/* -*-c-*-
*
- * $Id: mpmont.c,v 1.12 2000/10/08 15:48:35 mdw Exp $
+ * $Id: mpmont.c,v 1.18 2004/04/03 03:32:05 mdw Exp $
*
* Montgomery reduction
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpmont.c,v $
+ * Revision 1.18 2004/04/03 03:32:05 mdw
+ * General robustification.
+ *
+ * Revision 1.17 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 1.16 2002/01/13 13:40:31 mdw
+ * Avoid trashing arguments before we've used them.
+ *
+ * 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.
*
/* #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 %$R^2$% --- */
#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
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_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);
- 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