| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Elliptic curve definitions |
| 4 | * |
| 5 | * (c) 2001 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 "ec.h" |
| 31 | |
| 32 | /*----- Trivial wrappers --------------------------------------------------*/ |
| 33 | |
| 34 | /* --- @ec_samep@ --- * |
| 35 | * |
| 36 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
| 37 | * |
| 38 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
| 39 | * |
| 40 | * Use: Checks for sameness of curves. This function does the full |
| 41 | * check, not just the curve-type-specific check done by the |
| 42 | * @sampep@ field operation. |
| 43 | */ |
| 44 | |
| 45 | int ec_samep(ec_curve *c, ec_curve *d) |
| 46 | { |
| 47 | return (c == d || (field_samep(c->f, d->f) && |
| 48 | c->ops == d->ops && EC_SAMEP(c, d))); |
| 49 | } |
| 50 | |
| 51 | /* --- @ec_create@ --- * |
| 52 | * |
| 53 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
| 54 | * |
| 55 | * Returns: The argument @p@. |
| 56 | * |
| 57 | * Use: Initializes a new point. The initial value is the additive |
| 58 | * identity (which is universal for all curves). |
| 59 | */ |
| 60 | |
| 61 | ec *ec_create(ec *p) { EC_CREATE(p); return (p); } |
| 62 | |
| 63 | /* --- @ec_destroy@ --- * |
| 64 | * |
| 65 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
| 66 | * |
| 67 | * Returns: --- |
| 68 | * |
| 69 | * Use: Destroys a point, making it invalid. |
| 70 | */ |
| 71 | |
| 72 | void ec_destroy(ec *p) { EC_DESTROY(p); } |
| 73 | |
| 74 | /* --- @ec_atinf@ --- * |
| 75 | * |
| 76 | * Arguments: @const ec *p@ = pointer to a point |
| 77 | * |
| 78 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
| 79 | * otherwise. |
| 80 | */ |
| 81 | |
| 82 | int ec_atinf(const ec *p) { return (EC_ATINF(p)); } |
| 83 | |
| 84 | /* --- @ec_setinf@ --- * |
| 85 | * |
| 86 | * Arguments: @ec *p@ = pointer to a point |
| 87 | * |
| 88 | * Returns: The argument @p@. |
| 89 | * |
| 90 | * Use: Sets the given point to be the point %$O$% at infinity. |
| 91 | */ |
| 92 | |
| 93 | ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); } |
| 94 | |
| 95 | /* --- @ec_copy@ --- * |
| 96 | * |
| 97 | * Arguments: @ec *d@ = pointer to destination point |
| 98 | * @const ec *p@ = pointer to source point |
| 99 | * |
| 100 | * Returns: The destination @d@. |
| 101 | * |
| 102 | * Use: Creates a copy of an elliptic curve point. |
| 103 | */ |
| 104 | |
| 105 | ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); } |
| 106 | |
| 107 | /* --- @ec_eq@ --- * |
| 108 | * |
| 109 | * Arguments: @const ec *p, *q@ = two points |
| 110 | * |
| 111 | * Returns: Nonzero if the points are equal. Compares external-format |
| 112 | * points. |
| 113 | */ |
| 114 | |
| 115 | int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); } |
| 116 | |
| 117 | /*----- Standard curve operations -----------------------------------------*/ |
| 118 | |
| 119 | /* --- @ec_stdsamep@ --- * |
| 120 | * |
| 121 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
| 122 | * |
| 123 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
