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 #pragma ident "%Z%%M% %I% %E% SMI" 51 52 #include "ecp.h" 53 #include "mplogic.h" 54 #ifndef _KERNEL 55 #include <stdlib.h> 56 #endif 57 #ifdef ECL_DEBUG 58 #include <assert.h> 59 #endif 60 61 /* Converts a point P(px, py) from affine coordinates to Jacobian 62 * projective coordinates R(rx, ry, rz). Assumes input is already 63 * field-encoded using field_enc, and returns output that is still 64 * field-encoded. */ 65 mp_err 66 ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx, 67 mp_int *ry, mp_int *rz, const ECGroup *group) 68 { 69 mp_err res = MP_OKAY; 70 71 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { 72 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); 73 } else { 74 MP_CHECKOK(mp_copy(px, rx)); 75 MP_CHECKOK(mp_copy(py, ry)); 76 MP_CHECKOK(mp_set_int(rz, 1)); 77 if (group->meth->field_enc) { 78 MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth)); 79 } 80 } 81 CLEANUP: 82 return res; 83 } 84 85 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to 86 * affine coordinates R(rx, ry). P and R can share x and y coordinates. 87 * Assumes input is already field-encoded using field_enc, and returns 88 * output that is still field-encoded. */ 89 mp_err 90 ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz, 91 mp_int *rx, mp_int *ry, const ECGroup *group) 92 { 93 mp_err res = MP_OKAY; 94 mp_int z1, z2, z3; 95 96 MP_DIGITS(&z1) = 0; 97 MP_DIGITS(&z2) = 0; 98 MP_DIGITS(&z3) = 0; 99 MP_CHECKOK(mp_init(&z1, FLAG(px))); 100 MP_CHECKOK(mp_init(&z2, FLAG(px))); 101 MP_CHECKOK(mp_init(&z3, FLAG(px))); 102 103 /* if point at infinity, then set point at infinity and exit */ 104 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 105 MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry)); 106 goto CLEANUP; 107 } 108 109 /* transform (px, py, pz) into (px / pz^2, py / pz^3) */ 110 if (mp_cmp_d(pz, 1) == 0) { 111 MP_CHECKOK(mp_copy(px, rx)); 112 MP_CHECKOK(mp_copy(py, ry)); 113 } else { 114 MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth)); 115 MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth)); 116 MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth)); 117 MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth)); 118 MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth)); 119 } 120 121 CLEANUP: 122 mp_clear(&z1); 123 mp_clear(&z2); 124 mp_clear(&z3); 125 return res; 126 } 127 128 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian 129 * coordinates. */ 130 mp_err 131 ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz) 132 { 133 return mp_cmp_z(pz); 134 } 135 136 /* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian 137 * coordinates. */ 138 mp_err 139 ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz) 140 { 141 mp_zero(pz); 142 return MP_OKAY; 143 } 144 145 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is 146 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical. 147 * Uses mixed Jacobian-affine coordinates. Assumes input is already 148 * field-encoded using field_enc, and returns output that is still 149 * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and 150 * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime 151 * Fields. */ 152 mp_err 153 ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz, 154 const mp_int *qx, const mp_int *qy, mp_int *rx, 155 mp_int *ry, mp_int *rz, const ECGroup *group) 156 { 157 mp_err res = MP_OKAY; 158 mp_int A, B, C, D, C2, C3; 159 160 MP_DIGITS(&A) = 0; 161 MP_DIGITS(&B) = 0; 162 MP_DIGITS(&C) = 0; 163 MP_DIGITS(&D) = 0; 164 MP_DIGITS(&C2) = 0; 165 MP_DIGITS(&C3) = 0; 166 MP_CHECKOK(mp_init(&A, FLAG(px))); 167 MP_CHECKOK(mp_init(&B, FLAG(px))); 168 MP_CHECKOK(mp_init(&C, FLAG(px))); 169 MP_CHECKOK(mp_init(&D, FLAG(px))); 170 MP_CHECKOK(mp_init(&C2, FLAG(px))); 171 MP_CHECKOK(mp_init(&C3, FLAG(px))); 172 173 /* If either P or Q is the point at infinity, then return the other 174 * point */ 175 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 176 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group)); 177 goto CLEANUP; 178 } 179 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) { 180 MP_CHECKOK(mp_copy(px, rx)); 181 MP_CHECKOK(mp_copy(py, ry)); 182 MP_CHECKOK(mp_copy(pz, rz)); 183 goto CLEANUP; 184 } 185 186 /* A = qx * pz^2, B = qy * pz^3 */ 187 MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth)); 188 MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth)); 189 MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth)); 190 MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth)); 191 192 /* C = A - px, D = B - py */ 193 MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth)); 194 MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth)); 195 196 /* C2 = C^2, C3 = C^3 */ 197 MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth)); 198 MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth)); 199 200 /* rz = pz * C */ 201 MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth)); 202 203 /* C = px * C^2 */ 204 MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth)); 205 /* A = D^2 */ 206 MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth)); 207 208 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */ 209 MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth)); 210 MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth)); 211 MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth)); 212 213 /* C3 = py * C^3 */ 214 MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth)); 215 216 /* ry = D * (px * C^2 - rx) - py * C^3 */ 217 MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth)); 218 MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth)); 219 MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth)); 220 221 CLEANUP: 222 mp_clear(&A); 223 mp_clear(&B); 224 mp_clear(&C); 225 mp_clear(&D); 226 mp_clear(&C2); 227 mp_clear(&C3); 228 return res; 229 } 230 231 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses 232 * Jacobian coordinates. 233 * 234 * Assumes input is already field-encoded using field_enc, and returns 235 * output that is still field-encoded. 236 * 237 * This routine implements Point Doubling in the Jacobian Projective 238 * space as described in the paper "Efficient elliptic curve exponentiation 239 * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono. 240 */ 241 mp_err 242 ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz, 243 mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group) 244 { 245 mp_err res = MP_OKAY; 246 mp_int t0, t1, M, S; 247 248 MP_DIGITS(&t0) = 0; 249 MP_DIGITS(&t1) = 0; 250 MP_DIGITS(&M) = 0; 251 MP_DIGITS(&S) = 0; 252 MP_CHECKOK(mp_init(&t0, FLAG(px))); 253 MP_CHECKOK(mp_init(&t1, FLAG(px))); 254 MP_CHECKOK(mp_init(&M, FLAG(px))); 255 MP_CHECKOK(mp_init(&S, FLAG(px))); 256 257 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) { 258 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz)); 259 goto CLEANUP; 260 } 261 262 if (mp_cmp_d(pz, 1) == 0) { 263 /* M = 3 * px^2 + a */ 264 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); 265 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); 266 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); 267 MP_CHECKOK(group->meth-> 268 field_add(&t0, &group->curvea, &M, group->meth)); 269 } else if (mp_cmp_int(&group->curvea, -3, FLAG(px)) == 0) { 270 /* M = 3 * (px + pz^2) * (px - pz^2) */ 271 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); 272 MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth)); 273 MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth)); 274 MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth)); 275 MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth)); 276 MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth)); 277 } else { 278 /* M = 3 * (px^2) + a * (pz^4) */ 279 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth)); 280 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth)); 281 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth)); 282 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth)); 283 MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth)); 284 MP_CHECKOK(group->meth-> 285 field_mul(&M, &group->curvea, &M, group->meth)); 286 MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth)); 287 } 288 289 /* rz = 2 * py * pz */ 290 /* t0 = 4 * py^2 */ 291 if (mp_cmp_d(pz, 1) == 0) { 292 MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth)); 293 MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth)); 294 } else { 295 MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth)); 296 MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth)); 297 MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth)); 298 } 299 300 /* S = 4 * px * py^2 = px * (2 * py)^2 */ 301 MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth)); 302 303 /* rx = M^2 - 2 * S */ 304 MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth)); 305 MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth)); 306 MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth)); 307 308 /* ry = M * (S - rx) - 8 * py^4 */ 309 MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth)); 310 if (mp_isodd(&t1)) { 311 MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1)); 312 } 313 MP_CHECKOK(mp_div_2(&t1, &t1)); 314 MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth)); 315 MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth)); 316 MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth)); 317 318 CLEANUP: 319 mp_clear(&t0); 320 mp_clear(&t1); 321 mp_clear(&M); 322 mp_clear(&S); 323 return res; 324 } 325 326 /* by default, this routine is unused and thus doesn't need to be compiled */ 327 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC 328 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters 329 * a, b and p are the elliptic curve coefficients and the prime that 330 * determines the field GFp. Elliptic curve points P and R can be 331 * identical. Uses mixed Jacobian-affine coordinates. Assumes input is 332 * already field-encoded using field_enc, and returns output that is still 333 * field-encoded. Uses 4-bit window method. */ 334 mp_err 335 ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py, 336 mp_int *rx, mp_int *ry, const ECGroup *group) 337 { 338 mp_err res = MP_OKAY; 339 mp_int precomp[16][2], rz; 340 int i, ni, d; 341 342 MP_DIGITS(&rz) = 0; 343 for (i = 0; i < 16; i++) { 344 MP_DIGITS(&precomp[i][0]) = 0; 345 MP_DIGITS(&precomp[i][1]) = 0; 346 } 347 348 ARGCHK(group != NULL, MP_BADARG); 349 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG); 350 351 /* initialize precomputation table */ 352 for (i = 0; i < 16; i++) { 353 MP_CHECKOK(mp_init(&precomp[i][0])); 354 MP_CHECKOK(mp_init(&precomp[i][1])); 355 } 356 357 /* fill precomputation table */ 358 mp_zero(&precomp[0][0]); 359 mp_zero(&precomp[0][1]); 360 MP_CHECKOK(mp_copy(px, &precomp[1][0])); 361 MP_CHECKOK(mp_copy(py, &precomp[1][1])); 362 for (i = 2; i < 16; i++) { 363 MP_CHECKOK(group-> 364 point_add(&precomp[1][0], &precomp[1][1], 365 &precomp[i - 1][0], &precomp[i - 1][1], 366 &precomp[i][0], &precomp[i][1], group)); 367 } 368 369 d = (mpl_significant_bits(n) + 3) / 4; 370 371 /* R = inf */ 372 MP_CHECKOK(mp_init(&rz)); 373 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); 374 375 for (i = d - 1; i >= 0; i--) { 376 /* compute window ni */ 377 ni = MP_GET_BIT(n, 4 * i + 3); 378 ni <<= 1; 379 ni |= MP_GET_BIT(n, 4 * i + 2); 380 ni <<= 1; 381 ni |= MP_GET_BIT(n, 4 * i + 1); 382 ni <<= 1; 383 ni |= MP_GET_BIT(n, 4 * i); 384 /* R = 2^4 * R */ 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 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 /* R = R + (ni * P) */ 390 MP_CHECKOK(ec_GFp_pt_add_jac_aff 391 (rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry, 392 &rz, group)); 393 } 394 395 /* convert result S to affine coordinates */ 396 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); 397 398 CLEANUP: 399 mp_clear(&rz); 400 for (i = 0; i < 16; i++) { 401 mp_clear(&precomp[i][0]); 402 mp_clear(&precomp[i][1]); 403 } 404 return res; 405 } 406 #endif 407 408 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 409 * k2 * P(x, y), where G is the generator (base point) of the group of 410 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 411 * Uses mixed Jacobian-affine coordinates. Input and output values are 412 * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous 413 * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes. 414 * Software Implementation of the NIST Elliptic Curves over Prime Fields. */ 415 mp_err 416 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px, 417 const mp_int *py, mp_int *rx, mp_int *ry, 418 const ECGroup *group) 419 { 420 mp_err res = MP_OKAY; 421 mp_int precomp[4][4][2]; 422 mp_int rz; 423 const mp_int *a, *b; 424 int i, j; 425 int ai, bi, d; 426 427 for (i = 0; i < 4; i++) { 428 for (j = 0; j < 4; j++) { 429 MP_DIGITS(&precomp[i][j][0]) = 0; 430 MP_DIGITS(&precomp[i][j][1]) = 0; 431 } 432 } 433 MP_DIGITS(&rz) = 0; 434 435 ARGCHK(group != NULL, MP_BADARG); 436 ARGCHK(!