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   1 /* -*-c-*-
   2  *
   3  * $Id: mpcrt.c,v 1.5 2001/04/29 17:39:33 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 1.5  2001/04/29 17:39:33  mdw
  34  * Fix memory leak.
  35  *
  36  * Revision 1.4  2001/04/19 18:25:38  mdw
  37  * Use mpmul for the multiplication.
  38  *
  39  * Revision 1.3  2000/10/08 12:11:22  mdw
  40  * Use @MP_EQ@ instead of @MP_CMP@.
  41  *
  42  * Revision 1.2  1999/12/10 23:22:32  mdw
  43  * Interface changes for suggested destinations.  Use Barrett reduction.
  44  *
  45  * Revision 1.1  1999/11/22 20:50:57  mdw
  46  * Add support for solving Chinese Remainder Theorem problems.
  47  *
  48  */
  49
  50 /*----- Header files ------------------------------------------------------*/
  51
  52 #include "mp.h"
  53 #include "mpcrt.h"
  54 #include "mpmul.h"
  55 #include "mpbarrett.h"
  56
  57 /*----- Main code ---------------------------------------------------------*/
  58
  59 /* --- @mpcrt_create@ --- *
  60  *
  61  * Arguments:   @mpcrt *c@ = pointer to CRT context
  62  *              @mpcrt_mod *v@ = pointer to vector of moduli
  63  *              @size_t k@ = number of moduli
  64  *              @mp *n@ = product of all moduli (@MP_NEW@ if unknown)
  65  *
  66  * Returns:     ---
  67  *
  68  * Use:         Initializes a context for solving Chinese Remainder Theorem
  69  *              problems.  The vector of moduli can be incomplete.  Omitted
  70  *              items must be left as null pointers.  Not all combinations of
  71  *              missing things can be coped with, even if there is
  72  *              technically enough information to cope.  For example, if @n@
  73  *              is unspecified, all the @m@ values must be present, even if
  74  *              there is one modulus with both @m@ and @n@ (from which the
  75  *              product of all moduli could clearly be calculated).
  76  */
  77
  78 void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n)
  79 {
  80   size_t i;
  81
  82   /* --- Simple initialization things --- */
  83
  84   c->k = k;
  85   c->v = v;
  86
  87   /* --- Work out @n@ if I don't have it already --- */
  88
  89   if (n != MP_NEW)
  90     n = MP_COPY(n);
  91   else {
  92     mpmul mm;
  93     mpmul_init(&mm);
  94     for (i = 0; i < k; i++)
  95       mpmul_add(&mm, v[i].m);
  96     n = mpmul_done(&mm);
  97   }
  98
  99   /* --- A quick hack if %$k = 2$% --- */
 100
 101   if (k == 2) {
 102
 103     /* --- The %$n / n_i$% values are trivial in this case --- */
 104
 105     if (!v[0].n)
 106       v[0].n = MP_COPY(v[1].m);
 107     if (!v[1].n)
 108       v[1].n = MP_COPY(v[0].m);
 109
 110     /* --- Now sort out the inverses --- *
 111      *
 112      * @mp_gcd@ will ensure that the first argument is negative.
 113      */
 114
 115     if (!v[0].ni && !v[1].ni) {
 116       mp_gcd(0, &v[0].ni, &v[1].ni, v[0].n, v[1].n);
 117       v[0].ni = mp_add(v[0].ni, v[0].ni, v[1].n);
 118     } else {
 119       int i, j;
 120       mp *x;
 121
 122       if (!v[0].ni)
 123         i = 0, j = 1;
 124       else
 125         i = 1, j = 0;
 126
 127       x = mp_mul(MP_NEW, v[j].n, v[j].ni);
 128       x = mp_sub(x, x, MP_ONE);
 129       mp_div(&x, 0, x, v[i].n);
 130       v[i].ni = x;
 131     }
 132   }
 133
 134   /* --- Set up the Barrett context --- */
 135
 136   mpbarrett_create(&c->mb, n);
 137
 138   /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */
 139
 140   for (i = 0; i < k; i++) {
 141     if (!v[i].n)
 142       mp_div(&v[i].n, 0, n, v[i].m);
 143     if (!v[i].ni)
 144       mp_gcd(0, &v[i].ni, 0, v[i].n, v[i].m);
 145     if (!v[i].nni)
 146       v[i].nni = mp_mul(MP_NEW, v[i].n, v[i].ni);
 147   }
 148
 149   /* --- Done --- */
 150
 151   mp_drop(n);
 152 }
 153
 154 /* --- @mpcrt_destroy@ --- *
 155  *
 156  * Arguments:   @mpcrt *c@ - pointer to CRT context
 157  *
 158  * Returns:     ---
 159  *
 160  * Use:         Destroys a CRT context, releasing all the resources it holds.
 161  */
 162
 163 void mpcrt_destroy(mpcrt *c)
 164 {
 165   size_t i;
 166
 167   for (i = 0; i < c->k; i++) {
 168     if (c->v[i].m) mp_drop(c->v[i].m);
 169     if (c->v[i].n) mp_drop(c->v[i].n);
 170     if (c->v[i].ni) mp_drop(c->v[i].ni);
 171     if (c->v[i].nni) mp_drop(c->v[i].nni);
 172   }
 173   mpbarrett_destroy(&c->mb);
 174 }
 175
 176 /* --- @mpcrt_solve@ --- *
 177  *
 178  * Arguments:   @mpcrt *c@ = pointer to CRT context
 179  *              @mp *d@ = fake destination
 180  *              @mp **v@ = array of residues
 181  *
 182  * Returns:     The unique solution modulo the product of the individual
 183  *              moduli, which leaves the given residues.
