/* -*-c-*-
*
- * $Id: mpmont.c,v 1.10 2000/07/29 17:05:43 mdw Exp $
+ * $Id: mpmont.c,v 1.19 2004/04/08 01:36:15 mdw Exp $
*
* Montgomery reduction
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: mpmont.c,v $
- * 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.
- *
- * Revision 1.7 1999/12/11 01:51:14 mdw
- * Use a Karatsuba-based reduction for large moduli.
- *
- * 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.
- *
- * Revision 1.1 1999/11/17 18:02:16 mdw
- * New multiprecision integer arithmetic suite.
- *
- */
-
/*----- Header files ------------------------------------------------------*/
#include "mp.h"
/* #define MPMONT_DISABLE */
-/*----- Main code ---------------------------------------------------------*/
+/*----- Reduction and multiplication --------------------------------------*/
/* --- @mpmont_create@ --- *
*
mp *r2 = mp_new(2 * n + 1, 0);
mp r;
- /* --- 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);
+ assert(MP_ISPOS(m) && MP_ISODD(m));
mm->m = MP_COPY(m);
/* --- Determine %$R^2$% --- */
/* --- Find the magic value @mi@ --- */
mp_build(&r, r2->v + n, r2->vl);
- mm->mi = MP_NEW;
- mp_gcd(0, 0, &mm->mi, &r, m);
+ mm->mi = mp_modinv(MP_NEW, m, &r);
mm->mi = mp_sub(mm->mi, &r, mm->mi);
/* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
/* --- Check for serious Karatsuba reduction --- */
- if (n > KARATSUBA_CUTOFF * 3) {
+ if (n > MPK_THRESH * 3) {
mp al;
mpw *vl;
mp *u;
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 {
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
-/* --- @mpmont_expr@ --- *
- *
- * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @mp *d@ = fake destination
- * @mp *a@ = base
- * @mp *e@ = exponent
- *
- * Returns: Result, %$a^e R \bmod m$%.
- */
-
-#define WINSZ 5
-#define TABSZ (1 << (WINSZ - 1))
-
-#define THRESH (((MPW_BITS / WINSZ) << 2) + 1)
-
-static mp *exp_simple(mpmont *mm, mp *d, mp *a, mp *e)
-{
- mpscan sc;
- mp *ar;
- mp *x = MP_COPY(mm->r);
- mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
- unsigned 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 --- */
-
- ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
- for (;;) {
- sq++;
- while (sq) {
- mp *y;
- y = mp_sqr(spare, x);
- y = mpmont_reduce(mm, y, y);
- spare = x; x = y;
- sq--;
- }
- { mp *y = mpmont_mul(mm, spare, x, ar); spare = x; x = y; }
- sq = 0;
- 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 = mpmont_reduce(mm, y, y);
- spare = x; x = y;
- sq--;
- }
-
- /* --- Done --- */
-
- MP_DROP(ar);
-exit:
- if (spare != MP_NEW)
- MP_DROP(spare);
- if (d != MP_NEW)
- MP_DROP(d);
- return (x);
-}
-
-mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
-{
- mp **tab;
- mp *ar, *a2;
- mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
- mp *x = MP_COPY(mm->r);
- 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(mm, d, a, e));
- }
-
- /* --- Do the precomputation --- */
-
- ar = mpmont_mul(mm, MP_NEW, a, mm->r2);
- a2 = mp_sqr(MP_NEW, ar);
- a2 = mpmont_reduce(mm, a2, a2);
- tab = xmalloc(TABSZ * sizeof(mp *));
- tab[0] = ar;
- for (i = 1; i < TABSZ; i++)
- tab[i] = mpmont_mul(mm, MP_NEW, tab[i - 1], a2);
- 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 = mpmont_reduce(mm, y, y);
- spare = x; x = y;
- sq--;
- }
-
- /* --- Do the multiply --- */
-
- { mp *y = mpmont_mul(mm, spare, x, tab[i]); spare = x; x = 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 = mpmont_reduce(mm, y, y);
- spare = x; x = y;
- sq--;
- }
-
- /* --- Done --- */
-
- for (i = 0; i < TABSZ; i++)
- mp_drop(tab[i]);
- xfree(tab);
-exit:
- if (d != MP_NEW)
- mp_drop(d);
- if (spare)
- mp_drop(spare);
- return (x);
-}
-
-/* --- @mpmont_exp@ --- *
- *
- * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @mp *d@ = fake destination
- * @mp *a@ = base
- * @mp *e@ = exponent
- *
- * Returns: Result, %$a^e \bmod m$%.
- */
-
-mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e)
-{
- d = mpmont_expr(mm, d, a, e);
- d = mpmont_reduce(mm, d, d);
- return (d);
-}
-
/*----- Test rig ----------------------------------------------------------*/
#ifdef TEST_RIG
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);
return ok;
}
-static int texp(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;
-
- mpmont mm;
- mpmont_create(&mm, m);
-
- mr = mpmont_exp(&mm, MP_NEW, a, b);
-
- if (MP_CMP(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);
- 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);
- 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, 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