Add an internal-representation no-op function.

[u/mdw/catacomb] / mpbarrett.c

/* -*-c-*-
 *
 * $Id: mpbarrett.c,v 1.7 2001/04/19 18:25:26 mdw Exp $
 *
 * Barrett modular 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: mpbarrett.c,v $
 * Revision 1.7  2001/04/19 18:25:26  mdw
 * Use sliding-window exponentiation.
 *
 * Revision 1.6  2000/10/08 12:03:44  mdw
 * (mpbarrett_reduce): Cope with negative numbers.
 *
 * Revision 1.5  2000/07/29 17:04:33  mdw
 * Change to use left-to-right bitwise exponentiation.  This will improve
 * performance when the base is small.
 *
 * Revision 1.4  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 1.3  1999/12/12 15:08:52  mdw
 * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
 * significant digits.
 *
 * Revision 1.2  1999/12/11 01:50:56  mdw
 * Improve initialization slightly.
 *
 * Revision 1.1  1999/12/10 23:21:59  mdw
 * Barrett reduction support: works with even moduli.
 *
 */

/*----- Header files ------------------------------------------------------*/

#include "mp.h"
#include "mpbarrett.h"

/*----- Main code ---------------------------------------------------------*/

/* --- @mpbarrett_create@ --- *
 *
 * Arguments:	@mpbarrett *mb@ = pointer to Barrett reduction context
 *		@mp *m@ = modulus to work to
 *
 *
 * Returns:	---
 *
 * Use:		Initializes a Barrett reduction context ready for use.
 */

void mpbarrett_create(mpbarrett *mb, mp *m)
{
  mp *b;

  /* --- Validate the arguments --- */

  assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));

  /* --- Compute %$\mu$% --- */

  mp_shrink(m);
  mb->k = MP_LEN(m);
  mb->m = MP_COPY(m);
  b = mp_new(2 * mb->k + 1, 0);
  MPX_ZERO(b->v, b->vl - 1);
  b->vl[-1] = 1;
  mp_div(&b, 0, b, m);
  mb->mu = b;
}

/* --- @mpbarrett_destroy@ --- *
 *
 * Arguments:	@mpbarrett *mb@ = pointer to Barrett reduction context
 *
 * Returns:	---
 *
 * Use:		Destroys a Barrett reduction context releasing any resources
 *		claimed.
 */

void mpbarrett_destroy(mpbarrett *mb)
{
  mp_drop(mb->m);
  mp_drop(mb->mu);
}

/* --- @mpbarrett_reduce@ --- *
 *
 * Arguments:	@mpbarrett *mb@ = pointer to Barrett reduction context
 *		@mp *d@ = destination for result
 *		@mp *m@ = number to reduce
 *
 * Returns:	The residue of @m@ modulo the number in the reduction
 *		context.
 *
 * Use:		Performs an efficient modular reduction.
 */

mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
{
  mp *q;
  size_t k = mb->k;

  /* --- Special case if @m@ is too small --- */

  if (MP_LEN(m) < k) {
    m = MP_COPY(m);
    if (d)
      MP_DROP(d);
    return (m);
  }

  /* --- First stage --- */

  {
    mp qq;
    mp_build(&qq, m->v + (k - 1), m->vl);
    q = mp_mul(MP_NEW, &qq, mb->mu);
    if (MP_LEN(q) <= k) {
      m = MP_COPY(m);
      if (d)
	MP_DROP(d);
      return (m);
    }
  }

  /* --- Second stage --- */

  {
    mp *r;
    mpw *mvl;

    MP_COPY(m);
    if (MP_LEN(m) <= k + 1)
      mvl = m->vl;
    else
      mvl = m->v + k + 1;
    r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
    mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
    MP_DEST(d, k + 1, r->f);
    mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
    d->f = (m->f | r->f) & (MP_BURN | MP_NEG);
    MP_DROP(r);
    MP_DROP(q);
    MP_DROP(m);
  }

  /* --- Final stage --- */

  MP_SHRINK(d);
  while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
    mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);

  /* --- Fix up the sign --- */

  if (d->f & MP_NEG) {
    mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl);
    d->f &= ~MP_NEG;
  }

