --- Done --- */
- while (i < n) {
- mpw u = MPW(*dv * mm->mi);
- MPX_UMLAN(dv, dvl, mv, mvl, u);
- dv++;
- i++;
+ memmove(d->v, dv, MPWS(dvl - dv));
+ d->vl -= dv - d->v;
+ 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);
}
- /* --- Done --- */
-
- memmove(d->v, dv, MPWS(dvl - dv));
- d->vl -= dv - d->v;
- MP_SHRINK(d);
- d->f = (a->f | b->f) & MP_BURN;
- if (MP_CMP(d, >=, mm->m))
- d = mp_sub(d, d, mm->m);
return (d);
}
+#endif
+
/* --- @mpmont_expr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @const mp *a@ = base
- * @const mp *e@ = exponent
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
*
* Returns: Result, %$a^e R \bmod m$%.
*/
-mp *mpmont_expr(mpmont *mm, const mp *a, const mp *e)
+mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
{
mpscan sc;
mp *ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
- mp *d = MP_COPY(mm->r);
+ mp *x = MP_COPY(mm->r);
mp *spare = MP_NEW;
mp_scan(&sc, e);
mp *dd;
if (MP_BIT(&sc)) {
while (sq) {
- dd = mpmont_mul(mm, spare, ar, ar);
+ dd = mp_sqr(spare, ar);
+ dd = mpmont_reduce(mm, dd, dd);
spare = ar; ar = dd;
sq--;
}
- dd = mpmont_mul(mm, spare, d, ar);
- spare = d; d = dd;
+ dd = mpmont_mul(mm, spare, x, ar);
+ spare = x; x = dd;
}
sq++;
if (!MP_STEP(&sc))
MP_DROP(ar);
if (spare != MP_NEW)
MP_DROP(spare);
- return (d);
+ if (d != MP_NEW)
+ MP_DROP(d);
+ return (x);
}
/* --- @mpmont_exp@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @const mp *a@ = base
- * @const mp *e@ = exponent
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
*
* Returns: Result, %$a^e \bmod m$%.
*/
-mp *mpmont_exp(mpmont *mm, const mp *a, const mp *e)
+mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e)
{
- mp *d = mpmont_expr(mm, a, e);
+ d = mpmont_expr(mm, d, a, e);
d = mpmont_reduce(mm, d, d);
return (d);
}
MP_DROP(r);
MP_DROP(r2);
mpmont_destroy(&mm);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
return (ok);
}
mp *a = *(mp **)v[1].buf;
mp *b = *(mp **)v[2].buf;
mp *r = *(mp **)v[3].buf;
- mp *mr, *qr;
int ok = 1;
mpmont mm;
mpmont_create(&mm, m);
{
+ mp *qr = mp_mul(MP_NEW, a, b);
+ mp_div(0, &qr, qr, m);
+
+ if (MP_CMP(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);
+ fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
+ fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
+ fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
+ fputc('\n', stderr);
+ ok = 0;
+ }
+
+ mp_drop(qr);
+ }
+
+ {
mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
- mr = mpmont_mul(&mm, MP_NEW, ar, br);
+ mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
mr = mpmont_reduce(&mm, mr, mr);
+ if (MP_CMP(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);
+ fputs("\n b = ", 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(ar); MP_DROP(br);
+ mp_drop(mr);
}
- qr = mp_mul(MP_NEW, a, b);
- mp_div(0, &qr, qr, m);
-
- if (MP_CMP(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);
- fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
- fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- if (MP_CMP(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);
- fputs("\n b = ", 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);
- MP_DROP(qr);
mpmont_destroy(&mm);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
return ok;
}
mpmont mm;
mpmont_create(&mm, m);
- mr = mpmont_exp(&mm, a, b);
+ mr = mpmont_exp(&mm, MP_NEW, a, b);
if (MP_CMP(mr, !=, r)) {
fputs("\n*** montgomery modexp failed", stderr);
MP_DROP(r);
MP_DROP(mr);
mpmont_destroy(&mm);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
return ok;
}
static test_chunk tests[] = {
- { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp } },
- { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp } },
- { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp } },
+ { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
+ { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
+ { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
{ 0, 0, { 0 } },
};
projects / u / mdw / catacomb / blobdiff