[u/mdw/catacomb] / mpmont.c

/* -*-c-*-
 *
 * $Id: mpmont.c,v 1.18 2004/04/03 03:32:05 mdw Exp $
 *
 * Montgomery reduction
 *
 * (c) 1999 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------* 
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 * 
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 * 
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

/*----- 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.
 *
 * 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"

/*----- Tweakables --------------------------------------------------------*/

/* --- @MPMONT_DISABLE@ --- *
 *
 * Replace all the clever Montgomery reduction with good old-fashioned long
 * division.
 */

/* #define MPMONT_DISABLE */

/*----- Reduction and multiplication --------------------------------------*/

/* --- @mpmont_create@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
 *		@mp *m@ = modulus to use
 *
 * 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;
  mm->mi = MP_ONE;
}

#else

void mpmont_create(mpmont *mm, mp *m)
{
  size_t n = MP_LEN(m);
  mp *r2 = mp_new(2 * n + 1, 0);
  mp r;

  /* --- Take a copy of the modulus --- */

  assert(MP_ISPOS(m) && MP_ISODD(m));
  mm->m = MP_COPY(m);

  /* --- Determine %$R^2$% --- */

  mm->n = n;
  MPX_ZERO(r2->v, r2->vl - 1);
  r2->vl[-1] = 1;

  /* --- 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_sub(mm->mi, &r, mm->mi);

  /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */

  mm->r2 = MP_NEW;
  mp_div(0, &mm->r2, r2, m);
  mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
  MP_DROP(r2);
}

#endif

/* --- @mpmont_destroy@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to a Montgomery reduction context
 *
 * Returns:	---
 *
 * Use:		Disposes of a context when it's no longer of any use to
 *		anyone.
 */

void mpmont_destroy(mpmont *mm)
{
  MP_DROP(mm->m);
  MP_DROP(mm->r);
  MP_DROP(mm->r2);
  MP_DROP(mm->mi);
}

/* --- @mpmont_reduce@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
 *		@mp *d@ = destination
 *		@mp *a@ = source, assumed positive
 *
 * Returns:	Result, %$a R^{-1} \bmod m$%.
 */

#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)
{
  size_t n = mm->n;

  /* --- Check for serious Karatsuba reduction --- */

  if (n > MPK_THRESH * 3) {
    mp al;
    mpw *vl;
    mp *u;

    if (MP_LEN(a) >= n)
      vl = a->v + n;
    else
      vl = a->vl;
    mp_build(&al, a->v, vl);
    u = mp_mul(MP_NEW, &al, mm->mi);
    if (MP_LEN(u) > n)
      u->vl = u->v + n;
    u = mp_mul(u, u, mm->m);
    d = mp_add(d, a, u);
    mp_drop(u);
  }

  /* --- Otherwise do it the hard way --- */

  else {
    mpw *dv, *dvl;
    mpw *mv, *mvl;
    mpw mi;
    size_t k = n;

    /* --- Initial conditioning of the arguments --- */

    a = MP_COPY(a);
    if (d)
      MP_DROP(d);
    d = a;
    MP_DEST(d, 2 * n + 1, a->f);

    dv = d->v; dvl = d->vl;
    mv = mm->m->v; mvl = mm->m->vl;

    /* --- Let's go to work --- */

    mi = mm->mi->v[0];
    while (k--) {
      mpw u = MPW(*dv * mi);
      MPX_UMLAN(dv, dvl, mv, mvl, u);
      dv++;
    }
  }

  /* --- Wrap everything up --- */

  memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
  d->vl -= n;
  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);
}

#endif

/* --- @mpmont_mul@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
 *		@mp *d@ = destination
 *		@mp *a, *b@ = sources, assumed positive
 *
 * Returns:	Result, %$a b R^{-1} \bmod m$%.
 */

#ifdef MPMONT_DISABLE

mp *mpmont_mul(mpmont *mm, mp *d, mp *a, 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, mp *a, mp *b)
{
  if (mm->n > MPK_THRESH * 3) {
    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;
    mpw mi;

