Merge branch '2.4.x' into 2.5.x

[catacomb] / math / mpcrt.c

/* -*-c-*-
 *
 * Chinese Remainder Theorem computations (Gauss's algorithm)
 *
 * (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.
 */

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

#include "mp.h"
#include "mpcrt.h"
#include "mpmul.h"
#include "mpbarrett.h"

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

/* --- @mpcrt_create@ --- *
 *
 * Arguments:	@mpcrt *c@ = pointer to CRT context
 *		@mpcrt_mod *v@ = pointer to vector of moduli
 *		@size_t k@ = number of moduli
 *		@mp *n@ = product of all moduli (@MP_NEW@ if unknown)
 *
 * Returns:	---
 *
 * Use:		Initializes a context for solving Chinese Remainder Theorem
 *		problems.  The vector of moduli can be incomplete.  Omitted
 *		items must be left as null pointers.  Not all combinations of
 *		missing things can be coped with, even if there is
 *		technically enough information to cope.  For example, if @n@
 *		is unspecified, all the @m@ values must be present, even if
 *		there is one modulus with both @m@ and @n@ (from which the
 *		product of all moduli could clearly be calculated).
 */

void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n)
{
  size_t i;

  /* --- Simple initialization things --- */

  c->k = k;
  c->v = v;

  /* --- Work out @n@ if I don't have it already --- */

  if (n != MP_NEW)
    n = MP_COPY(n);
  else {
    mpmul mm;
    mpmul_init(&mm);
    for (i = 0; i < k; i++)
      mpmul_add(&mm, v[i].m);
    n = mpmul_done(&mm);
  }

  /* --- A quick hack if %$k = 2$% --- */

  if (k == 2) {

    /* --- The %$n / n_i$% values are trivial in this case --- */

    if (!v[0].n)
      v[0].n = MP_COPY(v[1].m);
    if (!v[1].n)
      v[1].n = MP_COPY(v[0].m);

    /* --- Now sort out the inverses --- *
     *
     * @mp_gcd@ will ensure that the first argument is negative.
     */

    if (!v[0].ni && !v[1].ni) {
      mp *g = MP_NEW;
      mp_gcd(&g, &v[0].ni, &v[1].ni, v[0].n, v[1].n);
      assert(MP_EQ(g, MP_ONE));
      mp_drop(g);
      v[0].ni = mp_add(v[0].ni, v[0].ni, v[1].n);
    } else {
      int i, j;
      mp *x;

      if (!v[0].ni)
	i = 0, j = 1;
      else
	i = 1, j = 0;

      x = mp_mul(MP_NEW, v[j].n, v[j].ni);
      x = mp_sub(x, x, MP_ONE);
      mp_div(&x, 0, x, v[i].n);
      v[i].ni = x;
    }
  }

  /* --- Set up the Barrett context --- */

  mpbarrett_create(&c->mb, n);

  /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */

  for (i = 0; i < k; i++) {
    if (!v[i].n)
      mp_div(&v[i].n, 0, n, v[i].m);
    if (!v[i].ni)
      v[i].ni = mp_modinv(MP_NEW, v[i].n, v[i].m);
    if (!v[i].nni)
      v[i].nni = mp_mul(MP_NEW, v[i].n, v[i].ni);
  }

  /* --- Done --- */

  mp_drop(n);
}

/* --- @mpcrt_destroy@ --- *
 *
 * Arguments:	@mpcrt *c@ - pointer to CRT context
 *
 * Returns:	---
 *
 * Use:		Destroys a CRT context, releasing all the resources it holds.
 */

void mpcrt_destroy(mpcrt *c)
{
  size_t i;

  for (i = 0; i < c->k; i++) {
    if (c->v[i].m) mp_drop(c->v[i].m);
    if (c->v[i].n) mp_drop(c->v[i].n);
    if (c->v[i].ni) mp_drop(c->v[i].ni);
    if (c->v[i].nni) mp_drop(c->v[i].nni);
  }
  mpbarrett_destroy(&c->mb);
}