 184  *
 185  * Use:         Constructs a result given its residue modulo an array of
 186  *              coprime integers.  This can be used to improve performance of
 187  *              RSA encryption or Blum-Blum-Shub generation if the factors
 188  *              of the modulus are known, since results can be computed mod
 189  *              each of the individual factors and then combined at the end.
 190  *              This is rather faster than doing the full-scale modular
 191  *              exponentiation.
 192  */
 193
 194 mp *mpcrt_solve(mpcrt *c, mp *d, mp **v)
 195 {
 196   mp *a = MP_ZERO;
 197   mp *x = MP_NEW;
 198   size_t i;
 199
 200   for (i = 0; i < c->k; i++) {
 201     x = mp_mul(x, c->v[i].nni, v[i]);
 202     x = mpbarrett_reduce(&c->mb, x, x);
 203     a = mp_add(a, a, x);
 204   }
 205   if (x)
 206     MP_DROP(x);
 207   a = mpbarrett_reduce(&c->mb, a, a);
 208   if (d != MP_NEW)
 209     MP_DROP(d);
 210   return (a);
 211 }
 212
 213 /*----- Test rig ----------------------------------------------------------*/
 214
 215 #ifdef TEST_RIG
 216
 217 static int verify(size_t n, dstr *v)
 218 {
 219   mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod));
 220   mp **r = xmalloc(n * sizeof(mp *));
 221   mpcrt c;
 222   mp *a, *b;
 223   size_t i;
 224   int ok = 1;
 225
 226   for (i = 0; i < n; i++) {
 227     r[i] = *(mp **)v[2 * i].buf;
 228     m[i].m = *(mp **)v[2 * i + 1].buf;
 229     m[i].n = 0;
 230     m[i].ni = 0;
 231     m[i].nni = 0;
 232   }
 233   a = *(mp **)v[2 * n].buf;
 234
 235   mpcrt_create(&c, m, n, 0);
 236   b = mpcrt_solve(&c, MP_NEW, r);
 237
 238   if (!MP_EQ(a, b)) {
 239     fputs("\n*** failed\n", stderr);
 240     fputs("n = ", stderr);
 241     mp_writefile(c.mb.m, stderr, 10);
 242     for (i = 0; i < n; i++) {
 243       fprintf(stderr, "\nr[%u] = ", i);
 244       mp_writefile(r[i], stderr, 10);
 245       fprintf(stderr, "\nm[%u] = ", i);
 246       mp_writefile(m[i].m, stderr, 10);
 247       fprintf(stderr, "\nN[%u] = ", i);
 248       mp_writefile(m[i].n, stderr, 10);
 249       fprintf(stderr, "\nM[%u] = ", i);
 250       mp_writefile(m[i].ni, stderr, 10);
 251     }
 252     fputs("\nresult = ", stderr);
 253     mp_writefile(b, stderr, 10);
 254     fputs("\nexpect = ", stderr);
 255     mp_writefile(a, stderr, 10);
 256     fputc('\n', stderr);
 257     ok = 0;
 258   }
 259
 260   for (i = 0; i < n; i++)
 261     mp_drop(r[i]);
 262   mp_drop(a);
 263   mp_drop(b);
 264   mpcrt_destroy(&c);
 265   free(m);
 266   free(r);
 267   assert(mparena_count(MPARENA_GLOBAL) == 0);
 268   return (ok);
 269 }
 270
 271 static int crt1(dstr *v) { return verify(1, v); }
 272 static int crt2(dstr *v) { return verify(2, v); }
 273 static int crt3(dstr *v) { return verify(3, v); }
 274 static int crt4(dstr *v) { return verify(4, v); }
 275 static int crt5(dstr *v) { return verify(5, v); }
 276
 277 static test_chunk tests[] = {
 278   { "crt-1", crt1, { &type_mp, &type_mp,
 279                     &type_mp, 0 } },
 280   { "crt-2", crt2, { &type_mp, &type_mp,
 281                     &type_mp, &type_mp,
 282                     &type_mp, 0 } },
 283   { "crt-3", crt3, { &type_mp, &type_mp,
 284                     &type_mp, &type_mp,
 285                     &type_mp, &type_mp,
 286                     &type_mp, 0 } },
 287   { "crt-4", crt4, { &type_mp, &type_mp,
 288                     &type_mp, &type_mp,
 289                     &type_mp, &type_mp,
 290                     &type_mp, &type_mp,
 291                     &type_mp, 0 } },
 292   { "crt-5", crt5, { &type_mp, &type_mp,
 293                     &type_mp, &type_mp,
 294                     &type_mp, &type_mp,
 295                     &type_mp, &type_mp,
 296                     &type_mp, &type_mp,
 297                     &type_mp, 0 } },
 298   { 0, 0, { 0 } }
 299 };
 300
 301 int main(int argc, char *argv[])
 302 {
 303   sub_init();
 304   test_run(argc, argv, tests, SRCDIR "/tests/mpcrt");
 305   return (0);
 306 }
 307
 308 #endif
 309
 310 /*----- That's all, folks -------------------------------------------------*/