    /* --- 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_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
    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;
    mi = mm->mi->v[0];
    while (i < n && av < avl) {
      mpw x = *av++;
      mpw u = MPW((*dv + x * y) * mi);
      MPX_UMLAN(dv, dvl, bv, bvl, x);
      MPX_UMLAN(dv, dvl, mv, mvl, u);
      dv++;
      i++;
    }

    /* --- Simpler Montgomery reduction phase --- */

    while (i < n) {
      mpw u = MPW(*dv * mi);
      MPX_UMLAN(dv, dvl, mv, mvl, u);
      dv++;
      i++;
    }

    /* --- Done --- */

    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;
    MP_DROP(a);
    MP_DROP(b);
  }

  return (d);
}

#endif

/*----- Test rig ----------------------------------------------------------*/

#ifdef TEST_RIG

static int tcreate(dstr *v)
{
  mp *m = *(mp **)v[0].buf;
  mp *mi = *(mp **)v[1].buf;
  mp *r = *(mp **)v[2].buf;
  mp *r2 = *(mp **)v[3].buf;

  mpmont mm;
  int ok = 1;

  mpmont_create(&mm, m);

  if (mm.mi->v[0] != mi->v[0]) {
    fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
	    (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
    fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
    fputc('\n', stderr);
    ok = 0;
  }

  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);
    fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
    fputc('\n', stderr);
    ok = 0;
  }

  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);
    fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
    fputc('\n', stderr);
    ok = 0;
  }

  MP_DROP(m);
  MP_DROP(mi);
  MP_DROP(r);
  MP_DROP(r2);
  mpmont_destroy(&mm);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return (ok);
}

static int tmul(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;
  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_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);
      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);
    mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
    mr = mpmont_reduce(&mm, mr, mr);
    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);
      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);
  }


  MP_DROP(m);
  MP_DROP(a);
  MP_DROP(b);
  MP_DROP(r);
  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 } },
  { 0, 0, { 0 } },
};

int main(int argc, char *argv[])
{
  sub_init();
  test_run(argc, argv, tests, SRCDIR "/tests/mpmont");
  return (0);
}

