1 /* 2 * ***** BEGIN LICENSE BLOCK ***** 3 * Version: MPL 1.1/GPL 2.0/LGPL 2.1 4 * 5 * The contents of this file are subject to the Mozilla Public License Version 6 * 1.1 (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * http://www.mozilla.org/MPL/ 9 * 10 * Software distributed under the License is distributed on an "AS IS" basis, 11 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License 12 * for the specific language governing rights and limitations under the 13 * License. 14 * 15 * The Original Code is the elliptic curve math library for prime field curves. 16 * 17 * The Initial Developer of the Original Code is 18 * Sun Microsystems, Inc. 19 * Portions created by the Initial Developer are Copyright (C) 2003 20 * the Initial Developer. All Rights Reserved. 21 * 22 * Contributor(s): 23 * Sheueling Chang-Shantz <sheueling.chang@sun.com>, 24 * Stephen Fung <fungstep@hotmail.com>, and 25 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories. 26 * Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>, 27 * Nils Larsch <nla@trustcenter.de>, and 28 * Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project 29 * 30 * Alternatively, the contents of this file may be used under the terms of 31 * either the GNU General Public License Version 2 or later (the "GPL"), or 32 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), 33 * in which case the provisions of the GPL or the LGPL are applicable instead 34 * of those above. If you wish to allow use of your version of this file only 35 * under the terms of either the GPL or the LGPL, and not to allow others to 36 * use your version of this file under the terms of the MPL, indicate your 37 * decision by deleting the provisions above and replace them with the notice 38 * and other provisions required by the GPL or the LGPL. If you do not delete 39 * the provisions above, a recipient may use your version of this file under 40 * the terms of any one of the MPL, the GPL or the LGPL. 41 * 42 * ***** END LICENSE BLOCK ***** */ 43 /* 44 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. 45 * Use is subject to license terms. 46 * 47 * Sun elects to use this software under the MPL license. 48 */ 49 50 #include "ecp.h" 51 #include "mplogic.h" 52 #ifndef _KERNEL 53 #include <stdlib.h> 54 #endif 55 #ifdef ECL_DEBUG 56 #include <assert.h> 57 #endif 58 59 /* Converts a point P(px, py) from affine coordinates to Jacobian 60 * projective coordinates R(rx, ry, rz). Assumes input is already 61 * field-encoded using field_enc, and returns output that is still 62 * field-encoded. */ 63 mp_err 64 ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx, 65 mp_int *ry, mp_int *rz, const ECGroup *group) 66 { 67 mp_err res = MP_OKAY; 68 69 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { 70 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); 71 } else { 72 MP_CHECKOK(mp_copy(px, rx)); 73 MP_CHECKOK(mp_copy(py, ry)); 74 MP_CHECKOK(mp_set_int(rz, 1)); 75 if (group->meth->field_enc) { 76 MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth)); 77 } 78 } 79 CLEANUP: 80 return res; 81 } 82 83 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to 84 * affine coordinates R(rx, ry). P and R can share x and y coordinates. 85 * Assumes input is already field-encoded using field_enc, and returns 86 * output that is still field-encoded. */ 87 mp_err 88 ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz, 89 mp_int *rx, mp_int *ry, const ECGroup *group) 90 { 91 mp_err res = MP_OKAY; 92 mp_int z1, z2, z3; 93 94 MP_DIGITS(&z1) = 0; 95 MP_DIGITS(&z2) = 0; 96 MP_DIGITS(&z3) = 0; 97 MP_CHECKOK(mp_init(&z1, FLAG(px))); 98 MP_CHECKOK(mp_init(&z2, FLAG(px))); 99 MP_CHECKOK(mp_init(&z3, FLAG(px))); 100 101 /* if point at infinity, then set point at infinity and exit */ 102 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 103 MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry)); 104 goto CLEANUP; 105 } 106 107 /* transform (px, py, pz) into (px / pz^2, py / pz^3) */ 108 if (mp_cmp_d(pz, 1) == 0) { 109 MP_CHECKOK(mp_copy(px, rx)); 110 MP_CHECKOK(mp_copy(py, ry)); 111 } else { 112 MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth)); 113 MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth)); 114 MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth)); 115 MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth)); 116 MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth)); 117 } 118 119 CLEANUP: 120 mp_clear(&z1); 121 mp_clear(&z2); 122 mp_clear(&z3); 123 return res; 124 } 125 126 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian 127 * coordinates. */ 128 mp_err 129 ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz) 130 { 131 return mp_cmp_z(pz); 132 } 133 134 /* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian 135 * coordinates. */ 136 mp_err 137 ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz) 