| 124 | * |
| 125 | * Use: Simple sameness check on @a@ and @b@ curve members. |
| 126 | */ |
| 127 | |
| 128 | int ec_stdsamep(ec_curve *c, ec_curve *d) |
| 129 | { return (MP_EQ(c->a, d->a) && MP_EQ(c->b, d->b)); } |
| 130 | |
| 131 | /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * |
| 132 | * |
| 133 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 134 | * @ec *d@ = pointer to the destination |
| 135 | * @const ec *p@ = pointer to a source point |
| 136 | * |
| 137 | * Returns: The destination @d@. |
| 138 | * |
| 139 | * Use: An identity operation if your curve has no internal |
| 140 | * representation. (The field internal representation is still |
| 141 | * used.) |
| 142 | */ |
| 143 | |
| 144 | ec *ec_idin(ec_curve *c, ec *d, const ec *p) |
| 145 | { |
| 146 | if (EC_ATINF(p)) |
| 147 | EC_SETINF(d); |
| 148 | else { |
| 149 | field *f = c->f; |
| 150 | d->x = F_IN(f, d->x, p->x); |
| 151 | d->y = F_IN(f, d->y, p->y); |
| 152 | mp_drop(d->z); d->z = 0; |
| 153 | } |
| 154 | return (d); |
| 155 | } |
| 156 | |
| 157 | ec *ec_idout(ec_curve *c, ec *d, const ec *p) |
| 158 | { |
| 159 | if (EC_ATINF(p)) |
| 160 | EC_SETINF(d); |
| 161 | else { |
| 162 | field *f = c->f; |
| 163 | d->x = F_OUT(f, d->x, p->x); |
| 164 | d->y = F_OUT(f, d->y, p->y); |
| 165 | mp_drop(d->z); d->z = 0; |
| 166 | } |
| 167 | return (d); |
| 168 | } |
| 169 | |
| 170 | ec *ec_idfix(ec_curve *c, ec *d, const ec *p) |
| 171 | { EC_COPY(d, p); return (d); } |
| 172 | |
| 173 | /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * |
| 174 | * |
| 175 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 176 | * @ec *d@ = pointer to the destination |
| 177 | * @const ec *p@ = pointer to a source point |
| 178 | * |
| 179 | * Returns: The destination @d@. |
| 180 | * |
| 181 | * Use: Conversion functions if your curve operations use a |
| 182 | * projective representation. |
| 183 | */ |
| 184 | |
| 185 | ec *ec_projin(ec_curve *c, ec *d, const ec *p) |
| 186 | { |
| 187 | if (EC_ATINF(p)) |
| 188 | EC_SETINF(d); |
| 189 | else { |
| 190 | field *f = c->f; |
| 191 | d->x = F_IN(f, d->x, p->x); |
| 192 | d->y = F_IN(f, d->y, p->y); |
| 193 | mp_drop(d->z); d->z = MP_COPY(f->one); |
| 194 | } |
| 195 | return (d); |
| 196 | } |
| 197 | |
| 198 | ec *ec_projout(ec_curve *c, ec *d, const ec *p) |
| 199 | { |
| 200 | if (EC_ATINF(p)) |
| 201 | EC_SETINF(d); |
| 202 | else { |
| 203 | mp *x, *y, *z, *zz; |
| 204 | field *f = c->f; |
| 205 | if (p->z == f->one) { |
| 206 | d->x = F_OUT(f, d->x, p->x); |
| 207 | d->y = F_OUT(f, d->y, p->y); |
| 208 | } else { |
| 209 | z = F_INV(f, MP_NEW, p->z); |
| 210 | zz = F_SQR(f, MP_NEW, z); |
| 211 | z = F_MUL(f, z, zz, z); |
| 212 | x = F_MUL(f, d->x, p->x, zz); |
| 213 | y = F_MUL(f, d->y, p->y, z); |
| 214 | mp_drop(z); |
| 215 | mp_drop(zz); |
| 216 | d->x = F_OUT(f, x, x); |
| 217 | d->y = F_OUT(f, y, y); |
| 218 | } |
| 219 | mp_drop(d->z); |
| 220 | d->z = 0; |
| 221 | } |
| 222 | return (d); |
| 223 | } |
| 224 | |
| 225 | ec *ec_projfix(ec_curve *c, ec *d, const ec *p) |