#endif

/*----- That's all, folks -------------------------------------------------*/
Commit	Line	Data
d3409d5e	1	/* --c--
d3409d5e	2	*
02d7884d	3	* $Id: mpmont.c,v 1.18 2004/04/03 03:32:05 mdw Exp $
d3409d5e	4	*
	5	* Montgomery reduction
	6	*
	7	* (c) 1999 Straylight/Edgeware
	8	*/
	9
	10	/----- Licensing notice --------------------------------------------------
	11	*
	12	* This file is part of Catacomb.
	13	*
	14	* Catacomb is free software; you can redistribute it and/or modify
	15	* it under the terms of the GNU Library General Public License as
	16	* published by the Free Software Foundation; either version 2 of the
	17	* License, or (at your option) any later version.
	18	*
	19	* Catacomb is distributed in the hope that it will be useful,
	20	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	21	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	22	* GNU Library General Public License for more details.
	23	*
	24	* You should have received a copy of the GNU Library General Public
	25	* License along with Catacomb; if not, write to the Free
	26	* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
	27	* MA 02111-1307, USA.
	28	*/
	29
	30	/----- Revision history --------------------------------------------------
	31	*
	32	* $Log: mpmont.c,v $
02d7884d	33	* Revision 1.18 2004/04/03 03:32:05 mdw
	34	* General robustification.
	35	*
34e4f738	36	* Revision 1.17 2004/04/01 12:50:09 mdw
	37	* Add cyclic group abstraction, with test code. Separate off exponentation
	38	* functions for better static linking. Fix a buttload of bugs on the way.
	39	* Generally ensure that negative exponents do inversion correctly. Add
	40	* table of standard prime-field subgroups. (Binary field subgroups are
	41	* currently unimplemented but easy to add if anyone ever finds a good one.)
	42	*
97490e68	43	* Revision 1.16 2002/01/13 13:40:31 mdw
	44	* Avoid trashing arguments before we've used them.
	45	*
4640a0dd	46	* Revision 1.15 2001/06/16 13:00:20 mdw
	47	* Use the generic exponentiation functions.
	48	*
b096ec7f	49	* Revision 1.14 2001/02/22 09:04:26 mdw
	50	* Cosmetic fix.
	51	*
f1140c41	52	* Revision 1.13 2001/02/03 12:00:29 mdw
	53	* Now @mp_drop@ checks its argument is non-NULL before attempting to free
	54	* it. Note that the macro version @MP_DROP@ doesn't do this.
	55	*
52cdaca9	56	* Revision 1.12 2000/10/08 15:48:35 mdw
	57	* Rename Karatsuba constants now that we have @gfx_kmul@ too.
	58	*
032099d1	59	* Revision 1.11 2000/10/08 12:04:27 mdw
	60	* (mpmont_reduce, mpmont_mul): Cope with negative numbers.
	61	*
c9d4c30b	62	* Revision 1.10 2000/07/29 17:05:43 mdw
	63	* (mpmont_expr): Use sliding window exponentiation, with a drop-through
	64	* for small exponents to use a simple left-to-right bitwise routine. This
	65	* can reduce modexp times by up to a quarter.
	66	*
d34decd2	67	* Revision 1.9 2000/06/17 11:45:09 mdw
	68	* Major memory management overhaul. Added arena support. Use the secure
	69	* arena for secret integers. Replace and improve the MP management macros
	70	* (e.g., replace MP_MODIFY by MP_DEST).
	71	*
01f6ed1a	72	* Revision 1.8 1999/12/22 15:55:00 mdw
	73	* Adjust Karatsuba parameters.
	74	*
f5f35081	75	* Revision 1.7 1999/12/11 01:51:14 mdw
	76	* Use a Karatsuba-based reduction for large moduli.
	77	*
ef5f4810	78	* Revision 1.6 1999/12/10 23:18:39 mdw
	79	* Change interface for suggested destinations.
	80	*
52e4b041	81	* Revision 1.5 1999/11/22 13:58:40 mdw
	82	* Add an option to disable Montgomery reduction, so that performance
	83	* comparisons can be done.
	84	*
93feaa6e	85	* Revision 1.4 1999/11/21 12:27:06 mdw
	86	* Remove a division from the Montgomery setup by calculating
	87	* %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
	88	* %$R^2$%.
