1/* 2 * Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved. 3 * Use is subject to license terms. 4 * 5 * This library is free software; you can redistribute it and/or 6 * modify it under the terms of the GNU Lesser General Public 7 * License as published by the Free Software Foundation; either 8 * version 2.1 of the License, or (at your option) any later version. 9 * 10 * This library is distributed in the hope that it will be useful, 11 * but WITHOUT ANY WARRANTY; without even the implied warranty of 12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 13 * Lesser General Public License for more details. 14 * 15 * You should have received a copy of the GNU Lesser General Public License 16 * along with this library; if not, write to the Free Software Foundation, 17 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. 18 * 19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 20 * or visit www.oracle.com if you need additional information or have any 21 * questions. 22 */ 23 24/* ********************************************************************* 25 * 26 * The Original Code is the elliptic curve math library for prime field curves. 27 * 28 * The Initial Developer of the Original Code is 29 * Sun Microsystems, Inc. 30 * Portions created by the Initial Developer are Copyright (C) 2003 31 * the Initial Developer. All Rights Reserved. 32 * 33 * Contributor(s): 34 * Sheueling Chang-Shantz <sheueling.chang@sun.com>, 35 * Stephen Fung <fungstep@hotmail.com>, and 36 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories. 37 * Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>, 38 * Nils Larsch <nla@trustcenter.de>, and 39 * Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project 40 * 41 * Last Modified Date from the Original Code: May 2017 42 *********************************************************************** */ 43 44#include "ecp.h" 45#include "mplogic.h" 46#ifndef _KERNEL 47#include <stdlib.h> 48#endif 49#ifdef ECL_DEBUG 50#include <assert.h> 51#endif 52 53/* Converts a point P(px, py) from affine coordinates to Jacobian 54 * projective coordinates R(rx, ry, rz). Assumes input is already 55 * field-encoded using field_enc, and returns output that is still 56 * field-encoded. */ 57mp_err 58ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx, 59 mp_int *ry, mp_int *rz, const ECGroup *group) 60{ 61 mp_err res = MP_OKAY; 62 63 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { 64 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); 65 } else { 66 MP_CHECKOK(mp_copy(px, rx)); 67 MP_CHECKOK(mp_copy(py, ry)); 68 MP_CHECKOK(mp_set_int(rz, 1)); 69 if (group->meth->field_enc) { 70 MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth)); 71 } 72 } 73 CLEANUP: 74 return res; 75} 76 77/* Converts a point P(px, py, pz) from Jacobian projective coordinates to 78 * affine coordinates R(rx, ry). P and R can share x and y coordinates. 79 * Assumes input is already field-encoded using field_enc, and returns 80 * output that is still field-encoded. */ 81mp_err 82ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz, 83 mp_int *rx, mp_int *ry, const ECGroup *group) 84{ 85 mp_err res = MP_OKAY; 86 mp_int z1, z2, z3; 87 88 MP_DIGITS(&z1) = 0; 89 MP_DIGITS(&z2) = 0; 90 MP_DIGITS(&z3) = 0; 91 MP_CHECKOK(mp_init(&z1, FLAG(px))); 92 MP_CHECKOK(mp_init(&z2, FLAG(px))); 93 MP_CHECKOK(mp_init(&z3, FLAG(px))); 94 95 /* if point at infinity, then set point at infinity and exit */ 96 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 97 MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry)); 98 goto CLEANUP; 99 } 100 101 /* transform (px, py, pz) into (px / pz^2, py / pz^3) */ 102 if (mp_cmp_d(pz, 1) == 0) { 103 MP_CHECKOK(mp_copy(px, rx)); 104 MP_CHECKOK(mp_copy(py, ry)); 105 } else { 106 MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth)); 107 MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth)); 108 MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth)); 109 MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth)); 110 MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth)); 111 } 112 113 CLEANUP: 114 mp_clear(&z1); 115 mp_clear(&z2); 116 mp_clear(&z3); 117 return res; 118} 119 120/* Checks if point P(px, py, pz) is at infinity. Uses Jacobian 121 * coordinates. */ 122mp_err 123ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz) 124{ 125 return mp_cmp_z(pz); 126} 127 128/* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian 129 * coordinates. */ 130mp_err 131ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz) 132{ 133 mp_zero(pz); 134 return MP_OKAY; 135} 136 137/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is 138 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical. 139 * Uses mixed Jacobian-affine coordinates. Assumes input is already 140 * field-encoded using field_enc, and returns output