/* --- @mpcrt_solve@ --- *
 *
 * Arguments:	@mpcrt *c@ = pointer to CRT context
 *		@mp *d@ = fake destination
 *		@mp **v@ = array of residues
 *
 * Returns:	The unique solution modulo the product of the individual
 *		moduli, which leaves the given residues.
 *
 * Use:		Constructs a result given its residue modulo an array of
 *		coprime integers.  This can be used to improve performance of
 *		RSA encryption or Blum-Blum-Shub generation if the factors
 *		of the modulus are known, since results can be computed mod
 *		each of the individual factors and then combined at the end.
 *		This is rather faster than doing the full-scale modular
 *		exponentiation.
 */

mp *mpcrt_solve(mpcrt *c, mp *d, mp **v)
{
  mp *a = MP_ZERO;
  mp *x = MP_NEW;
  size_t i;

  for (i = 0; i < c->k; i++) {
    x = mp_mul(x, c->v[i].nni, v[i]);
    x = mpbarrett_reduce(&c->mb, x, x);
    a = mp_add(a, a, x);
  }
  if (x)
    MP_DROP(x);
  a = mpbarrett_reduce(&c->mb, a, a);
  if (d != MP_NEW)
    MP_DROP(d);
  return (a);
}

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

#ifdef TEST_RIG

static int verify(size_t n, dstr *v)
{
  mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod));
  mp **r = xmalloc(n * sizeof(mp *));
  mpcrt c;
  mp *a, *b;
  size_t i;
  int ok = 1;

  for (i = 0; i < n; i++) {
    r[i] = *(mp **)v[2 * i].buf;
    m[i].m = *(mp **)v[2 * i + 1].buf;
    m[i].n = 0;
    m[i].ni = 0;
    m[i].nni = 0;
  }
  a = *(mp **)v[2 * n].buf;

  mpcrt_create(&c, m, n, 0);
  b = mpcrt_solve(&c, MP_NEW, r);

  if (!MP_EQ(a, b)) {
    fputs("\n*** failed\n", stderr);
    fputs("n = ", stderr);
    mp_writefile(c.mb.m, stderr, 10);
    for (i = 0; i < n; i++) {
      fprintf(stderr, "\nr[%lu] = ", (unsigned long)i);
      mp_writefile(r[i], stderr, 10);
      fprintf(stderr, "\nm[%lu] = ", (unsigned long)i);
      mp_writefile(m[i].m, stderr, 10);
      fprintf(stderr, "\nN[%lu] = ", (unsigned long)i);
      mp_writefile(m[i].n, stderr, 10);
      fprintf(stderr, "\nM[%lu] = ", (unsigned long)i);
      mp_writefile(m[i].ni, stderr, 10);
    }
    fputs("\nresult = ", stderr);
    mp_writefile(b, stderr, 10);
    fputs("\nexpect = ", stderr);
    mp_writefile(a, stderr, 10);
    fputc('\n', stderr);
    ok = 0;
  }

  for (i = 0; i < n; i++)
    mp_drop(r[i]);
  mp_drop(a);
  mp_drop(b);
  mpcrt_destroy(&c);
  xfree(m);
  xfree(r);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return (ok);
}

static int crt1(dstr *v) { return verify(1, v); }
static int crt2(dstr *v) { return verify(2, v); }
static int crt3(dstr *v) { return verify(3, v); }
static int crt4(dstr *v) { return verify(4, v); }
static int crt5(dstr *v) { return verify(5, v); }

static test_chunk tests[] = {
  { "crt-1", crt1, { &type_mp, &type_mp,
		    &type_mp, 0 } },
  { "crt-2", crt2, { &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, 0 } },
  { "crt-3", crt3, { &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, 0 } },
  { "crt-4", crt4, { &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, 0 } },
  { "crt-5", crt5, { &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, &type_mp,
		    &type_mp, &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 "/t/mpcrt");
  return (0);
}

#endif

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