	89	*
79a34029	90	* Revision 1.3 1999/11/21 11:35:10 mdw
	91	* Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
	92	* @mpmont_mul@ for squaring in exponentiation.
	93	*
17ad212e	94	* Revision 1.2 1999/11/19 13:17:26 mdw
	95	* Add extra interface to exponentiation which returns a Montgomerized
	96	* result.
	97	*
d3409d5e	98	* Revision 1.1 1999/11/17 18:02:16 mdw
	99	* New multiprecision integer arithmetic suite.
	100	*
	101	*/
	102
	103	/----- Header files ------------------------------------------------------/
	104
	105	#include "mp.h"
	106	#include "mpmont.h"
	107
52e4b041	108	/----- Tweakables --------------------------------------------------------/
	109
	110	/* --- @MPMONT_DISABLE@ --- *
	111	*
	112	* Replace all the clever Montgomery reduction with good old-fashioned long
	113	* division.
	114	*/
	115
	116	/* #define MPMONT_DISABLE */
	117
4640a0dd	118	/----- Reduction and multiplication --------------------------------------/
d3409d5e	119
	120	/* --- @mpmont_create@ --- *
	121	*
	122	* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
	123	* @mp *m@ = modulus to use
	124	*
	125	* Returns: ---
	126	*
	127	* Use: Initializes a Montgomery reduction context ready for use.
ef5f4810	128	* The argument @m@ must be a positive odd integer.
d3409d5e	129	*/
d3409d5e	130
52e4b041	131	#ifdef MPMONT_DISABLE
	132
	133	void mpmont_create(mpmont mm, mp m)
	134	{
	135	mp_shrink(m);
	136	mm->m = MP_COPY(m);
	137	mm->r = MP_ONE;
	138	mm->r2 = MP_ONE;
f5f35081	139	mm->mi = MP_ONE;
52e4b041	140	}
	141
	142	#else
	143
d3409d5e	144	void mpmont_create(mpmont mm, mp m)
d3409d5e	145	{
f5f35081	146	size_t n = MP_LEN(m);
d34decd2	147	mp r2 = mp_new(2 n + 1, 0);
f5f35081	148	mp r;
f5f35081	149
d3409d5e	150	/* --- Take a copy of the modulus --- */
d3409d5e	151
02d7884d	152	assert(MP_ISPOS(m) && MP_ISODD(m));
d3409d5e	153	mm->m = MP_COPY(m);
d3409d5e	154
f5f35081	155	/* --- Determine %$R^2$% --- */
d3409d5e	156
f5f35081	157	mm->n = n;
	158	MPX_ZERO(r2->v, r2->vl - 1);
	159	r2->vl[-1] = 1;
d3409d5e	160
f5f35081	161	/* --- Find the magic value @mi@ --- */
	162
	163	mp_build(&r, r2->v + n, r2->vl);
	164	mm->mi = MP_NEW;
	165	mp_gcd(0, 0, &mm->mi, &r, m);
	166	mm->mi = mp_sub(mm->mi, &r, mm->mi);
d3409d5e	167
	168	/* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
	169
f5f35081	170	mm->r2 = MP_NEW;
	171	mp_div(0, &mm->r2, r2, m);
	172	mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
	173	MP_DROP(r2);
d3409d5e	174	}
d3409d5e	175
52e4b041	176	#endif
52e4b041	177
d3409d5e	178	/* --- @mpmont_destroy@ --- *
	179	*
	180	* Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
	181	*
	182	* Returns: ---
	183	*
	184	* Use: Disposes of a context when it's no longer of any use to
	185	* anyone.
	186	*/
	187
	188	void mpmont_destroy(mpmont *mm)
	189	{
	190	MP_DROP(mm->m);
	191	MP_DROP(mm->r);
	192	MP_DROP(mm->r2);
f5f35081	193	MP_DROP(mm->mi);
d3409d5e	194	}
	195
	196	/* --- @mpmont_reduce@ --- *
	197	*
	198	* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
	199	* @mp *d@ = destination
ef5f4810	200	* @mp *a@ = source, assumed positive
d3409d5e	201	*
	202	* Returns: Result, %$a R^{-1} \bmod m$%.
	203	*/
	204
52e4b041	205	#ifdef MPMONT_DISABLE
52e4b041	206
ef5f4810	207	mp mpmont_reduce(mpmont mm, mp d, mp a)
52e4b041	208	{
	209	mp_div(0, &d, a, mm->m);
	210	return (d);
	211	}
	212
	213	#else
	214
ef5f4810	215	mp mpmont_reduce(mpmont mm, mp d, mp a)
d3409d5e	216	{
f5f35081	217	size_t n = mm->n;
	218
	219	/* --- Check for serious Karatsuba reduction --- */
	220
52cdaca9	221	if (n > MPK_THRESH * 3) {
f5f35081	222	mp al;
	223	mpw *vl;
	224	mp *u;
	225
	226	if (MP_LEN(a) >= n)
	227	vl = a->v + n;
	228	else
	229	vl = a->vl;
	230	mp_build(&al, a->v, vl);
	231	u = mp_mul(MP_NEW, &al, mm->mi);
