/* -*-c-*-
*
- * $Id: mpmont.c,v 1.1 1999/11/17 18:02:16 mdw Exp $
+ * $Id: mpmont.c,v 1.5 1999/11/22 13:58:40 mdw Exp $
*
* Montgomery reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpmont.c,v $
+ * 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.
+ *
* Revision 1.1 1999/11/17 18:02:16 mdw
* New multiprecision integer arithmetic suite.
*
#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@ --- *
* Use: Initializes a Montgomery reduction context ready for use.
*/
+#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)
{
/* --- Take a copy of the modulus --- */
{
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
* Returns: Result, %$a R^{-1} \bmod m$%.
*/
+#ifdef MPMONT_DISABLE
+
+mp *mpmont_reduce(mpmont *mm, mp *d, const mp *a)
+{
+ mp_div(0, &d, a, mm->m);
+ return (d);
+}
+
+#else
+
mp *mpmont_reduce(mpmont *mm, mp *d, const mp *a)
{
mpw *dv, *dvl;
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)));
}
d->vl -= dv - d->v;
MP_SHRINK(d);
d->f = a->f & MP_BURN;
+ if (MP_CMP(d, >=, mm->m))
+ d = mp_sub(d, d, mm->m);
return (d);
}
+#endif
+
/* --- @mpmont_mul@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* Returns: Result, %$a b R^{-1} \bmod m$%.
*/
+#ifdef MPMONT_DISABLE
+
+mp *mpmont_mul(mpmont *mm, mp *d, const mp *a, const mp *b)
+{
+ d = mp_mul(d, a, b);
+ mp_div(0, &d, d, mm->m);
+ return (d);
+}
+
+#else
+
mp *mpmont_mul(mpmont *mm, mp *d, const mp *a, const mp *b)
{
mpw *dv, *dvl;
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);
}
-/* --- @mpmont_exp@ --- *
+#endif
+
+/* --- @mpmont_expr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @const mp *a@ = base
* @const mp *e@ = exponent
*
- * Returns: Result, %$a^e \bmod m$%.
+ * Returns: Result, %$a^e R \bmod m$%.
*/
-mp *mpmont_exp(mpmont *mm, const mp *a, const mp *e)
+mp *mpmont_expr(mpmont *mm, const mp *a, const mp *e)
{
mpscan sc;
mp *ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
mp *d = 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)) {
- dd = mpmont_mul(mm, MP_NEW, d, ar);
- MP_DROP(d);
- d = dd;
+ while (sq) {
+ 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;
}
+ sq++;
if (!MP_STEP(&sc))
break;
- dd = mpmont_mul(mm, MP_NEW, ar, ar);
- MP_DROP(ar);
- ar = dd;
}
}
MP_DROP(ar);
- return (mpmont_reduce(mm, d, d));
+ if (spare != MP_NEW)
+ MP_DROP(spare);
+ return (d);
+}
+
+/* --- @mpmont_exp@ --- *
+ *
+ * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
+ * @const mp *a@ = base
+ * @const mp *e@ = exponent
+ *
+ * Returns: Result, %$a^e \bmod m$%.
+ */
+
+mp *mpmont_exp(mpmont *mm, const mp *a, const mp *e)
+{
+ mp *d = mpmont_expr(mm, a, e);
+ d = mpmont_reduce(mm, d, d);
+ return (d);
}
/*----- Test rig ----------------------------------------------------------*/
fputs("\n*** bad r", stderr);
fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
- fputs("\n found ", stderr); mp_writefile(r, stderr, 10);
+ fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10);
fputc('\n', stderr);
ok = 0;
}
fputs("\n*** bad r2", stderr);
fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
- fputs("\n found ", stderr); mp_writefile(r2, stderr, 10);
+ fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10);
fputc('\n', stderr);
ok = 0;
}
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);
return ok;
}
projects / u / mdw / catacomb / blobdiff