((k1 == NULL) 437 && ((k2 == NULL) || (px == NULL) 438 || (py == NULL))), MP_BADARG); 439 440 /* if some arguments are not defined used ECPoint_mul */ 441 if (k1 == NULL) { 442 return ECPoint_mul(group, k2, px, py, rx, ry); 443 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { 444 return ECPoint_mul(group, k1, NULL, NULL, rx, ry); 445 } 446 447 /* initialize precomputation table */ 448 for (i = 0; i < 4; i++) { 449 for (j = 0; j < 4; j++) { 450 MP_CHECKOK(mp_init(&precomp[i][j][0], FLAG(k1))); 451 MP_CHECKOK(mp_init(&precomp[i][j][1], FLAG(k1))); 452 } 453 } 454 455 /* fill precomputation table */ 456 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ 457 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { 458 a = k2; 459 b = k1; 460 if (group->meth->field_enc) { 461 MP_CHECKOK(group->meth-> 462 field_enc(px, &precomp[1][0][0], group->meth)); 463 MP_CHECKOK(group->meth-> 464 field_enc(py, &precomp[1][0][1], group->meth)); 465 } else { 466 MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); 467 MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); 468 } 469 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); 470 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); 471 } else { 472 a = k1; 473 b = k2; 474 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); 475 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); 476 if (group->meth->field_enc) { 477 MP_CHECKOK(group->meth-> 478 field_enc(px, &precomp[0][1][0], group->meth)); 479 MP_CHECKOK(group->meth-> 480 field_enc(py, &precomp[0][1][1], group->meth)); 481 } else { 482 MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); 483 MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); 484 } 485 } 486 /* precompute [*][0][*] */ 487 mp_zero(&precomp[0][0][0]); 488 mp_zero(&precomp[0][0][1]); 489 MP_CHECKOK(group-> 490 point_dbl(&precomp[1][0][0], &precomp[1][0][1], 491 &precomp[2][0][0], &precomp[2][0][1], group)); 492 MP_CHECKOK(group-> 493 point_add(&precomp[1][0][0], &precomp[1][0][1], 494 &precomp[2][0][0], &precomp[2][0][1], 495 &precomp[3][0][0], &precomp[3][0][1], group)); 496 /* precompute [*][1][*] */ 497 for (i = 1; i < 4; i++) { 498 MP_CHECKOK(group-> 499 point_add(&precomp[0][1][0], &precomp[0][1][1], 500 &precomp[i][0][0], &precomp[i][0][1], 501 &precomp[i][1][0], &precomp[i][1][1], group)); 502 } 503 /* precompute [*][2][*] */ 504 MP_CHECKOK(group-> 505 point_dbl(&precomp[0][1][0], &precomp[0][1][1], 506 &precomp[0][2][0], &precomp[0][2][1], group)); 507 for (i = 1; i < 4; i++) { 508 MP_CHECKOK(group-> 509 point_add(&precomp[0][2][0], &precomp[0][2][1], 510 &precomp[i][0][0], &precomp[i][0][1], 511 &precomp[i][2][0], &precomp[i][2][1], group)); 512 } 513 /* precompute [*][3][*] */ 514 MP_CHECKOK(group-> 515 point_add(&precomp[0][1][0], &precomp[0][1][1], 516 &precomp[0][2][0], &precomp[0][2][1], 517 &precomp[0][3][0], &precomp[0][3][1], group)); 518 for (i = 1; i < 4; i++) { 519 MP_CHECKOK(group-> 520 point_add(&precomp[0][3][0], &precomp[0][3][1], 521 &precomp[i][0][0], &precomp[i][0][1], 522 &precomp[i][3][0], &precomp[i][3][1], group)); 523 } 524 525 d = (mpl_significant_bits(a) + 1) / 2; 526 527 /* R = inf */ 528 MP_CHECKOK(mp_init(&rz, FLAG(k1))); 529 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz)); 530 531 for (i = d - 1; i >= 0; i--) { 532 ai = MP_GET_BIT(a, 2 * i + 1); 533 ai <<= 1; 534 ai |= MP_GET_BIT(a, 2 * i); 535 bi = MP_GET_BIT(b, 2 * i + 1); 536 bi <<= 1; 537 bi |= MP_GET_BIT(b, 2 * i); 538 /* R = 2^2 * R */ 539 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 540 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group)); 541 /* R = R + (ai * A + bi * B) */ 542 MP_CHECKOK(ec_GFp_pt_add_jac_aff 543 (rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1], 544 rx, ry, &rz, group)); 545 } 546 547 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group)); 548 549 if (group->meth->field_dec) { 550 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 551 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 552 } 553 554 CLEANUP: 555 mp_clear(&rz); 556 for (i = 0; i < 4; i++) { 557 for (j = 0; j < 4; j++) { 558 mp_clear(&precomp[i][j][0]); 559 mp_clear(&precomp[i][j][1]); 560 } 561 } 562 return res; 563 } 564