git.distorted.org.uk Git - u/mdw/catacomb/blob - mpcrt.c

   1 /* -*-c-*-
   2  *
   3  * $Id: mpcrt.c,v 1.4 2001/04/19 18:25:38 mdw Exp $
   4  *
   5  * Chinese Remainder Theorem computations (Gauss's algorithm)
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: mpcrt.c,v $
  33  * Revision 1.4  2001/04/19 18:25:38  mdw
  34  * Use mpmul for the multiplication.
  35  *
  36  * Revision 1.3  2000/10/08 12:11:22  mdw
  37  * Use @MP_EQ@ instead of @MP_CMP@.
  38  *
  39  * Revision 1.2  1999/12/10 23:22:32  mdw
  40  * Interface changes for suggested destinations.  Use Barrett reduction.
  41  *
  42  * Revision 1.1  1999/11/22 20:50:57  mdw
  43  * Add support for solving Chinese Remainder Theorem problems.
  44  *
  45  */
  46
  47 /*----- Header files ------------------------------------------------------*/
  48
  49 #include "mp.h"
  50 #include "mpcrt.h"
  51 #include "mpmul.h"
  52 #include "mpbarrett.h"
  53
  54 /*----- Main code ---------------------------------------------------------*/
  55
  56 /* --- @mpcrt_create@ --- *
  57  *
  58  * Arguments:   @mpcrt *c@ = pointer to CRT context
  59  *              @mpcrt_mod *v@ = pointer to vector of moduli
  60  *              @size_t k@ = number of moduli
  61  *              @mp *n@ = product of all moduli (@MP_NEW@ if unknown)
  62  *
  63  * Returns:     ---
  64  *
  65  * Use:         Initializes a context for solving Chinese Remainder Theorem
  66  *              problems.  The vector of moduli can be incomplete.  Omitted
  67  *              items must be left as null pointers.  Not all combinations of
  68  *              missing things can be coped with, even if there is
  69  *              technically enough information to cope.  For example, if @n@
  70  *              is unspecified, all the @m@ values must be present, even if
  71  *              there is one modulus with both @m@ and @n@ (from which the
  72  *              product of all moduli could clearly be calculated).
  73  */
  74
  75 void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n)
  76 {
  77   size_t i;
  78
  79   /* --- Simple initialization things --- */
  80
  81   c->k = k;
  82   c->v = v;
  83
  84   /* --- Work out @n@ if I don't have it already --- */
  85
  86   if (n != MP_NEW)
  87     n = MP_COPY(n);
  88   else {
  89     mpmul mm;
  90     mpmul_init(&mm);
  91     n = MP_COPY(v[0].m);
  92     for (i = 0; i < k; i++)
  93       mpmul_add(&mm, v[i].m);
  94     n = mpmul_done(&mm);
  95   }
  96
  97   /* --- A quick hack if %$k = 2$% --- */
  98
  99   if (k == 2) {
 100
 101     /* --- The %$n / n_i$% values are trivial in this case --- */
 102
 103     if (!v[0].n)
 104       v[0].n = MP_COPY(v[1].m);
 105     if (!v[1].n)
 106       v[1].n = MP_COPY(v[0].m);
 107
 108     /* --- Now sort out the inverses --- *
 109      *
 110      * @mp_gcd@ will ensure that the first argument is negative.
 111      */
 112
 113     if (!v[0].ni && !v[1].ni) {
 114       mp_gcd(0, &v[0].ni, &v[1].ni, v[0].n, v[1].n);
 115       v[0].ni = mp_add(v[0].ni, v[0].ni, v[1].n);
 116     } else {
 117       int i, j;
 118       mp *x;
 119
 120       if (!v[0].ni)
 121         i = 0, j = 1;
 122       else
 123         i = 1, j = 0;
 124
 125       x = mp_mul(MP_NEW, v[j].n, v[j].ni);
 126       x = mp_sub(x, x, MP_ONE);
 127       mp_div(&x, 0, x, v[i].n);
 128       v[i].ni = x;
 129     }
 130   }
 131
 132   /* --- Set up the Barrett context --- */
 133
 134   mpbarrett_create(&c->mb, n);
 135
 136   /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */
 137
 138   for (i = 0; i < k; i++) {
 139     if (!v[i].n)
 140       mp_div(&v[i].n, 0, n, v[i].m);
 141     if (!v[i].ni)
 142       mp_gcd(0, &v[i].ni, 0, v[i].n, v[i].m);
 143     if (!v[i].nni)
 144       v[i].nni = mp_mul(MP_NEW, v[i].n, v[i].ni);
 145   }
 146
 147   /* --- Done --- */
 148
 149   mp_drop(n);
 150 }
 151
 152 /* --- @mpcrt_destroy@ --- *
 153  *
 154  * Arguments:   @mpcrt *c@ - pointer to CRT context
 155  *
 156  * Returns:     ---
 157  *
 158  * Use:         Destroys a CRT context, releasing all the resources it holds.
 159  */
 160
 161 void mpcrt_destroy(mpcrt *c)
 162 {
 163   size_t i;
 164
 165   for (i = 0; i < c->k; i++) {
 166     if (c->v[i].m) mp_drop(c->v[i].m);
 167     if (c->v[i].n) mp_drop(c->v[i].n);
 168     if (c->v[i].ni) mp_drop(c->v[i].ni);
 169     if (c->v[i].nni) mp_drop(c->v[i].nni);
 170   }
 171   mpbarrett_destroy(&c->mb);
 172 }
 173
 174 /* --- @mpcrt_solve@ --- *
 175  *
 176  * Arguments:   @mpcrt *c@ = pointer to CRT context
 177  *              @mp *d@ = fake destination
 178  *              @mp **v@ = array of residues
 179  *
 180  * Returns:     The unique solution modulo the product of the individual
 181  *              moduli, which leaves the given residues.
