| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mpbarrett.c,v 1.2 1999/12/11 01:50:56 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 1.2 1999/12/11 01:50:56 mdw |
| 34 | * Improve initialization slightly. |
| 35 | * |
| 36 | * Revision 1.1 1999/12/10 23:21:59 mdw |
| 37 | * Barrett reduction support: works with even moduli. |
| 38 | * |
| 39 | */ |
| 40 | |
| 41 | /*----- Header files ------------------------------------------------------*/ |
| 42 | |
| 43 | #include "mp.h" |
| 44 | #include "mpbarrett.h" |
| 45 | |
| 46 | /*----- Main code ---------------------------------------------------------*/ |
| 47 | |
| 48 | /* --- @mpbarrett_create@ --- * |
| 49 | * |
| 50 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 51 | * @mp *m@ = modulus to work to |
| 52 | * |
| 53 | * |
| 54 | * Returns: --- |
| 55 | * |
| 56 | * Use: Initializes a Barrett reduction context ready for use. |
| 57 | */ |
| 58 | |
| 59 | void mpbarrett_create(mpbarrett *mb, mp *m) |
| 60 | { |
| 61 | mp *b; |
| 62 | |
| 63 | /* --- Validate the arguments --- */ |
| 64 | |
| 65 | assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0)); |
| 66 | |
| 67 | /* --- Compute %$\mu$% --- */ |
| 68 | |
| 69 | mp_shrink(m); |
| 70 | mb->k = MP_LEN(m); |
| 71 | mb->m = MP_COPY(m); |
| 72 | b = mp_create(2 * mb->k + 1); |
| 73 | MPX_ZERO(b->v, b->vl - 1); |
| 74 | b->vl[-1] = 1; |
| 75 | mp_div(&b, 0, b, m); |
| 76 | mb->mu = b; |
| 77 | } |
| 78 | |
| 79 | /* --- @mpbarrett_destroy@ --- * |
| 80 | * |
| 81 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 82 | * |
| 83 | * Returns: --- |
| 84 | * |
| 85 | * Use: Destroys a Barrett reduction context releasing any resources |
| 86 | * claimed. |
| 87 | */ |
| 88 | |
| 89 | void mpbarrett_destroy(mpbarrett *mb) |
| 90 | { |
| 91 | mp_drop(mb->m); |
| 92 | mp_drop(mb->mu); |
| 93 | } |
| 94 | |
| 95 | /* --- @mpbarrett_reduce@ --- * |
| 96 | * |
| 97 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 98 | * @mp *d@ = destination for result |
| 99 | * @mp *m@ = number to reduce |
| 100 | * |
| 101 | * Returns: The residue of @m@ modulo the number in the reduction |
| 102 | * context. |
| 103 | * |
| 104 | * Use: Performs an efficient modular reduction. The argument is |
| 105 | * assumed to be positive. |
| 106 | */ |
| 107 | |
| 108 | mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m) |
| 109 | { |
| 110 | mp *q; |
| 111 | size_t k = mb->k; |
| 112 | |
| 113 | /* --- Special case if @m@ is too small --- */ |
| 114 | |
| 115 | if (MP_LEN(m) < k) { |
| 116 | m = MP_COPY(m); |
| 117 | MP_DROP(d); |
| 118 | return (m); |
| 119 | } |
| 120 | |
| 121 | /* --- First stage --- */ |
| 122 | |
| 123 | { |
| 124 | mp qq; |
| 125 | mp_build(&qq, m->v + (k - 1), m->vl); |
| 126 | q = mp_mul(MP_NEW, &qq, mb->mu); |
| 127 | q = mp_lsr(q, q, MPW_BITS * (k + 1)); |
| 128 | } |
| 129 | |
| 130 | /* --- Second stage --- */ |
| 131 | |
| 132 | { |
| 133 | mp *r; |
| 134 | mpw *mvl; |
| 135 | |
| 136 | MP_COPY(m); |
| 137 | if (MP_LEN(m) <= k + 1) |
| 138 | mvl = m->vl; |
| 139 | else |
| 140 | mvl = m->v + k + 1; |
| 141 | r = mp_create(k + 1); |
| 142 | mpx_umul(r->v, r->vl, q->v, q->vl, mb->m->v, mb->m->vl); |
| 143 | r->f = (q->f | mb->m->f) & MP_BURN; |
| 144 | MP_MODIFY(d, k + 1); |
| 145 | mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl); |
| 146 | d->f = (m->f | r->f) & MP_BURN; |
| 147 | MP_DROP(r); |
| 148 | MP_DROP(q); |
| 149 | MP_DROP(m); |
| 150 | } |
| 151 | |
| 152 | /* --- Final stage --- */ |
| 153 | |
| 154 | MP_SHRINK(d); |
| 155 | while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl)) |
| 156 | mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl); |
| 157 | |
| 158 | MP_SHRINK(d); |
| 159 | return (d); |
| 160 | } |
| 161 | |
| 162 | /* --- @mpbarrett_exp@ --- * |
| 163 | * |