that is still 141 * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and 142 * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime 143 * Fields. */ 144mp_err 145ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz, 146 const mp_int *qx, const mp_int *qy, mp_int *rx, 147 mp_int *ry, mp_int *rz, const ECGroup *group) 148{ 149 mp_err res = MP_OKAY; 150 mp_int A, B, C, D, C2, C3; 151 152 MP_DIGITS(&A) = 0; 153 MP_DIGITS(&B) = 0; 154 MP_DIGITS(&C) = 0; 155 MP_DIGITS(&D) = 0; 156 MP_DIGITS(&C2) = 0; 157 MP_DIGITS(&C3) = 0; 158 MP_CHECKOK(mp_init(&A, FLAG(px))); 159 MP_CHECKOK(mp_init(&B, FLAG(px))); 160 MP_CHECKOK(mp_init(&C, FLAG(px))); 161 MP_CHECKOK(mp_init(&D, FLAG(px))); 162 MP_CHECKOK(mp_init(&C2, FLAG(px))); 163 MP_CHECKOK(mp_init(&C3, FLAG(px))); 164 165 /* If either P or Q is the point at infinity, then return the other 166 * point */ 167 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 168 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group)); 169 goto CLEANUP; 170 } 171 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) { 172 MP_CHECKOK(mp_copy(px, rx)); 173 MP_CHECKOK(mp_copy(py, ry)); 174 MP_CHECKOK(mp_copy(pz, rz)); 175 goto CLEANUP; 176 } 177 178 /* A = qx * pz^2, B = qy * pz^3 */ 179 MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth)); 180 MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth)); 181 MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth)); 182 MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth)); 183 184 /* 185 * Additional checks for point equality and point at infinity 186 */ 187 if (mp_cmp(px, &A) == 0 && mp_cmp(py, &B) == 0) { 188 /* POINT_DOUBLE(P) */ 189 MP_CHECKOK(ec_GFp_pt_dbl_jac(px, py, pz, rx, ry, rz, group)); 190 goto CLEANUP; 191 } 192 193 /* C = A - px, D = B - py */ 194 MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth)); 195 MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth)); 196 197 /* C2 = C^2, C3 = C^3 */ 198 MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth)); 199 MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth)); 200 201 /* rz = pz * C */ 202 MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth)); 203 204 /* C = px * C^2 */ 205 MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth)); 206 /* A = D^2 */ 207 MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth)); 208 209 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */ 210 MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth)); 211 MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth)); 212 MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth)); 213 214 /* C3 = py * C^3 */ 215 MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth)); 216 217 /* ry = D * (px * C^2 - rx) - py * C^3 */ 218 MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth)); 219 MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth)); 220 MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth)); 221 222 CLEANUP: 223 mp_clear(&A); 224 mp_clear(&B); 225 mp_clear(&C); 226 mp_clear(&D); 227 mp_clear(&C2); 228 mp_clear(&C3); 229 return res; 230} 231 232/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses 233 * Jacobian coordinates. 234 * 235 * Assumes input is already field-encoded using field_enc, and returns 236 * output that is still field-encoded. 237 * 238 * This routine implements Point Doubling in the Jacobian Projective 239 * space as described in the paper "Efficient elliptic curve exponentiation 240 * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono. 241 */ 242mp_err 243ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz, 244 mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group) 245{ 246 mp_err res = MP_OKAY; 247 mp_int t0, t1, M, S; 248 249 MP_DIGITS(&t0) = 0; 250 MP_DIGITS(&t1) = 0; 251 MP_DIGITS(&M) = 0; 252 MP_DIGITS(&S) = 0; 253 MP_CHECKOK(mp_init(&t0, FLAG(px))); 254 MP_CHECKOK(mp_init(&t1, FLAG(px))); 255 MP_CHECKOK(mp_init(&M, FLAG(px))); 256 MP_CHECKOK(mp_init(&S, FLAG(px))); 257 258 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 259 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); 260 goto CLEANUP; 261 } 262 263 if (mp_cmp_d(pz, 1) == 0) { 264 /* M = 3 * px^2 + a */ 265 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); 266 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); 267 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); 268 MP_CHECKOK(group->meth-> 269 field_add(&t0, &group->curvea, &M, group->meth)); 270 } else if (mp_cmp_int(&group->curvea, -3, FLAG(px)) == 0) { 271 /* M = 3 * (px + pz^2) * (px - pz^2) */ 272 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); 273 MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth)); 274 MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth)); 275 MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth)); 276 MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth)); 