X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/math/mpcrt.c

diff --git a/math/mpcrt.c b/math/mpcrt.c
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+/* -*-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[%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;
+  }
+
+  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 -------------------------------------------------*/