| 164 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 165 | * @mp *d@ = fake destination |
| 166 | * @mp *a@ = base |
| 167 | * @mp *e@ = exponent |
| 168 | * |
| 169 | * Returns: Result, %$a^e \bmod m$%. |
| 170 | */ |
| 171 | |
| 172 | mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e) |
| 173 | { |
| 174 | mpscan sc; |
| 175 | mp *x = MP_ONE; |
| 176 | mp *spare = MP_NEW; |
| 177 | |
| 178 | a = MP_COPY(a); |
| 179 | mp_scan(&sc, e); |
| 180 | if (MP_STEP(&sc)) { |
| 181 | size_t sq = 0; |
| 182 | for (;;) { |
| 183 | mp *dd; |
| 184 | if (MP_BIT(&sc)) { |
| 185 | while (sq) { |
| 186 | dd = mp_sqr(spare, a); |
| 187 | dd = mpbarrett_reduce(mb, dd, dd); |
| 188 | spare = a; a = dd; |
| 189 | sq--; |
| 190 | } |
| 191 | dd = mp_mul(spare, x, a); |
| 192 | dd = mpbarrett_reduce(mb, dd, dd); |
| 193 | spare = x; x = dd; |
| 194 | } |
| 195 | sq++; |
| 196 | if (!MP_STEP(&sc)) |
| 197 | break; |
| 198 | } |
| 199 | } |
| 200 | |
| 201 | MP_DROP(a); |
| 202 | if (spare != MP_NEW) |
| 203 | MP_DROP(spare); |
| 204 | if (d != MP_NEW) |
| 205 | MP_DROP(d); |
| 206 | return (x); |
| 207 | } |
| 208 | |
| 209 | /*----- Test rig ----------------------------------------------------------*/ |
| 210 | |
| 211 | #ifdef TEST_RIG |
| 212 | |
| 213 | static int vmod(dstr *v) |
| 214 | { |
| 215 | mp *x = *(mp **)v[0].buf; |
| 216 | mp *n = *(mp **)v[1].buf; |
| 217 | mp *r = *(mp **)v[2].buf; |
| 218 | mp *s; |
| 219 | mpbarrett mb; |
| 220 | int ok = 1; |
| 221 | |
| 222 | mpbarrett_create(&mb, n); |
| 223 | s = mpbarrett_reduce(&mb, MP_NEW, x); |
| 224 | |
| 225 | if (MP_CMP(s, !=, r)) { |
| 226 | fputs("\n*** barrett reduction failure\n", stderr); |
| 227 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
| 228 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
| 229 | fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr); |
| 230 | fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr); |
| 231 | ok = 0; |
| 232 | } |
| 233 | |
| 234 | mpbarrett_destroy(&mb); |
| 235 | mp_drop(x); |
| 236 | mp_drop(n); |
| 237 | mp_drop(r); |
| 238 | mp_drop(s); |
| 239 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 240 | return (ok); |
| 241 | } |
| 242 | |
| 243 | static int vexp(dstr *v) |
| 244 | { |
| 245 | mp *m = *(mp **)v[0].buf; |
| 246 | mp *a = *(mp **)v[1].buf; |
| 247 | mp *b = *(mp **)v[2].buf; |
| 248 | mp *r = *(mp **)v[3].buf; |
| 249 | mp *mr; |
| 250 | int ok = 1; |
| 251 | |
| 252 | mpbarrett mb; |
| 253 | mpbarrett_create(&mb, m); |
| 254 | |
| 255 | mr = mpbarrett_exp(&mb, MP_NEW, a, b); |
| 256 | |
| 257 | if (MP_CMP(mr, !=, r)) { |
| 258 | fputs("\n*** barrett modexp failed", stderr); |
| 259 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
| 260 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
| 261 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
| 262 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
| 263 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
| 264 | fputc('\n', stderr); |
| 265 | ok = 0; |
| 266 | } |
| 267 | |
| 268 | mp_drop(m); |
| 269 | mp_drop(a); |
| 270 | mp_drop(b); |
| 271 | mp_drop(r); |
| 272 | mp_drop(mr); |
| 273 | mpbarrett_destroy(&mb); |
| 274 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 275 | return ok; |
| 276 | } |
| 277 | |
| 278 | static test_chunk tests[] = { |
| 279 | { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } }, |
| 280 | { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
| 281 | { 0, 0, { 0 } } |
| 282 | }; |
| 283 | |
| 284 | int main(int argc, char *argv[]) |
| 285 | { |
| 286 | sub_init(); |
| 287 | test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett"); |
| 288 | return (0); |
| 289 | } |
| 290 | |
| 291 | #endif |
| 292 | |
| 293 | /*----- That's all, folks -------------------------------------------------*/ |