 182  *
 183  * Use:         Constructs a result given its residue modulo an array of
 184  *              coprime integers.  This can be used to improve performance of
 185  *              RSA encryption or Blum-Blum-Shub generation if the factors
 186  *              of the modulus are known, since results can be computed mod
 187  *              each of the individual factors and then combined at the end.
 188  *              This is rather faster than doing the full-scale modular
 189  *              exponentiation.
 190  */
 191
 192 mp *mpcrt_solve(mpcrt *c, mp *d, mp **v)
 193 {
 194   mp *a = MP_ZERO;
 195   mp *x = MP_NEW;
 196   size_t i;
 197
 198   for (i = 0; i < c->k; i++) {
 199     x = mp_mul(x, c->v[i].nni, v[i]);
 200     x = mpbarrett_reduce(&c->mb, x, x);
 201     a = mp_add(a, a, x);
 202   }
 203   if (x)
 204     MP_DROP(x);
 205   a = mpbarrett_reduce(&c->mb, a, a);
 206   if (d != MP_NEW)
 207     MP_DROP(d);
 208   return (a);
 209 }
 210
 211 /*----- Test rig ----------------------------------------------------------*/
 212
 213 #ifdef TEST_RIG
 214
 215 static int verify(size_t n, dstr *v)
 216 {
 217   mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod));
 218   mp **r = xmalloc(n * sizeof(mp *));
 219   mpcrt c;
 220   mp *a, *b;
 221   size_t i;
 222   int ok = 1;
 223
 224   for (i = 0; i < n; i++) {
 225     r[i] = *(mp **)v[2 * i].buf;
 226     m[i].m = *(mp **)v[2 * i + 1].buf;
 227     m[i].n = 0;
 228     m[i].ni = 0;
 229     m[i].nni = 0;
 230   }
 231   a = *(mp **)v[2 * n].buf;
 232
 233   mpcrt_create(&c, m, n, 0);
 234   b = mpcrt_solve(&c, MP_NEW, r);
 235
 236   if (!MP_EQ(a, b)) {
 237     fputs("\n*** failed\n", stderr);
 238     fputs("n = ", stderr);
 239     mp_writefile(c.mb.m, stderr, 10);
 240     for (i = 0; i < n; i++) {
 241       fprintf(stderr, "\nr[%u] = ", i);
 242       mp_writefile(r[i], stderr, 10);
 243       fprintf(stderr, "\nm[%u] = ", i);
 244       mp_writefile(m[i].m, stderr, 10);
 245       fprintf(stderr, "\nN[%u] = ", i);
 246       mp_writefile(m[i].n, stderr, 10);
 247       fprintf(stderr, "\nM[%u] = ", i);
 248       mp_writefile(m[i].ni, stderr, 10);
 249     }
 250     fputs("\nresult = ", stderr);
 251     mp_writefile(b, stderr, 10);
 252     fputs("\nexpect = ", stderr);
 253     mp_writefile(a, stderr, 10);
 254     fputc('\n', stderr);
 255     ok = 0;
 256   }
 257
 258   for (i = 0; i < n; i++)
 259     mp_drop(r[i]);
 260   mp_drop(a);
 261   mp_drop(b);
 262   mpcrt_destroy(&c);
 263   free(m);
 264   free(r);
 265   assert(mparena_count(MPARENA_GLOBAL) == 0);
 266   return (ok);
 267 }
 268
 269 static int crt1(dstr *v) { return verify(1, v); }
 270 static int crt2(dstr *v) { return verify(2, v); }
 271 static int crt3(dstr *v) { return verify(3, v); }
 272 static int crt4(dstr *v) { return verify(4, v); }
 273 static int crt5(dstr *v) { return verify(5, v); }
 274
 275 static test_chunk tests[] = {
 276   { "crt-1", crt1, { &type_mp, &type_mp,
 277                     &type_mp, 0 } },
 278   { "crt-2", crt2, { &type_mp, &type_mp,
 279                     &type_mp, &type_mp,
 280                     &type_mp, 0 } },
 281   { "crt-3", crt3, { &type_mp, &type_mp,
 282                     &type_mp, &type_mp,
 283                     &type_mp, &type_mp,
 284                     &type_mp, 0 } },
 285   { "crt-4", crt4, { &type_mp, &type_mp,
 286                     &type_mp, &type_mp,
 287                     &type_mp, &type_mp,
 288                     &type_mp, &type_mp,
 289                     &type_mp, 0 } },
 290   { "crt-5", crt5, { &type_mp, &type_mp,
 291                     &type_mp, &type_mp,
 292                     &type_mp, &type_mp,
 293                     &type_mp, &type_mp,
 294                     &type_mp, &type_mp,
 295                     &type_mp, 0 } },
 296   { 0, 0, { 0 } }
 297 };
 298
 299 int main(int argc, char *argv[])
 300 {
 301   sub_init();
 302   test_run(argc, argv, tests, SRCDIR "/tests/mpcrt");
 303   return (0);
 304 }
 305
 306 #endif
 307
 308 /*----- That's all, folks -------------------------------------------------*/