| 226 | { |
| 227 | if (EC_ATINF(p)) |
| 228 | EC_SETINF(d); |
| 229 | else if (p->z == c->f->one) |
| 230 | EC_COPY(d, p); |
| 231 | else { |
| 232 | mp *z, *zz; |
| 233 | field *f = c->f; |
| 234 | z = F_INV(f, MP_NEW, p->z); |
| 235 | zz = F_SQR(f, MP_NEW, z); |
| 236 | z = F_MUL(f, z, zz, z); |
| 237 | d->x = F_MUL(f, d->x, p->x, zz); |
| 238 | d->y = F_MUL(f, d->y, p->y, z); |
| 239 | mp_drop(z); |
| 240 | mp_drop(zz); |
| 241 | mp_drop(d->z); |
| 242 | d->z = MP_COPY(f->one); |
| 243 | } |
| 244 | return (d); |
| 245 | } |
| 246 | |
| 247 | /* --- @ec_stdsub@ --- * |
| 248 | * |
| 249 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 250 | * @ec *d@ = pointer to the destination |
| 251 | * @const ec *p, *q@ = the operand points |
| 252 | * |
| 253 | * Returns: The destination @d@. |
| 254 | * |
| 255 | * Use: Standard point subtraction operation, in terms of negation |
| 256 | * and addition. This isn't as efficient as a ready-made |
| 257 | * subtraction operator. |
| 258 | */ |
| 259 | |
| 260 | ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q) |
| 261 | { |
| 262 | ec t = EC_INIT; |
| 263 | EC_NEG(c, &t, q); |
| 264 | EC_ADD(c, d, p, &t); |
| 265 | EC_DESTROY(&t); |
| 266 | return (d); |
| 267 | } |
| 268 | |
| 269 | /*----- Creating curves ---------------------------------------------------*/ |
| 270 | |
| 271 | /* --- @ec_destroycurve@ --- * |
| 272 | * |
| 273 | * Arguments: @ec_curve *c@ = pointer to an ellptic curve |
| 274 | * |
| 275 | * Returns: --- |
| 276 | * |
| 277 | * Use: Destroys a description of an elliptic curve. |
| 278 | */ |
| 279 | |
| 280 | void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); } |
| 281 | |
| 282 | /*----- Real arithmetic ---------------------------------------------------*/ |
| 283 | |
| 284 | /* --- @ec_find@ --- * |
| 285 | * |
| 286 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 287 | * @ec *d@ = pointer to the destination point |
| 288 | * @mp *x@ = a possible x-coordinate |
| 289 | * |
| 290 | * Returns: Zero if OK, nonzero if there isn't a point there. |
| 291 | * |
| 292 | * Use: Finds a point on an elliptic curve with a given x-coordinate. |
| 293 | */ |
| 294 | |
| 295 | ec *ec_find(ec_curve *c, ec *d, mp *x) |
| 296 | { |
| 297 | x = F_IN(c->f, MP_NEW, x); |
| 298 | if ((d = EC_FIND(c, d, x)) != 0) |
| 299 | EC_OUT(c, d, d); |
| 300 | MP_DROP(x); |
| 301 | return (d); |
| 302 | } |
| 303 | |
| 304 | /* --- @ec_neg@ --- * |
| 305 | * |
| 306 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 307 | * @ec *d@ = pointer to the destination point |
| 308 | * @const ec *p@ = pointer to the operand point |
| 309 | * |
| 310 | * Returns: The destination point. |
| 311 | * |
| 312 | * Use: Computes the negation of the given point. |
| 313 | */ |
| 314 | |
| 315 | ec *ec_neg(ec_curve *c, ec *d, const ec *p) |
| 316 | { EC_IN(c, d, p); EC_NEG(c, d, d); return (EC_OUT(c, d, d)); } |
| 317 | |
| 318 | /* --- @ec_add@ --- * |
| 319 | * |
| 320 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 321 | * @ec *d@ = pointer to the destination point |