138 { 139 mp_zero(pz); 140 return MP_OKAY; 141 } 142 143 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is 144 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical. 145 * Uses mixed Jacobian-affine coordinates. Assumes input is already 146 * field-encoded using field_enc, and returns output that is still 147 * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and 148 * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime 149 * Fields. */ 150 mp_err 151 ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz, 152 const mp_int *qx, const mp_int *qy, mp_int *rx, 153 mp_int *ry, mp_int *rz, const ECGroup *group) 154 { 155 mp_err res = MP_OKAY; 156 mp_int A, B, C, D, C2, C3; 157 158 MP_DIGITS(&A) = 0; 159 MP_DIGITS(&B) = 0; 160 MP_DIGITS(&C) = 0; 161 MP_DIGITS(&D) = 0; 162 MP_DIGITS(&C2) = 0; 163 MP_DIGITS(&C3) = 0; 164 MP_CHECKOK(mp_init(&A, FLAG(px))); 165 MP_CHECKOK(mp_init(&B, FLAG(px))); 166 MP_CHECKOK(mp_init(&C, FLAG(px))); 167 MP_CHECKOK(mp_init(&D, FLAG(px))); 168 MP_CHECKOK(mp_init(&C2, FLAG(px))); 169 MP_CHECKOK(mp_init(&C3, FLAG(px))); 170 171 /* If either P or Q is the point at infinity, then return the other 172 * point */ 173 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 174 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group)); 175 goto CLEANUP; 176 } 177 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) { 178 MP_CHECKOK(mp_copy(px, rx)); 179 MP_CHECKOK(mp_copy(py, ry)); 180 MP_CHECKOK(mp_copy(pz, rz)); 181 goto CLEANUP; 182 } 183 184 /* A = qx * pz^2, B = qy * pz^3 */ 185 MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth)); 186 MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth)); 187 MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth)); 188 MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth)); 189 190 /* C = A - px, D = B - py */ 191 MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth)); 192 MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth)); 193 194 /* C2 = C^2, C3 = C^3 */ 195 MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth)); 196 MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth)); 197 198 /* rz = pz * C */ 199 MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth)); 200 201 /* C = px * C^2 */ 202 MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth)); 203 /* A = D^2 */ 204 MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth)); 205 206 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */ 207 MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth)); 208 MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth)); 209 MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth)); 210 211 /* C3 = py * C^3 */ 212 MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth)); 213 214 /* ry = D * (px * C^2 - rx) - py * C^3 */ 215 MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth)); 216 MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth)); 217 MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth)); 218 219 CLEANUP: 220 mp_clear(&A); 221 mp_clear(&B); 222 mp_clear(&C); 223 mp_clear(&D); 224 mp_clear(&C2); 225 mp_clear(&C3); 226 return res; 227 } 228 229 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses 230 * Jacobian coordinates. 231 * 232 * Assumes input is already field-encoded using field_enc, and returns 233 * output that is still field-encoded. 234 * 235 * This routine implements Point Doubling in the Jacobian Projective 236 * space as described in the paper "Efficient elliptic curve exponentiation 237 * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono. 238 */ 239 mp_err 240 ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz, 241 mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group) 242 { 243 mp_err res = MP_OKAY; 244 mp_int t0, t1, M, S; 245 246 MP_DIGITS(&t0) = 0; 247 MP_DIGITS(&t1) = 0; 248 MP_DIGITS(&M) = 0; 249 MP_DIGITS(&S) = 0; 250 MP_CHECKOK(mp_init(&t0, FLAG(px))); 251 MP_CHECKOK(mp_init(&t1, FLAG(px))); 252 MP_CHECKOK(mp_init(&M, FLAG(px))); 253 MP_CHECKOK(mp_init(&S, FLAG(px))); 254 255 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 256 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); 257 goto CLEANUP; 258 } 259 260 if (mp_cmp_d(pz, 1) == 0) { 261 /* M = 3 * px^2 + a */ 262 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); 263 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); 264 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); 265 MP_CHECKOK(group->meth-> 266 field_add(&t0, &group->curvea, &M, group->meth)); 267 } else if (mp_cmp_int(&group->curvea, -3, FLAG(px)) == 0) { 268 /* M = 3 * (px + pz^2) * (px - pz^2) */ 269 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); 270 MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth)); 271 MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth)); 272 MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth)); 273 MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth)); 274 MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth)); 275 } else { 276 /* M = 3 * (px^2) + a * (pz^4) */ 277 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); 278 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); 279 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); 280 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); 281 MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth)); 282 MP_CHECKOK(group->meth-> 283 field_mul(&M, &group->curvea, &M, group->meth)); 284 MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth)); 285 } 286 287 /* rz = 2 * py * pz */ 288 /* t0 = 4 * py^2 */ 289 if (mp_cmp_d(pz, 1) == 0) { 290 MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth)); 291 MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth)); 292 } else { 293 MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth)); 294 MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth)); 295 MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth)); 296 } 297 298 /* S = 4 * px * py^2 = px * (2 * py)^2 */ 299 MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth)); 300 301 /* rx = M^2 - 2 * S */ 302 MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth)); 303 MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth)); 304 MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth)); 305 306 /* ry = M * (S - rx) - 8 * py^4 */ 307 MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth)); 308 if (mp_isodd(&t1)) { 309 MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1)); 310 } 311 MP_CHECKOK(mp_div_2(&t1, &t1)); 312 MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth)); 313 MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth)); 314 MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth)); 315 316 CLEANUP: 317 mp_clear(&t0); 318 mp_clear(&t1); 319 mp_clear(&M); 320 mp_clear(&S); 321 return res; 322 } 323 324 /* by default, this routine is unused and thus doesn't need to be compiled */ 325 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC 326 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters 327 * a, b and p are the elliptic curve coefficients and the prime that 328 * determines the field GFp. Elliptic curve points P and R can be 329 * identical. Uses mixed Jacobian-affine coordinates. Assumes input is 330 * already field-encoded using field_enc, and returns output that is still 331 * field-encoded. Uses 4-bit window method. */ 332 mp_err 333 ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py, 334 mp_int *rx, mp_int *ry, const ECGroup *group) 335 { 336 mp_err res = MP_OKAY; 337 mp_int precomp[16][2], rz; 338 int i, ni, d; 339 340 MP_DIGITS(&rz) = 0; 341 for (i = 0; i < 16; i++) { 342 MP_DIGITS(&precomp[i][0]) = 0; 343 MP_DIGITS(&precomp[i][1]) = 0; 344 } 345 346 ARGCHK(group != NULL, MP_BADARG); 347 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG); 348 349 /* initialize precomputation table */ 350 for (i = 0; i < 16; i++) { 351 MP_CHECKOK(mp_init(&precomp[i][0])); 352 MP_CHECKOK(mp_init(&precomp[i][1])); 353 } 354 355 /* fill precomputation table */ 356 mp_zero(&precomp[0][0]); 357 mp_zero(&precomp[0][1]); 358 MP_CHECKOK(mp_copy(px, &precomp[1][0])); 359 MP_CHECKOK(mp_copy(py, &precomp[1][1])); 360 for (i = 2; i < 16; i++) { 361 MP_CHECKOK(group-> 362 point_add(&precomp[1][0], &precomp[1][1], 363 &precomp[i - 1][0], &precomp[i - 1][1], 364 &precomp[i][0], &precomp[i][1], group)); 365 } 366 367 d = (mpl_significant_bits(n) + 3) / 4; 368 369 /* R = inf */ 370 MP_CHECKOK(mp_init(&rz)); 371 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); 372 373 for (i = d - 1; i >= 0; i--) { 374 /* compute window ni */ 375 ni = MP_GET_BIT(n, 4 * i + 3); 376 ni <<= 1; 377 ni |= MP_GET_BIT(n, 4 * i + 2); 378 ni <<= 1; 379 ni |= MP_GET_BIT(n, 4 * i + 1); 380 ni <<= 1; 381 ni |= MP_GET_BIT(n, 4 * i); 382 /* R = 2^4 * R */ 383 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 384 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 385 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 386 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 387 /* R = R + (ni * P) */ 388 MP_CHECKOK(ec_GFp_pt_add_jac_aff 389 (rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry, 390 &rz, group)); 391 } 392 393 /* convert result S to affine coordinates */ 394 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); 395 396 CLEANUP: 397 mp_clear(&rz); 398 for (i = 0; i < 16; i++) { 399 mp_clear(&precomp[i][0]); 400 mp_clear(&precomp[i][1]); 401 } 402 return res; 403 } 404 #endif 405 406 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 407 * k2 * P(x, y), where G is the generator (base point) of the group of 408 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 409 * Uses mixed Jacobian-affine coordinates. Input and output values are 410 * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous 411 * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes. 412 * Software Implementation of the NIST Elliptic Curves over Prime Fields. */ 413 mp_err 414 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px, 415 const mp_int *py, mp_int *rx, mp_int *ry, 416 const ECGroup *group) 417 { 418 mp_err res = MP_OKAY; 419 mp_int precomp[4][4][2]; 420 mp_int rz; 421 const mp_int *a, *b; 422 int i, j; 423 int ai, bi, d; 424 425 for (i = 0; i < 4; i++) { 426 for (j = 0; j < 4; j++) { 427 MP_DIGITS(&precomp[i][j][0]) = 0; 428 MP_DIGITS(&precomp[i][j][1]) = 0; 429 } 430 } 431 MP_DIGITS(&rz) = 0; 432 433 ARGCHK(group != NULL, MP_BADARG); 434 ARGCHK(!