| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Normal-basis translation for binary fields |
| 4 | * |
| 5 | * (c) 2004 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of Catacomb. |
| 11 | * |
| 12 | * Catacomb is free software; you can redistribute it and/or modify |
| 13 | * it under the terms of the GNU Library General Public License as |
| 14 | * published by the Free Software Foundation; either version 2 of the |
| 15 | * License, or (at your option) any later version. |
| 16 | * |
| 17 | * Catacomb is distributed in the hope that it will be useful, |
| 18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 20 | * GNU Library General Public License for more details. |
| 21 | * |
| 22 | * You should have received a copy of the GNU Library General Public |
| 23 | * License along with Catacomb; if not, write to the Free |
| 24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 25 | * MA 02111-1307, USA. |
| 26 | */ |
| 27 | |
| 28 | /*----- Header files ------------------------------------------------------*/ |
| 29 | |
| 30 | #include "gfreduce.h" |
| 31 | #include "gfn.h" |
| 32 | |
| 33 | /*----- Main code ---------------------------------------------------------*/ |
| 34 | |
| 35 | /* --- @gfn_copy@ --- * |
| 36 | * |
| 37 | * Arguments: @gfn *d@ = where to put the copy |
| 38 | * @const gfn *s@ = where the source is |
| 39 | * |
| 40 | * Returns: --- |
| 41 | * |
| 42 | * Use: Makes a copy of a translation matrix. |
| 43 | */ |
| 44 | |
| 45 | void gfn_copy(gfn *d, const gfn *s) |
| 46 | { |
| 47 | size_t i; |
| 48 | |
| 49 | d->n = s->n; |
| 50 | d->r = xmalloc(s->n * sizeof(mp *)); |
| 51 | for (i = 0; i < s->n; i++) |
| 52 | d->r[i] = MP_COPY(s->r[i]); |
| 53 | } |
| 54 | |
| 55 | /* --- @gfn_destroy@ --- * |
| 56 | * |
| 57 | * Arguments: @gfn *m@ = a transformation matrix to free |
| 58 | * |
| 59 | * Returns: --- |
| 60 | * |
| 61 | * Use: Frees up a transformation matrix when it's no longer wanted. |
| 62 | */ |
| 63 | |
| 64 | void gfn_destroy(gfn *m) |
| 65 | { size_t i; for (i = 0; i < m->n; i++) MP_DROP(m->r[i]); xfree(m->r); } |
| 66 | |
| 67 | /* --- @gfn_identity@ --- * |
| 68 | * |
| 69 | * Arguments: @gfn *m@ = where to put the matrix |
| 70 | * @size_t n@ = size of the matrix |
| 71 | * |
| 72 | * Returns: --- |
| 73 | * |
| 74 | * Use: Fills @m@ with an identity matrix. |
| 75 | */ |
| 76 | |
| 77 | void gfn_identity(gfn *m, size_t n) |
| 78 | { |
| 79 | size_t i; |
| 80 | |
| 81 | m->n = n; |
| 82 | m->r = xmalloc(n * sizeof(mp *)); |
| 83 | m->r[0] = MP_ONE; |
| 84 | for (i = 1; i < n; i++) |
| 85 | m->r[i] = mp_lsl(MP_NEW, m->r[i - 1], 1); |
| 86 | } |
| 87 | |
| 88 | /* --- @gfn_invert@ --- * |
| 89 | * |
| 90 | * Arguments: @gfn *m@ = a transformation matrix |
| 91 | * |
| 92 | * Returns: Zero if successful, nonzero if the matrix was singular. |
| 93 | * |