| 322 | * @const ec *p, *q@ = pointers to the operand points |
| 323 | * |
| 324 | * Returns: --- |
| 325 | * |
| 326 | * Use: Adds two points on an elliptic curve. |
| 327 | */ |
| 328 | |
| 329 | ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q) |
| 330 | { |
| 331 | ec pp = EC_INIT, qq = EC_INIT; |
| 332 | EC_IN(c, &pp, p); |
| 333 | EC_IN(c, &qq, q); |
| 334 | EC_ADD(c, d, &pp, &qq); |
| 335 | EC_OUT(c, d, d); |
| 336 | EC_DESTROY(&pp); |
| 337 | EC_DESTROY(&qq); |
| 338 | return (d); |
| 339 | } |
| 340 | |
| 341 | /* --- @ec_sub@ --- * |
| 342 | * |
| 343 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 344 | * @ec *d@ = pointer to the destination point |
| 345 | * @const ec *p, *q@ = pointers to the operand points |
| 346 | * |
| 347 | * Returns: The destination @d@. |
| 348 | * |
| 349 | * Use: Subtracts one point from another on an elliptic curve. |
| 350 | */ |
| 351 | |
| 352 | ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q) |
| 353 | { |
| 354 | ec pp = EC_INIT, qq = EC_INIT; |
| 355 | EC_IN(c, &pp, p); |
| 356 | EC_IN(c, &qq, q); |
| 357 | EC_SUB(c, d, &pp, &qq); |
| 358 | EC_OUT(c, d, d); |
| 359 | EC_DESTROY(&pp); |
| 360 | EC_DESTROY(&qq); |
| 361 | return (d); |
| 362 | } |
| 363 | |
| 364 | /* --- @ec_dbl@ --- * |
| 365 | * |
| 366 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 367 | * @ec *d@ = pointer to the destination point |
| 368 | * @const ec *p@ = pointer to the operand point |
| 369 | * |
| 370 | * Returns: --- |
| 371 | * |
| 372 | * Use: Doubles a point on an elliptic curve. |
| 373 | */ |
| 374 | |
| 375 | ec *ec_dbl(ec_curve *c, ec *d, const ec *p) |
| 376 | { EC_IN(c, d, p); EC_DBL(c, d, d); return (EC_OUT(c, d, d)); } |
| 377 | |
| 378 | /* --- @ec_check@ --- * |
| 379 | * |
| 380 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 381 | * @const ec *p@ = pointer to the point |
| 382 | * |
| 383 | * Returns: Zero if OK, nonzero if this is an invalid point. |
| 384 | * |
| 385 | * Use: Checks that a point is actually on an elliptic curve. |
| 386 | */ |
| 387 | |
| 388 | int ec_check(ec_curve *c, const ec *p) |
| 389 | { |
| 390 | ec t = EC_INIT; |
| 391 | int rc; |
| 392 | |
| 393 | if (EC_ATINF(p)) |
| 394 | return (0); |
| 395 | EC_IN(c, &t, p); |
| 396 | rc = EC_CHECK(c, &t); |
| 397 | EC_DESTROY(&t); |
| 398 | return (rc); |
| 399 | } |
| 400 | |
| 401 | /* --- @ec_rand@ --- * |
| 402 | * |
| 403 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
| 404 | * @ec *d@ = pointer to the destination point |
| 405 | * @grand *r@ = random number source |
| 406 | * |
| 407 | * Returns: The destination @d@. |
| 408 | * |
| 409 | * Use: Finds a random point on the given curve. |
| 410 | */ |
| 411 | |
| 412 | ec *ec_rand(ec_curve *c, ec *d, grand *r) |
| 413 | { |
| 414 | mp *x = MP_NEW; |
| 415 | do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x)); |
| 416 | mp_drop(x); |
| 417 | if (grand_range(r, 2)) EC_NEG(c, d, d); |
| 418 | return (EC_OUT(c, d, d)); |
| 419 | } |
| 420 | |
| 421 | /*----- That's all, folks -------------------------------------------------*/ |