  MP_SHRINK(d);
  return (d);
}

/* --- @mpbarrett_exp@ --- *
 *
 * Arguments:	@mpbarrett *mb@ = pointer to Barrett reduction context
 *              @mp *d@ = fake destination
 *              @mp *a@ = base
 *              @mp *e@ = exponent
 *
 * Returns:     Result, %$a^e \bmod m$%.
 */

#define WINSZ 5
#define TABSZ (1 << (WINSZ - 1))

#define THRESH (((MPW_BITS / WINSZ) << 2) + 1)

static mp *exp_simple(mpbarrett *mb, mp *d, mp *a, mp *e)
{
  mpscan sc;
  mp *x = MP_ONE;
  mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
  unsigned sq = 0;

  a = MP_COPY(a);
  mp_rscan(&sc, e);
  if (!MP_RSTEP(&sc))
    goto exit;
  while (!MP_RBIT(&sc))
    MP_RSTEP(&sc);

  /* --- Do the main body of the work --- */

  for (;;) {
    sq++;
    while (sq) {
      mp *y;
      y = mp_sqr(spare, x);
      y = mpbarrett_reduce(mb, y, y);
      spare = x; x = y;
      sq--;
    }
    {
      mp *y = mp_mul(spare, x, a);
      y = mpbarrett_reduce(mb, y, y);
      spare = x; x = y;
    }
    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 = mpbarrett_reduce(mb, y, y);
    spare = x; x = y;
    sq--;
  }  

exit:
  MP_DROP(a);
  if (spare != MP_NEW)
    MP_DROP(spare);
  if (d != MP_NEW)
    MP_DROP(d);
  return (x);
}

mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
{
  mp **tab;
  mp *a2;
  mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
  mp *x = MP_ONE;
  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(mb, d, a, e));
  }

  /* --- Do the precomputation --- */

  a2 = mp_sqr(MP_NEW, a);
  a2 = mpbarrett_reduce(mb, a2, a2);
  tab = xmalloc(TABSZ * sizeof(mp *));
  tab[0] = MP_COPY(a);
  for (i = 1; i < TABSZ; i++) {
    mp *x = mp_mul(MP_NEW, tab[i - 1], a2);
    tab[i] = mpbarrett_reduce(mb, x, x);
  }
  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 = mpbarrett_reduce(mb, y, y);
      spare = x; x = y;
      sq--;
    }

    /* --- Do the multiply --- */

    { mp *y = mp_mul(spare, x, tab[i]); spare = x;
      x = mpbarrett_reduce(mb, y, 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 = mpbarrett_reduce(mb, y, y);
    spare = x; x = y;
    sq--;
  }

  /* --- Done --- */

  for (i = 0; i < TABSZ; i++)
    mp_drop(tab[i]);
  xfree(tab);
exit:
  mp_drop(d);
  mp_drop(spare);
  return (x);
}

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

#ifdef TEST_RIG

static int vmod(dstr *v)
{
  mp *x = *(mp **)v[0].buf;
  mp *n = *(mp **)v[1].buf;
  mp *r = *(mp **)v[2].buf;
  mp *s;
  mpbarrett mb;
  int ok = 1;

  mpbarrett_create(&mb, n);
  s = mpbarrett_reduce(&mb, MP_NEW, x);

  if (!MP_EQ(s, r)) {
    fputs("\n*** barrett reduction failure\n", stderr);
    fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
    fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
    fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
    fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
    ok = 0;
  }

  mpbarrett_destroy(&mb);
  mp_drop(x);
  mp_drop(n);
  mp_drop(r);
  mp_drop(s);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return (ok);
}

static int vexp(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;

  mpbarrett mb;
  mpbarrett_create(&mb, m);

  mr = mpbarrett_exp(&mb, MP_NEW, a, b);

  if (!MP_EQ(mr, r)) {
    fputs("\n*** barrett 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);
  mpbarrett_destroy(&mb);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return ok;
}

static test_chunk tests[] = {
  { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
  { "mpbarrett-exp", vexp, { &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/mpbarrett");
  return (0);
}

#endif

/*----- That's all, folks -------------------------------------------------*/