| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mpbarrett.c,v 1.5 2000/07/29 17:04:33 mdw Exp $ |
| 4 | * |
| 5 | * Barrett modular reduction |
| 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: mpbarrett.c,v $ |
| 33 | * Revision 1.5 2000/07/29 17:04:33 mdw |
| 34 | * Change to use left-to-right bitwise exponentiation. This will improve |
| 35 | * performance when the base is small. |
| 36 | * |
| 37 | * Revision 1.4 2000/06/17 11:45:09 mdw |
| 38 | * Major memory management overhaul. Added arena support. Use the secure |
| 39 | * arena for secret integers. Replace and improve the MP management macros |
| 40 | * (e.g., replace MP_MODIFY by MP_DEST). |
| 41 | * |
| 42 | * Revision 1.3 1999/12/12 15:08:52 mdw |
| 43 | * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least |
| 44 | * significant digits. |
| 45 | * |
| 46 | * Revision 1.2 1999/12/11 01:50:56 mdw |
| 47 | * Improve initialization slightly. |
| 48 | * |
| 49 | * Revision 1.1 1999/12/10 23:21:59 mdw |
| 50 | * Barrett reduction support: works with even moduli. |
| 51 | * |
| 52 | */ |
| 53 | |
| 54 | /*----- Header files ------------------------------------------------------*/ |
| 55 | |
| 56 | #include "mp.h" |
| 57 | #include "mpbarrett.h" |
| 58 | |
| 59 | /*----- Main code ---------------------------------------------------------*/ |
| 60 | |
| 61 | /* --- @mpbarrett_create@ --- * |
| 62 | * |
| 63 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 64 | * @mp *m@ = modulus to work to |
| 65 | * |
| 66 | * |
| 67 | * Returns: --- |
| 68 | * |
| 69 | * Use: Initializes a Barrett reduction context ready for use. |
| 70 | */ |
| 71 | |
| 72 | void mpbarrett_create(mpbarrett *mb, mp *m) |
| 73 | { |
| 74 | mp *b; |
| 75 | |
| 76 | /* --- Validate the arguments --- */ |
| 77 | |
| 78 | assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0)); |
| 79 | |
| 80 | /* --- Compute %$\mu$% --- */ |
| 81 | |
| 82 | mp_shrink(m); |
| 83 | mb->k = MP_LEN(m); |
| 84 | mb->m = MP_COPY(m); |
| 85 | b = mp_new(2 * mb->k + 1, 0); |
| 86 | MPX_ZERO(b->v, b->vl - 1); |
| 87 | b->vl[-1] = 1; |
| 88 | mp_div(&b, 0, b, m); |
| 89 | mb->mu = b; |
| 90 | } |
| 91 | |
| 92 | /* --- @mpbarrett_destroy@ --- * |
| 93 | * |
| 94 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 95 | * |
| 96 | * Returns: --- |
| 97 | * |
| 98 | * Use: Destroys a Barrett reduction context releasing any resources |
| 99 | * claimed. |
| 100 | */ |
| 101 | |
| 102 | void mpbarrett_destroy(mpbarrett *mb) |
| 103 | { |
| 104 | mp_drop(mb->m); |
| 105 | mp_drop(mb->mu); |
| 106 | } |
| 107 | |
| 108 | /* --- @mpbarrett_reduce@ --- * |
| 109 | * |
| 110 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 111 | * @mp *d@ = destination for result |
| 112 | * @mp *m@ = number to reduce |
| 113 | * |
| 114 | * Returns: The residue of @m@ modulo the number in the reduction |
| 115 | * context. |
| 116 | * |
| 117 | * Use: Performs an efficient modular reduction. The argument is |
| 118 | * assumed to be positive. |
| 119 | */ |
| 120 | |
| 121 | mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m) |
| 122 | { |
| 123 | mp *q; |
| 124 | size_t k = mb->k; |
| 125 | |
| 126 | /* --- Special case if @m@ is too small --- */ |
| 127 | |
| 128 | if (MP_LEN(m) < k) { |
| 129 | m = MP_COPY(m); |
| 130 | if (d) |
| 131 | MP_DROP(d); |
| 132 | return (m); |
| 133 | } |
| 134 | |
| 135 | /* --- First stage --- */ |
| 136 | |
| 137 | { |
| 138 | mp qq; |
| 139 | mp_build(&qq, m->v + (k - 1), m->vl); |
| 140 | q = mp_mul(MP_NEW, &qq, mb->mu); |
| 141 | if (MP_LEN(q) <= k) { |
| 142 | m = MP_COPY(m); |
| 143 | if (d) |
| 144 | MP_DROP(d); |
| 145 | return (m); |
| 146 | } |
| 147 | } |
| 148 | |
| 149 | /* --- Second stage --- */ |
| 150 | |
| 151 | { |
| 152 | mp *r; |
| 153 | mpw *mvl; |
| 154 | |
| 155 | MP_COPY(m); |
| 156 | if (MP_LEN(m) <= k + 1) |
| 157 | mvl = m->vl; |
| 158 | else |
| 159 | mvl = m->v + k + 1; |
| 160 | r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN); |
| 161 | mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl); |
| 162 | MP_DEST(d, k + 1, r->f); |
| 163 | mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl); |
| 164 | d->f = (m->f | r->f) & MP_BURN; |
| 165 | MP_DROP(r); |
| 166 | MP_DROP(q); |
| 167 | MP_DROP(m); |
| 168 | } |
| 169 | |
| 170 | /* --- Final stage --- */ |
| 171 | |
| 172 | MP_SHRINK(d); |
| 173 | while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl)) |
| 174 | mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl); |