277 MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth)); 278 } else { 279 /* M = 3 * (px^2) + a * (pz^4) */ 280 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); 281 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); 282 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); 283 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); 284 MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth)); 285 MP_CHECKOK(group->meth-> 286 field_mul(&M, &group->curvea, &M, group->meth)); 287 MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth)); 288 } 289 290 /* rz = 2 * py * pz */ 291 /* t0 = 4 * py^2 */ 292 if (mp_cmp_d(pz, 1) == 0) { 293 MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth)); 294 MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth)); 295 } else { 296 MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth)); 297 MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth)); 298 MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth)); 299 } 300 301 /* S = 4 * px * py^2 = px * (2 * py)^2 */ 302 MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth)); 303 304 /* rx = M^2 - 2 * S */ 305 MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth)); 306 MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth)); 307 MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth)); 308 309 /* ry = M * (S - rx) - 8 * py^4 */ 310 MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth)); 311 if (mp_isodd(&t1)) { 312 MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1)); 313 } 314 MP_CHECKOK(mp_div_2(&t1, &t1)); 315 MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth)); 316 MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth)); 317 MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth)); 318 319 CLEANUP: 320 mp_clear(&t0); 321 mp_clear(&t1); 322 mp_clear(&M); 323 mp_clear(&S); 324 return res; 325} 326 327/* by default, this routine is unused and thus doesn't need to be compiled */ 328#ifdef ECL_ENABLE_GFP_PT_MUL_JAC 329/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters 330 * a, b and p are the elliptic curve coefficients and the prime that 331 * determines the field GFp. Elliptic curve points P and R can be 332 * identical. Uses mixed Jacobian-affine coordinates. Assumes input is 333 * already field-encoded using field_enc, and returns output that is still 334 * field-encoded. Uses 4-bit window method. */ 335mp_err 336ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py, 337 mp_int *rx, mp_int *ry, const ECGroup *group) 338{ 339 mp_err res = MP_OKAY; 340 mp_int precomp[16][2], rz; 341 int i, ni, d; 342 343 MP_DIGITS(&rz) = 0; 344 for (i = 0; i < 16; i++) { 345 MP_DIGITS(&precomp[i][0]) = 0; 346 MP_DIGITS(&precomp[i][1]) = 0; 347 } 348 349 ARGCHK(group != NULL, MP_BADARG); 350 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG); 351 352 /* initialize precomputation table */ 353 for (i = 0; i < 16; i++) { 354 MP_CHECKOK(mp_init(&precomp[i][0])); 355 MP_CHECKOK(mp_init(&precomp[i][1])); 356 } 357 358 /* fill precomputation table */ 359 mp_zero(&precomp[0][0]); 360 mp_zero(&precomp[0][1]); 361 MP_CHECKOK(mp_copy(px, &precomp[1][0])); 362 MP_CHECKOK(mp_copy(py, &precomp[1][1])); 363 for (i = 2; i < 16; i++) { 364 MP_CHECKOK(group-> 365 point_add(&precomp[1][0], &precomp[1][1], 366 &precomp[i - 1][0], &precomp[i - 1][1], 367 &precomp[i][0], &precomp[i][1], group)); 368 } 369 370 d = (mpl_significant_bits(n) + 3) / 4; 371 372 /* R = inf */ 373 MP_CHECKOK(mp_init(&rz)); 374 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); 375 376 for (i = d - 1; i >= 0; i--) { 377 /* compute window ni */ 378 ni = MP_GET_BIT(n, 4 * i + 3); 379 ni <<= 1; 380 ni |= MP_GET_BIT(n, 4 * i + 2); 381 ni <<= 1; 382 ni |= MP_GET_BIT(n, 4 * i + 1); 383 ni <<= 1; 384 ni |= MP_GET_BIT(n, 4 * i); 385 /* R = 2^4 * R */ 386 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 387 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 388 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 389 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 390 /* R = R + (ni * P) */ 391 MP_CHECKOK(ec_GFp_pt_add_jac_aff 392 (rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry, 393 &rz, group)); 394 } 395 396 /* convert result S to affine coordinates */ 397 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); 398 399 CLEANUP: 400 mp_clear(&rz); 401 for (i = 0; i < 16; i++) { 402 mp_clear(&precomp[i][0]); 403 mp_clear(&precomp[i][1]); 404 } 405 return res; 406} 407#endif 408 409/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 410 * k2 * P(x, y), where G is the generator (base point) of the group of 411 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 412 * Uses mixed Jacobian-affine coordinates. Input and output values are 413 * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous 414 * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes. 415 * Software Implementation of the NIST Elliptic Curves over Prime Fields. */ 416mp_err 417ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px, 418 const mp_int *py, mp_int *rx, mp_int *ry, 419 const ECGroup *group, int timing) 420{ 421 mp_err res = MP_OKAY; 422 mp_int precomp[4][4][2]; 423 mp_int rz; 424 const mp_int *a, *b; 425 int i, j; 426 int ai, bi, d; 427 428 for (i = 0; i < 4; i++) { 429 for (j = 0; j < 4; j++) { 430 MP_DIGITS(&precomp[i][j][0]) = 0; 431 MP_DIGITS(&precomp[i][j][1]) = 0; 432 } 433 } 434 MP_DIGITS(&rz) = 0; 435 436 ARGCHK(group != NULL, MP_BADARG); 437 ARGCHK(!