ct.c, ct.h: New constant-time operations.

[u/mdw/catacomb] / gf-arith.c

/* -*-c-*-
 *
 * $Id$
 *
 * Basic arithmetic on binary polynomials
 *
 * (c) 2004 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.
 */

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

#include "gf.h"

/*----- Macros ------------------------------------------------------------*/

#define MAX(x, y) ((x) >= (y) ? (x) : (y))

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

/* --- @gf_add@ --- *
 *
 * Arguments:	@mp *d@ = destination
 *		@mp *a, *b@ = sources
 *
 * Returns:	Result, @a@ added to @b@.
 */

mp *gf_add(mp *d, mp *a, mp *b)
{
  MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & MP_BURN);
  gfx_add(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  d->f = (a->f | b->f) & MP_BURN;
  MP_SHRINK(d);
  return (d);
}

/* --- @gf_mul@ --- *
 *
 * Arguments:	@mp *d@ = destination
 *		@mp *a, *b@ = sources
 *
 * Returns:	Result, @a@ multiplied by @b@.
 */

mp *gf_mul(mp *d, mp *a, mp *b)
{
  a = MP_COPY(a);
  b = MP_COPY(b);

  if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= GFK_THRESH) {
    MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
    gfx_mul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  } else {
    size_t m = MAX(MP_LEN(a), MP_LEN(b));
    mpw *s;
    MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF);
    s = mpalloc(d->a, 3 * m);
    gfx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 3 * m);
    mpfree(d->a, s);
  }

  d->f = (a->f | b->f) & MP_BURN;
  MP_SHRINK(d);
  MP_DROP(a);
  MP_DROP(b);
  return (d);
}

/* --- @gf_sqr@ --- *
 *
 * Arguments:	@mp *d@ = destination
 *		@mp *a@ = source
 *
 * Returns:	Result, @a@ squared.
 */

mp *gf_sqr(mp *d, mp *a)
{
  MP_COPY(a);
  MP_DEST(d, 2 * MP_LEN(a), a->f & MP_BURN);
  gfx_sqr(d->v, d->vl, a->v, a->vl);
  d->f = a->f & MP_BURN;
  MP_SHRINK(d);
  MP_DROP(a);
  return (d);
}

/* --- @gf_div@ --- *
 *
 * Arguments:	@mp **qq, **rr@ = destination, quotient and remainder
 *		@mp *a, *b@ = sources
 *
 * Use:		Calculates the quotient and remainder when @a@ is divided by
 *		@b@.  The destinations @*qq@ and @*rr@ must be distinct.
 *		Either of @qq@ or @rr@ may be null to indicate that the
 *		result is irrelevant.  (Discarding both results is silly.)
 *		There is a performance advantage if @a == *rr@.
 */

void gf_div(mp **qq, mp **rr, mp *a, mp *b)
 {
  mp *r = rr ? *rr : MP_NEW;
  mp *q = qq ? *qq : MP_NEW;

  /* --- Set the remainder up right --- */

  b = MP_COPY(b);
  a = MP_COPY(a);
  if (r)
    MP_DROP(r);
  r = a;
  MP_DEST(r, MP_LEN(b) + 2, a->f | b->f);

  /* --- Fix up the quotient too --- */

  r = MP_COPY(r);
  MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
  MP_DROP(r);

  /* --- Perform the calculation --- */

  gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl);

  /* --- Sort out the sign of the results --- *
   *
   * If the signs of the arguments differ, and the remainder is nonzero, I
   * must add one to the absolute value of the quotient and subtract the
   * remainder from @b@.
   */

  q->f = (r->f | b->f) & MP_BURN;
  r->f = (r->f | b->f) & MP_BURN;

