/* -*-c-*-
*
- * $Id: mpmont.c,v 1.15 2001/06/16 13:00:20 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 1.15 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.
- *
- * 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"
#include "mpmont.h"
-#include "mpmont-exp.h"
/*----- Tweakables --------------------------------------------------------*/
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 %$R^2 \bmod m$% --- */
#endif
-/*----- Exponentiation ----------------------------------------------------*/
-
-/* --- @mpmont_expr@ --- *
- *
- * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @mp *d@ = fake destination
- * @mp *a@ = base
- * @mp *e@ = exponent
- *
- * Returns: Result, %$(a R^{-1})^e R \bmod m$%.
- */
-
-mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
-{
- mp *x = MP_COPY(mm->r);
- 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);
-}
-
-/* --- @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_mul(mm, d, a, mm->r2);
- d = mpmont_expr(mm, d, d, 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