| 175 | |
| 176 | MP_SHRINK(d); |
| 177 | return (d); |
| 178 | } |
| 179 | |
| 180 | /* --- @mpbarrett_exp@ --- * |
| 181 | * |
| 182 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 183 | * @mp *d@ = fake destination |
| 184 | * @mp *a@ = base |
| 185 | * @mp *e@ = exponent |
| 186 | * |
| 187 | * Returns: Result, %$a^e \bmod m$%. |
| 188 | */ |
| 189 | |
| 190 | mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e) |
| 191 | { |
| 192 | mpscan sc; |
| 193 | mp *x = MP_ONE; |
| 194 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
| 195 | unsigned sq = 0; |
| 196 | |
| 197 | a = MP_COPY(a); |
| 198 | mp_rscan(&sc, e); |
| 199 | if (!MP_RSTEP(&sc)) |
| 200 | goto exit; |
| 201 | while (!MP_RBIT(&sc)) |
| 202 | MP_RSTEP(&sc); |
| 203 | |
| 204 | /* --- Do the main body of the work --- */ |
| 205 | |
| 206 | for (;;) { |
| 207 | sq++; |
| 208 | while (sq) { |
| 209 | mp *y; |
| 210 | y = mp_sqr(spare, x); |
| 211 | y = mpbarrett_reduce(mb, y, y); |
| 212 | spare = x; x = y; |
| 213 | sq--; |
| 214 | } |
| 215 | { |
| 216 | mp *y = mp_mul(spare, x, a); |
| 217 | y = mpbarrett_reduce(mb, y, y); |
| 218 | spare = x; x = y; |
| 219 | } |
| 220 | for (;;) { |
| 221 | if (!MP_RSTEP(&sc)) |
| 222 | goto done; |
| 223 | if (MP_RBIT(&sc)) |
| 224 | break; |
| 225 | sq++; |
| 226 | } |
| 227 | } |
| 228 | |
| 229 | /* --- Do a final round of squaring --- */ |
| 230 | |
| 231 | done: |
| 232 | while (sq) { |
| 233 | mp *y; |
| 234 | y = mp_sqr(spare, x); |
| 235 | y = mpbarrett_reduce(mb, y, y); |
| 236 | spare = x; x = y; |
| 237 | sq--; |
| 238 | } |
| 239 | |
| 240 | exit: |
| 241 | MP_DROP(a); |
| 242 | if (spare != MP_NEW) |
| 243 | MP_DROP(spare); |
| 244 | if (d != MP_NEW) |
| 245 | MP_DROP(d); |
| 246 | return (x); |
| 247 | } |
| 248 | |
| 249 | /*----- Test rig ----------------------------------------------------------*/ |
| 250 | |
| 251 | #ifdef TEST_RIG |
| 252 | |
| 253 | static int vmod(dstr *v) |
| 254 | { |
| 255 | mp *x = *(mp **)v[0].buf; |
| 256 | mp *n = *(mp **)v[1].buf; |
| 257 | mp *r = *(mp **)v[2].buf; |
| 258 | mp *s; |
| 259 | mpbarrett mb; |
| 260 | int ok = 1; |
| 261 | |
| 262 | mpbarrett_create(&mb, n); |
| 263 | s = mpbarrett_reduce(&mb, MP_NEW, x); |
| 264 | |
| 265 | if (MP_CMP(s, !=, r)) { |
| 266 | fputs("\n*** barrett reduction failure\n", stderr); |
| 267 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
| 268 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
| 269 | fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr); |
| 270 | fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr); |
| 271 | ok = 0; |
| 272 | } |
| 273 | |
| 274 | mpbarrett_destroy(&mb); |
| 275 | mp_drop(x); |
| 276 | mp_drop(n); |
| 277 | mp_drop(r); |
| 278 | mp_drop(s); |
| 279 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 280 | return (ok); |
| 281 | } |
| 282 | |
| 283 | static int vexp(dstr *v) |
| 284 | { |
| 285 | mp *m = *(mp **)v[0].buf; |
| 286 | mp *a = *(mp **)v[1].buf; |
| 287 | mp *b = *(mp **)v[2].buf; |
| 288 | mp *r = *(mp **)v[3].buf; |
| 289 | mp *mr; |
| 290 | int ok = 1; |
| 291 | |
| 292 | mpbarrett mb; |
| 293 | mpbarrett_create(&mb, m); |
| 294 | |
| 295 | mr = mpbarrett_exp(&mb, MP_NEW, a, b); |
| 296 | |
| 297 | if (MP_CMP(mr, !=, r)) { |
| 298 | fputs("\n*** barrett modexp failed", stderr); |
| 299 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
| 300 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
| 301 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
| 302 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
| 303 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
| 304 | fputc('\n', stderr); |
| 305 | ok = 0; |
| 306 | } |
| 307 | |
| 308 | mp_drop(m); |
| 309 | mp_drop(a); |
| 310 | mp_drop(b); |
| 311 | mp_drop(r); |
| 312 | mp_drop(mr); |
| 313 | mpbarrett_destroy(&mb); |
| 314 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 315 | return ok; |
| 316 | } |
| 317 | |
| 318 | static test_chunk tests[] = { |
| 319 | { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } }, |
| 320 | { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
| 321 | { 0, 0, { 0 } } |
| 322 | }; |
| 323 | |
| 324 | int main(int argc, char *argv[]) |
| 325 | { |
| 326 | sub_init(); |
| 327 | test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett"); |
| 328 | return (0); |
| 329 | } |
| 330 | |
| 331 | #endif |
| 332 | |
| 333 | /*----- That's all, folks -------------------------------------------------*/ |