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