((k1 == NULL) 435 && ((k2 == NULL) || (px == NULL) 436 || (py == NULL))), MP_BADARG); 437 438 /* if some arguments are not defined used ECPoint_mul */ 439 if (k1 == NULL) { 440 return ECPoint_mul(group, k2, px, py, rx, ry); 441 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { 442 return ECPoint_mul(group, k1, NULL, NULL, rx, ry); 443 } 444 445 /* initialize precomputation table */ 446 for (i = 0; i < 4; i++) { 447 for (j = 0; j < 4; j++) { 448 MP_CHECKOK(mp_init(&precomp[i][j][0], FLAG(k1))); 449 MP_CHECKOK(mp_init(&precomp[i][j][1], FLAG(k1))); 450 } 451 } 452 453 /* fill precomputation table */ 454 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ 455 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { 456 a = k2; 457 b = k1; 458 if (group->meth->field_enc) { 459 MP_CHECKOK(group->meth-> 460 field_enc(px, &precomp[1][0][0], group->meth)); 461 MP_CHECKOK(group->meth-> 462 field_enc(py, &precomp[1][0][1], group->meth)); 463 } else { 464 MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); 465 MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); 466 } 467 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); 468 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); 469 } else { 470 a = k1; 471 b = k2; 472 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); 473 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); 474 if (group->meth->field_enc) { 475 MP_CHECKOK(group->meth-> 476 field_enc(px, &precomp[0][1][0], group->meth)); 477 MP_CHECKOK(group->meth-> 478 field_enc(py, &precomp[0][1][1], group->meth)); 479 } else { 480 MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); 481 MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); 482 } 483 } 484 /* precompute [*][0][*] */ 485 mp_zero(&precomp[0][0][0]); 486 mp_zero(&precomp[0][0][1]); 487 MP_CHECKOK(group-> 488 point_dbl(&precomp[1][0][0], &precomp[1][0][1], 489 &precomp[2][0][0], &precomp[2][0][1], group)); 490 MP_CHECKOK(group-> 491 point_add(&precomp[1][0][0], &precomp[1][0][1], 492 &precomp[2][0][0], &precomp[2][0][1], 493 &precomp[3][0][0], &precomp[3][0][1], group)); 494 /* precompute [*][1][*] */ 495 for (i = 1; i < 4; i++) { 496 MP_CHECKOK(group-> 497 point_add(&precomp[0][1][0], &precomp[0][1][1], 498 &precomp[i][0][0], &precomp[i][0][1], 499 &precomp[i][1][0], &precomp[i][1][1], group)); 500 } 501 /* precompute [*][2][*] */ 502 MP_CHECKOK(group-> 503 point_dbl(&precomp[0][1][0], &precomp[0][1][1], 504 &precomp[0][2][0], &precomp[0][2][1], group)); 505 for (i = 1; i < 4; i++) { 506 MP_CHECKOK(group-> 507 point_add(&precomp[0][2][0], &precomp[0][2][1], 508 &precomp[i][0][0], &precomp[i][0][1], 509 &precomp[i][2][0], &precomp[i][2][1], group)); 510 } 511 /* precompute [*][3][*] */ 512 MP_CHECKOK(group-> 513 point_add(&precomp[0][1][0], &precomp[0][1][1], 514 &precomp[0][2][0], &precomp[0][2][1], 515 &precomp[0][3][0], &precomp[0][3][1], group)); 516 for (i = 1; i < 4; i++) { 517 MP_CHECKOK(group-> 518 point_add(&precomp[0][3][0], &precomp[0][3][1], 519 &precomp[i][0][0], &precomp[i][0][1], 520 &precomp[i][3][0], &precomp[i][3][1], group)); 521 } 522 523 d = (mpl_significant_bits(a) + 1) / 2; 524 525 /* R = inf */ 526 MP_CHECKOK(mp_init(&rz, FLAG(k1))); 527 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); 528 529 for (i = d - 1; i >= 0; i--) { 530 ai = MP_GET_BIT(a, 2 * i + 1); 531 ai <<= 1; 532 ai |= MP_GET_BIT(a, 2 * i); 533 bi = MP_GET_BIT(b, 2 * i + 1); 534 bi <<= 1; 535 bi |= MP_GET_BIT(b, 2 * i); 536 /* R = 2^2 * R */ 537 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 538 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 539 /* R = R + (ai * A + bi * B) */ 540 MP_CHECKOK(ec_GFp_pt_add_jac_aff 541 (rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1], 542 rx, ry, &rz, group)); 543 } 544 545 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); 546 547 if (group->meth->field_dec) { 548 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 549 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 550 } 551 552 CLEANUP: 553 mp_clear(&rz); 554 for (i = 0; i < 4; i++) { 555 for (j = 0; j < 4; j++) { 556 mp_clear(&precomp[i][j][0]); 557 mp_clear(&precomp[i][j][1]); 558 } 559 } 560 return res; 561 } 562