((k1 == NULL) 438 && ((k2 == NULL) || (px == NULL) 439 || (py == NULL))), MP_BADARG); 440 441 /* if some arguments are not defined used ECPoint_mul */ 442 if (k1 == NULL) { 443 return ECPoint_mul(group, k2, px, py, rx, ry, timing); 444 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { 445 return ECPoint_mul(group, k1, NULL, NULL, rx, ry, timing); 446 } 447 448 /* initialize precomputation table */ 449 for (i = 0; i < 4; i++) { 450 for (j = 0; j < 4; j++) { 451 MP_CHECKOK(mp_init(&precomp[i][j][0], FLAG(k1))); 452 MP_CHECKOK(mp_init(&precomp[i][j][1], FLAG(k1))); 453 } 454 } 455 456 /* fill precomputation table */ 457 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ 458 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { 459 a = k2; 460 b = k1; 461 if (group->meth->field_enc) { 462 MP_CHECKOK(group->meth-> 463 field_enc(px, &precomp[1][0][0], group->meth)); 464 MP_CHECKOK(group->meth-> 465 field_enc(py, &precomp[1][0][1], group->meth)); 466 } else { 467 MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); 468 MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); 469 } 470 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); 471 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); 472 } else { 473 a = k1; 474 b = k2; 475 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); 476 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); 477 if (group->meth->field_enc) { 478 MP_CHECKOK(group->meth-> 479 field_enc(px, &precomp[0][1][0], group->meth)); 480 MP_CHECKOK(group->meth-> 481 field_enc(py, &precomp[0][1][1], group->meth)); 482 } else { 483 MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); 484 MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); 485 } 486 } 487 /* precompute [*][0][*] */ 488 mp_zero(&precomp[0][0][0]); 489 mp_zero(&precomp[0][0][1]); 490 MP_CHECKOK(group-> 491 point_dbl(&precomp[1][0][0], &precomp[1][0][1], 492 &precomp[2][0][0], &precomp[2][0][1], group)); 493 MP_CHECKOK(group-> 494 point_add(&precomp[1][0][0], &precomp[1][0][1], 495 &precomp[2][0][0], &precomp[2][0][1], 496 &precomp[3][0][0], &precomp[3][0][1], group)); 497 /* precompute [*][1][*] */ 498 for (i = 1; i < 4; i++) { 499 MP_CHECKOK(group-> 500 point_add(&precomp[0][1][0], &precomp[0][1][1], 501 &precomp[i][0][0], &precomp[i][0][1], 502 &precomp[i][1][0], &precomp[i][1][1], group)); 503 } 504 /* precompute [*][2][*] */ 505 MP_CHECKOK(group-> 506 point_dbl(&precomp[0][1][0], &precomp[0][1][1], 507 &precomp[0][2][0], &precomp[0][2][1], group)); 508 for (i = 1; i < 4; i++) { 509 MP_CHECKOK(group-> 510 point_add(&precomp[0][2][0], &precomp[0][2][1], 511 &precomp[i][0][0], &precomp[i][0][1], 512 &precomp[i][2][0], &precomp[i][2][1], group)); 513 } 514 /* precompute [*][3][*] */ 515 MP_CHECKOK(group-> 516 point_add(&precomp[0][1][0], &precomp[0][1][1], 517 &precomp[0][2][0], &precomp[0][2][1], 518 &precomp[0][3][0], &precomp[0][3][1], group)); 519 for (i = 1; i < 4; i++) { 520 MP_CHECKOK(group-> 521 point_add(&precomp[0][3][0], &precomp[0][3][1], 522 &precomp[i][0][0], &precomp[i][0][1], 523 &precomp[i][3][0], &precomp[i][3][1], group)); 524 } 525 526 d = (mpl_significant_bits(a) + 1) / 2; 527 528 /* R = inf */ 529 MP_CHECKOK(mp_init(&rz, FLAG(k1))); 530 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); 531 532 for (i = d - 1; i >= 0; i--) { 533 ai = MP_GET_BIT(a, 2 * i + 1); 534 ai <<= 1; 535 ai |= MP_GET_BIT(a, 2 * i); 536 bi = MP_GET_BIT(b, 2 * i + 1); 537 bi <<= 1; 538 bi |= MP_GET_BIT(b, 2 * i); 539 /* R = 2^2 * R */ 540 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 541 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 542 /* R = R + (ai * A + bi * B) */ 543 MP_CHECKOK(ec_GFp_pt_add_jac_aff 544 (rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1], 545 rx, ry, &rz, group)); 546 } 547 548 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); 549 550 if (group->meth->field_dec) { 551 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 552 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 553 } 554 555 CLEANUP: 556 mp_clear(&rz); 557 for (i = 0; i < 4; i++) { 558 for (j = 0; j < 4; j++) { 559 mp_clear(&precomp[i][j][0]); 560 mp_clear(&precomp[i][j][1]); 561 } 562 } 563 return res; 564} 565