| 94 | * Use: Inverts a transformation matrix. |
| 95 | */ |
| 96 | |
| 97 | int gfn_invert(gfn *m) |
| 98 | { |
| 99 | size_t i, j; |
| 100 | gfn mm; |
| 101 | mp *t; |
| 102 | int rc = -1; |
| 103 | |
| 104 | mm = *m; |
| 105 | gfn_identity(m, mm.n); |
| 106 | for (i = 0; i < mm.n; i++) { |
| 107 | if (!mp_testbit(mm.r[i], i)) { |
| 108 | for (j = i + 1; j < mm.n; j++) { |
| 109 | if (mp_testbit(mm.r[j], i)) |
| 110 | goto found_set; |
| 111 | } |
| 112 | goto fail; |
| 113 | found_set: |
| 114 | t = mm.r[i]; mm.r[i] = mm.r[j]; mm.r[j] = t; |
| 115 | t = m->r[i]; m->r[i] = m->r[j]; m->r[j] = t; |
| 116 | } |
| 117 | for (j = 0; j < mm.n; j++) { |
| 118 | if (j == i) continue; |
| 119 | if (mp_testbit(mm.r[j], i)) { |
| 120 | mm.r[j] = mp_xor(mm.r[j], mm.r[j], mm.r[i]); |
| 121 | m->r[j] = mp_xor(m->r[j], m->r[j], m->r[i]); |
| 122 | } |
| 123 | } |
| 124 | } |
| 125 | rc = 0; |
| 126 | fail: |
| 127 | gfn_destroy(&mm); |
| 128 | return (rc); |
| 129 | } |
| 130 | |
| 131 | /* --- @gfn_transform@ --- * |
| 132 | * |
| 133 | * Arguments: @gfn *m@ = conversion matrix to apply |
| 134 | * @mp *d@ = destination pointer |
| 135 | * @mp *x@ = input value |
| 136 | * |
| 137 | * Returns: The transformed element. |
| 138 | * |
| 139 | * Use: Transforms a field element according to the given matrix. |
| 140 | */ |
| 141 | |
| 142 | mp *gfn_transform(gfn *m, mp *d, mp *x) |
| 143 | { |
| 144 | mp *y = MP_ZERO; |
| 145 | size_t i; |
| 146 | mpscan sc; |
| 147 | |
| 148 | for (i = 0, mp_scan(&sc, x); i < m->n && mp_step(&sc); i++) |
| 149 | if (mp_bit(&sc)) y = mp_xor(y, y, m->r[i]); |
| 150 | mp_drop(d); |
| 151 | return (y); |
| 152 | } |
| 153 | |
| 154 | /* --- @gfn_create@ --- * |
| 155 | * |
| 156 | * Arguments: @mp *p@ = modulus for polynomial basis |
| 157 | * @mp *beta@ = the generator of the normal basis, expressed |
| 158 | * relative to the polynomial basis |
| 159 | * @gfn *ntop@ = output normal-to-polynomail conversion matrix |
| 160 | * @gfn *pton@ = output polynomial-to-normal conversion matrix |
| 161 | * |
| 162 | * Returns: Zero if it worked, nonzero otherwise (e.g., if %$\beta$% |
| 163 | * doesn't generate a proper basis). |
| 164 | * |
| 165 | * Use: Constructs conversion matrices between polynomial and normal |
| 166 | * basis representations of binary field elements. |
| 167 | */ |
| 168 | |
| 169 | int gfn_create(mp *p, mp *beta, gfn *ntop, gfn *pton) |
| 170 | { |
| 171 | size_t m = mp_bits(p) - 1; |
| 172 | size_t i; |
| 173 | gfreduce gr; |
| 174 | gfn *np, tmp; |
| 175 | |
| 176 | /* --- We start by building the the @ntop@ matrix --- * |
| 177 | * |
| 178 | * For mad reasons, the string representation of normal-basis elements is |
| 179 | * backwards. |
| 180 | */ |
| 181 | |
| 182 | gfreduce_create(&gr, p); |
| 183 | np = ntop ? ntop : &tmp; |
| 184 | np->n = m; |
| 185 | np->r = xmalloc(m * sizeof(mp *)); |