	232	if (MP_LEN(u) > n)
	233	u->vl = u->v + n;
	234	u = mp_mul(u, u, mm->m);
	235	d = mp_add(d, a, u);
	236	mp_drop(u);
	237	}
d3409d5e	238
f5f35081	239	/* --- Otherwise do it the hard way --- */
d3409d5e	240
d3409d5e	241	else {
f5f35081	242	mpw dv, dvl;
	243	mpw mv, mvl;
	244	mpw mi;
	245	size_t k = n;
	246
	247	/* --- Initial conditioning of the arguments --- */
	248
d34decd2	249	a = MP_COPY(a);
	250	if (d)
	251	MP_DROP(d);
	252	d = a;
	253	MP_DEST(d, 2 * n + 1, a->f);
	254
f5f35081	255	dv = d->v; dvl = d->vl;
f5f35081	256	mv = mm->m->v; mvl = mm->m->vl;
d3409d5e	257
f5f35081	258	/* --- Let's go to work --- */
d3409d5e	259
f5f35081	260	mi = mm->mi->v[0];
	261	while (k--) {
	262	mpw u = MPW(dv mi);
	263	MPX_UMLAN(dv, dvl, mv, mvl, u);
	264	dv++;
	265	}
d3409d5e	266	}
d3409d5e	267
f5f35081	268	/* --- Wrap everything up --- */
d3409d5e	269
f5f35081	270	memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
f5f35081	271	d->vl -= n;
032099d1	272	if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
	273	mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
	274	if (d->f & MP_NEG) {
	275	mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
	276	d->f &= ~MP_NEG;
	277	}
f5f35081	278	MP_SHRINK(d);
d3409d5e	279	return (d);
	280	}
	281
52e4b041	282	#endif
52e4b041	283
d3409d5e	284	/* --- @mpmont_mul@ --- *
	285	*
	286	* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
	287	* @mp *d@ = destination
ef5f4810	288	* @mp a, b@ = sources, assumed positive
d3409d5e	289	*
	290	* Returns: Result, %$a b R^{-1} \bmod m$%.
	291	*/
	292
52e4b041	293	#ifdef MPMONT_DISABLE
52e4b041	294
ef5f4810	295	mp mpmont_mul(mpmont mm, mp d, mp a, mp *b)
52e4b041	296	{
	297	d = mp_mul(d, a, b);
	298	mp_div(0, &d, d, mm->m);
	299	return (d);
	300	}
	301
	302	#else
	303
ef5f4810	304	mp mpmont_mul(mpmont mm, mp d, mp a, mp *b)
d3409d5e	305	{
52cdaca9	306	if (mm->n > MPK_THRESH * 3) {
ef5f4810	307	d = mp_mul(d, a, b);
	308	d = mpmont_reduce(mm, d, d);
	309	} else {
	310	mpw dv, dvl;
	311	mpw av, avl;
	312	mpw bv, bvl;
	313	mpw mv, mvl;
	314	mpw y;
	315	size_t n, i;
f5f35081	316	mpw mi;
ef5f4810	317
	318	/* --- Initial conditioning of the arguments --- */
	319
	320	if (MP_LEN(a) > MP_LEN(b)) {
	321	mp *t = a; a = b; b = t;
	322	}
	323	n = MP_LEN(mm->m);
d3409d5e	324
ef5f4810	325	a = MP_COPY(a);
ef5f4810	326	b = MP_COPY(b);
d34decd2	327	MP_DEST(d, 2 * n + 1, a->f \| b->f \| MP_UNDEF);
ef5f4810	328	dv = d->v; dvl = d->vl;
	329	MPX_ZERO(dv, dvl);
	330	av = a->v; avl = a->vl;
	331	bv = b->v; bvl = b->vl;
	332	mv = mm->m->v; mvl = mm->m->vl;
	333	y = *bv;
	334
	335	/* --- Montgomery multiplication phase --- */
	336
	337	i = 0;
f5f35081	338	mi = mm->mi->v[0];
ef5f4810	339	while (i < n && av < avl) {
ef5f4810	340	mpw x = *av++;
f5f35081	341	mpw u = MPW((dv + x y) * mi);
ef5f4810	342	MPX_UMLAN(dv, dvl, bv, bvl, x);
	343	MPX_UMLAN(dv, dvl, mv, mvl, u);
	344	dv++;
	345	i++;
	346	}
d3409d5e	347
ef5f4810	348	/* --- Simpler Montgomery reduction phase --- */
d3409d5e	349
ef5f4810	350	while (i < n) {
f5f35081	351	mpw u = MPW(dv mi);
ef5f4810	352	MPX_UMLAN(dv, dvl, mv, mvl, u);
	353	dv++;
	354	i++;
	355	}
d3409d5e	356
ef5f4810	357	/* --- Done --- */
d3409d5e	358
ef5f4810	359	memmove(d->v, dv, MPWS(dvl - dv));
ef5f4810	360	d->vl -= dv - d->v;
032099d1	361	if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
	362	mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
	363	if ((a->f ^ b->f) & MP_NEG)
	364	mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
ef5f4810	365	MP_SHRINK(d);
ef5f4810	366	d->f = (a->f \| b->f) & MP_BURN;
ef5f4810	367	MP_DROP(a);
ef5f4810	368	MP_DROP(b);
d3409d5e	369	}
d3409d5e	370
d3409d5e	371	return (d);
	372	}
	373
52e4b041	374	#endif
52e4b041	375