  /* --- Store the return values --- */

  MP_DROP(b);

  if (!qq)
    MP_DROP(q);
  else {
    MP_SHRINK(q);
    *qq = q;
  }

  if (!rr)
    MP_DROP(r);
  else {
    MP_SHRINK(r);
    *rr = r;
  }
}

/* --- @gf_irreduciblep@ --- *
 *
 * Arguments:	@mp *f@ = a polynomial
 *
 * Returns:	Nonzero if the polynomial is irreducible; otherwise zero.
 */

int gf_irreduciblep(mp *f)
{
  unsigned long m;
  mp *u = MP_TWO;
  mp *v = MP_NEW;

  if (MP_ZEROP(f))
    return (0);
  else if (MP_LEN(f) == 1) {
    if (f->v[0] < 2) return (0);
    if (f->v[0] < 4) return (1);
  }
  m = (mp_bits(f) - 1)/2;
  while (m) {
    u = gf_sqr(u, u);
    gf_div(0, &u, u, f);
    v = gf_add(v, u, MP_TWO);
    gf_gcd(&v, 0, 0, v, f);
    if (!MP_EQ(v, MP_ONE)) break;
    m--;
  }
  MP_DROP(u);
  MP_DROP(v);
  return (!m);
}

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

#ifdef TEST_RIG

static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
{
  if (!MP_EQ(expect, result)) {
    fprintf(stderr, "\n*** %s failed", op);
    fputs("\n*** a	= ", stderr); mp_writefile(a, stderr, 16);
    fputs("\n*** b	= ", stderr); mp_writefile(b, stderr, 16);
    fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16);
    fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16);
    fputc('\n', stderr);
    return (0);
  }
  return (1);
}

#define RIG(name, op)							\
  static int t##name(dstr *v)						\
  {									\
    mp *a = *(mp **)v[0].buf;						\
    mp *b = *(mp **)v[1].buf;						\
    mp *r = *(mp **)v[2].buf;						\
    mp *c = op(MP_NEW, a, b);						\
    int ok = verify(#name, r, c, a, b);					\
    mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r);			\
    assert(mparena_count(MPARENA_GLOBAL) == 0);				\
    return (ok);							\
  }

RIG(add, gf_add)
RIG(mul, gf_mul)
RIG(exp, gf_exp)

#undef RIG

static int tsqr(dstr *v)
{
  mp *a = *(mp **)v[0].buf;
  mp *r = *(mp **)v[1].buf;
  mp *c = MP_NEW;
  int ok = 1;
  c = gf_sqr(MP_NEW, a);
  ok &= verify("sqr", r, c, a, MP_ZERO);
  mp_drop(a); mp_drop(r); mp_drop(c);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return (ok);
}

static int tdiv(dstr *v)
{
  mp *a = *(mp **)v[0].buf;
  mp *b = *(mp **)v[1].buf;
  mp *q = *(mp **)v[2].buf;
  mp *r = *(mp **)v[3].buf;
  mp *c = MP_NEW, *d = MP_NEW;
  int ok = 1;
  gf_div(&c, &d, a, b);
  ok &= verify("div(quotient)", q, c, a, b);
  ok &= verify("div(remainder)", r, d, a, b);
  mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return (ok);
}

static int tirred(dstr *v)
{
  mp *a = *(mp **)v[0].buf;
  int r = *(int *)v[1].buf;
  int c = gf_irreduciblep(a);
  int ok = 1;
  if (r != c) {
    ok = 0;
    fprintf(stderr, "\n*** irred failed");
    fputs("\n*** a	= ", stderr); mp_writefile(a, stderr, 16);
    fprintf(stderr, "\n*** r	  = %d\n", r);
    fprintf(stderr, "*** c	= %d\n", c);
  }
  mp_drop(a);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return (ok);
}

static test_chunk tests[] = {
  { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
  { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
  { "sqr", tsqr, { &type_mp, &type_mp, 0 } },
  { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
  { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } },
  { "irred", tirred, { &type_mp, &type_int, 0 } },
  { 0, 0, { 0 } },
};

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

#endif

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