| 186 | np->r[m - 1] = MP_COPY(beta); |
| 187 | for (i = m - 1; i--; ) { |
| 188 | mp *x = gf_sqr(MP_NEW, np->r[i + 1]); |
| 189 | np->r[i] = gfreduce_do(&gr, x, x); |
| 190 | } |
| 191 | gfreduce_destroy(&gr); |
| 192 | |
| 193 | /* --- That was easy -- now invert it --- */ |
| 194 | |
| 195 | if (pton) { |
| 196 | if (ntop) gfn_copy(pton, np); else *pton = *np; |
| 197 | if (gfn_invert(pton)) { |
| 198 | gfn_destroy(pton); |
| 199 | if (ntop) gfn_destroy(ntop); |
| 200 | return (-1); |
| 201 | } |
| 202 | } |
| 203 | |
| 204 | /* --- And we're done --- */ |
| 205 | |
| 206 | return (0); |
| 207 | } |
| 208 | |
| 209 | /*----- Test rig ----------------------------------------------------------*/ |
| 210 | |
| 211 | #ifdef TEST_RIG |
| 212 | |
| 213 | static int check(dstr *v) |
| 214 | { |
| 215 | mp *p = *(mp **)v[0].buf; |
| 216 | mp *beta = *(mp **)v[1].buf; |
| 217 | mp *xp = *(mp **)v[2].buf; |
| 218 | mp *xn = *(mp **)v[3].buf; |
| 219 | mp *y = MP_NEW; |
| 220 | gfn pton, ntop, ii; |
| 221 | size_t i; |
| 222 | int ok = 1; |
| 223 | |
| 224 | gfn_create(p, beta, &ntop, &pton); |
| 225 | gfn_identity(&ii, pton.n); |
| 226 | for (i = 0; i < pton.n; i++) { |
| 227 | y = gfn_transform(&ntop, y, pton.r[i]); |
| 228 | if (!MP_EQ(y, ii.r[i])) { |
| 229 | ok = 0; |
| 230 | fprintf(stderr, "*** inverse pton->ntop check failed (row %lu)\n", |
| 231 | (unsigned long)i); |
| 232 | MP_EPRINTX("*** p", p); MP_EPRINTX("*** beta", beta); |
| 233 | MP_EPRINTX("*** computed", y); |
| 234 | } |
| 235 | } |
| 236 | gfn_destroy(&ii); |
| 237 | y = gfn_transform(&pton, y, xp); |
| 238 | if (!MP_EQ(y, xn)) { |
| 239 | ok = 0; |
| 240 | fprintf(stderr, "*** pton failed\n"); |
| 241 | MP_EPRINTX("*** p", p); MP_EPRINTX("*** beta", beta); |
| 242 | MP_EPRINTX("*** xp", xp); MP_EPRINTX("*** xn", xn); |
| 243 | MP_EPRINTX("*** computed", y); |
| 244 | } |
| 245 | y = gfn_transform(&ntop, y, xn); |
| 246 | if (!MP_EQ(y, xp)) { |
| 247 | ok = 0; |
| 248 | fprintf(stderr, "*** ntop failed\n"); |
| 249 | MP_EPRINTX("*** p", p); MP_EPRINTX("*** beta", beta); |
| 250 | MP_EPRINTX("*** xp", xp); MP_EPRINTX("*** xn", xn); |
| 251 | MP_EPRINTX("*** computed", y); |
| 252 | } |
| 253 | gfn_destroy(&pton); gfn_destroy(&ntop); |
| 254 | mp_drop(p); mp_drop(beta); mp_drop(xp); mp_drop(xn); mp_drop(y); |
| 255 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 256 | return (ok); |
| 257 | } |
| 258 | |
| 259 | static test_chunk tests[] = { |
| 260 | { "gfn", check, { &type_mp, &type_mp, &type_mp, &type_mp } }, |
| 261 | { 0 } |
| 262 | }; |
| 263 | |
| 264 | int main(int argc, char *argv[]) |
| 265 | { |
| 266 | test_run(argc, argv, tests, SRCDIR "/t/gfn"); |
| 267 | return (0); |
| 268 | } |
| 269 | |
| 270 | #endif |
| 271 | |
| 272 | /*----- That's all, folks -------------------------------------------------*/ |