d3409d5e	376	/----- Test rig ----------------------------------------------------------/
	377
	378	#ifdef TEST_RIG
	379
	380	static int tcreate(dstr *v)
	381	{
	382	mp m = (mp **)v[0].buf;
	383	mp mi = (mp **)v[1].buf;
	384	mp r = (mp **)v[2].buf;
	385	mp r2 = (mp **)v[3].buf;
	386
	387	mpmont mm;
	388	int ok = 1;
	389
	390	mpmont_create(&mm, m);
	391
f5f35081	392	if (mm.mi->v[0] != mi->v[0]) {
d3409d5e	393	fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
f5f35081	394	(unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
d3409d5e	395	fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
	396	fputc('\n', stderr);
	397	ok = 0;
	398	}
	399
032099d1	400	if (!MP_EQ(mm.r, r)) {
d3409d5e	401	fputs("\n*** bad r", stderr);
	402	fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
	403	fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
17ad212e	404	fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10);
d3409d5e	405	fputc('\n', stderr);
	406	ok = 0;
	407	}
	408
032099d1	409	if (!MP_EQ(mm.r2, r2)) {
d3409d5e	410	fputs("\n*** bad r2", stderr);
	411	fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
	412	fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
17ad212e	413	fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10);
d3409d5e	414	fputc('\n', stderr);
	415	ok = 0;
	416	}
	417
	418	MP_DROP(m);
	419	MP_DROP(mi);
	420	MP_DROP(r);
	421	MP_DROP(r2);
	422	mpmont_destroy(&mm);
ef5f4810	423	assert(mparena_count(MPARENA_GLOBAL) == 0);
d3409d5e	424	return (ok);
	425	}
	426
	427	static int tmul(dstr *v)
	428	{
	429	mp m = (mp **)v[0].buf;
	430	mp a = (mp **)v[1].buf;
	431	mp b = (mp **)v[2].buf;
	432	mp r = (mp **)v[3].buf;
d3409d5e	433	int ok = 1;
	434
	435	mpmont mm;
	436	mpmont_create(&mm, m);
	437
	438	{
79a34029	439	mp *qr = mp_mul(MP_NEW, a, b);
	440	mp_div(0, &qr, qr, m);
	441
032099d1	442	if (!MP_EQ(qr, r)) {
79a34029	443	fputs("\n*** classical modmul failed", stderr);
	444	fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
	445	fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
	446	fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
	447	fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
	448	fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
	449	fputc('\n', stderr);
	450	ok = 0;
	451	}
	452
	453	mp_drop(qr);
	454	}
	455
	456	{
d3409d5e	457	mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
d3409d5e	458	mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
79a34029	459	mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
d3409d5e	460	mr = mpmont_reduce(&mm, mr, mr);
032099d1	461	if (!MP_EQ(mr, r)) {
79a34029	462	fputs("\n*** montgomery modmul failed", stderr);
	463	fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
	464	fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
	465	fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
	466	fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
	467	fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
	468	fputc('\n', stderr);
	469	ok = 0;
	470	}
d3409d5e	471	MP_DROP(ar); MP_DROP(br);
79a34029	472	mp_drop(mr);
d3409d5e	473	}
d3409d5e	474
d3409d5e	475
	476	MP_DROP(m);
	477	MP_DROP(a);
	478	MP_DROP(b);
	479	MP_DROP(r);
d3409d5e	480	mpmont_destroy(&mm);
ef5f4810	481	assert(mparena_count(MPARENA_GLOBAL) == 0);
d3409d5e	482	return ok;
	483	}
	484
d3409d5e	485	static test_chunk tests[] = {
ef5f4810	486	{ "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
ef5f4810	487	{ "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
d3409d5e	488	{ 0, 0, { 0 } },
	489	};
	490
	491	int main(int argc, char *argv[])
	492	{
	493	sub_init();
	494	test_run(argc, argv, tests, SRCDIR "/tests/mpmont");
	495	return (0);
	496	}
	497
	498	#endif
	499
	500	/----- That's all, folks -------------------------------------------------/