Add support for solving Chinese Remainder Theorem problems.

diff --git a/mpcrt.c b/mpcrt.c
new file mode 100644 (file)
index 0000000..3b1ee22
--- /dev/null
+++ b/mpcrt.c
@@ -0,0 +1,262 @@
+/* -*-c-*-
+ *
+ * $Id: mpcrt.c,v 1.1 1999/11/22 20:50:57 mdw Exp $
+ *
+ * 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.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: mpcrt.c,v $
+ * Revision 1.1  1999/11/22 20:50:57  mdw
+ * Add support for solving Chinese Remainder Theorem problems.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mpcrt.h"
+#include "mpmont.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)
+{
+  mp *x = MP_NEW, *y = MP_NEW;
+  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(v[0].m);
+    for (i = 1; i < k; i++) {
+      mp *d = mp_mul(x, n, v[i].m);
+      x = n;
+      n = d;
+    }
+  }
+
+  /* --- Set up the Montgomery context --- */
+
+  mpmont_create(&c->mm, 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)
+      mp_gcd(0, &v[i].ni, 0, v[i].n, v[i].m);
+    if (!v[i].nnir) {
+      x = mpmont_mul(&c->mm, x, v[i].n, c->mm.r2);
+      y = mpmont_mul(&c->mm, y, v[i].ni, c->mm.r2);
+      v[i].nnir = mpmont_mul(&c->mm, MP_NEW, x, y);
+    }
+  }
+
+  /* --- Done --- */
+
+  if (x)
+    mp_drop(x);
+  if (y)
+    mp_drop(y);
+}
+
+/* --- @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].nnir) mp_drop(c->v[i].nnir);
+  }
+  mpmont_destroy(&c->mm);
+}
+
+/* --- @mpcrt_solve@ --- *
+ *
+ * Arguments:  @mpcrt *c@ = pointer to CRT context
+ *             @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 **v)
+{
+  mp *a = MP_ZERO;
+  mp *x = MP_NEW;
+  size_t i;
+
+  for (i = 0; i < c->k; i++) {
+    x = mpmont_mul(&c->mm, x, c->v[i].nnir, v[i]);
+    a = mp_add(a, a, x);
+  }
+  if (x)
+    mp_drop(x);
+  if (MP_CMP(a, >=, c->mm.m))
+    mp_div(0, &a, a, c->mm.m);
+  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].nnir = 0;
+  }
+  a = *(mp **)v[2 * n].buf;
+
+  mpcrt_create(&c, m, n, 0);
+  b = mpcrt_solve(&c, r);
+
+  if (MP_CMP(a, !=, b)) {
+    fputs("\n*** failed\n", stderr);
+    fputs("n = ", stderr);
+    mp_writefile(c.mm.m, stderr, 10);
+    for (i = 0; i < n; i++) {
+      fprintf(stderr, "\nr[%u] = ", i);
+      mp_writefile(r[i], stderr, 10);
+      fprintf(stderr, "\nm[%u] = ", i);
+      mp_writefile(m[i].m, stderr, 10);
+      fprintf(stderr, "\nN[%u] = ", i);
+      mp_writefile(m[i].n, stderr, 10);
+      fprintf(stderr, "\nM[%u] = ", 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;
+  }
+
+  mp_drop(a);
+  mp_drop(b);
+  mpcrt_destroy(&c);
+  free(m);
+  free(r);
+  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 "/tests/mpcrt");
+  return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/

diff --git a/mpcrt.h b/mpcrt.h
new file mode 100644 (file)
index 0000000..5474a92
--- /dev/null
+++ b/mpcrt.h
@@ -0,0 +1,132 @@
+/* -*-c-*-
+ *
+ * $Id: mpcrt.h,v 1.1 1999/11/22 20:50:57 mdw Exp $
+ *
+ * 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.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: mpcrt.h,v $
+ * Revision 1.1  1999/11/22 20:50:57  mdw
+ * Add support for solving Chinese Remainder Theorem problems.
+ *
+ */
+
+#ifndef MPCRT_H
+#define MPCRT_H
+
+#ifdef __cplusplus
+  extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#include <stddef.h>
+
+#ifndef MP_H
+#  include "mp.h"
+#endif
+
+#ifndef MPMONT_H
+#  include "mpmont.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef struct mpcrt_mod {
+  mp *m;                               /* %$n_i$% -- the modulus */
+  mp *n;                               /* %$N_i = n / n_i$% */
+  mp *ni;                              /* %$M_i = N_i^{-1} \bmod n_i$% */
+  mp *nnir;                            /* %$N_i M_i R \bmod m$% */
+} mpcrt_mod;
+
+typedef struct mpcrt {
+  size_t k;                            /* Number of distinct moduli */
+  mpmont mm;                           /* Montgomery context for product */
+  mpcrt_mod *v;                                /* Vector of information for each */
+} mpcrt;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @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).
+ */
+
+extern void mpcrt_create(mpcrt */*c*/, mpcrt_mod */*v*/,
+                        size_t /*k*/, mp */*n*/);
+
+/* --- @mpcrt_destroy@ --- *
+ *
+ * Arguments:  @mpcrt *c@ - pointer to CRT context
+ *
+ * Returns:    ---
+ *
+ * Use:                Destroys a CRT context, releasing all the resources it holds.
+ */
+
+extern void mpcrt_destroy(mpcrt */*c*/);
+
+/* --- @mpcrt_solve@ --- *
+ *
+ * Arguments:  @mpcrt *c@ = pointer to CRT context
+ *             @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.
+ */
+
+extern mp *mpcrt_solve(mpcrt */*c*/, mp **/*v*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+  }
+#endif
+
+#endif

diff --git a/tests/mpcrt b/tests/mpcrt
new file mode 100644 (file)
index 0000000..4d08d90
--- /dev/null
+++ b/tests/mpcrt
@@ -0,0 +1,21 @@
+# Test vectors for Chinese Remainder Theorem solution (Gauss's algorithm)
+#
+# $Id: mpcrt,v 1.1 1999/11/22 20:51:19 mdw Exp $
+
+crt-1 {
+  1 5 1;
+  3498243289823 4534543545463431 3498243289823;
+}
+
+crt-2 {
+  3 7 7 13 59;
+  39845 435435221 43534545 32423423467 13736097689153284731;
+
+  2200541929485233317342398 498459898455435345676576793
+  13046769915260439091721075347560767438958354488807168684311588308214063361125238823412234206191582332588 40831929843180254171317254073271577309351168965431122042755102715326515941762786951037109689522493526197
+ 14756532044160797319048143986538019326281096778844833416304858521742332925502855547148214406728673769162624068049034315018936294558;
+}
+
+crt-4 {
+  2 5 1 7 3 11 8 13 2192;
+}
\ No newline at end of file