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. 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 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories 24 * 25 * Alternatively, the contents of this file may be used under the terms of 26 * either the GNU General Public License Version 2 or later (the "GPL"), or 27 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), 28 * in which case the provisions of the GPL or the LGPL are applicable instead 29 * of those above. If you wish to allow use of your version of this file only 30 * under the terms of either the GPL or the LGPL, and not to allow others to 31 * use your version of this file under the terms of the MPL, indicate your 32 * decision by deleting the provisions above and replace them with the notice 33 * and other provisions required by the GPL or the LGPL. If you do not delete 34 * the provisions above, a recipient may use your version of this file under 35 * the terms of any one of the MPL, the GPL or the LGPL. 36 * 37 * ***** END LICENSE BLOCK ***** */ 38 /* 39 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. 40 * Use is subject to license terms. 41 * 42 * Sun elects to use this software under the MPL license. 43 */ 44 45 #include "mpi.h" 46 #include "mplogic.h" 47 #include "ecl.h" 48 #include "ecl-priv.h" 49 #ifndef _KERNEL 50 #include <stdlib.h> 51 #endif 52 53 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x, 54 * y). If x, y = NULL, then P is assumed to be the generator (base point) 55 * of the group of points on the elliptic curve. Input and output values 56 * are assumed to be NOT field-encoded. */ 57 mp_err 58 ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px, 59 const mp_int *py, mp_int *rx, mp_int *ry) 60 { 61 mp_err res = MP_OKAY; 62 mp_int kt; 63 64 ARGCHK((k != NULL) && (group != NULL), MP_BADARG); 65 MP_DIGITS(&kt) = 0; 66 67 /* want scalar to be less than or equal to group order */ 68 if (mp_cmp(k, &group->order) > 0) { 69 MP_CHECKOK(mp_init(&kt, FLAG(k))); 70 MP_CHECKOK(mp_mod(k, &group->order, &kt)); 71 } else { 72 MP_SIGN(&kt) = MP_ZPOS; 73 MP_USED(&kt) = MP_USED(k); 74 MP_ALLOC(&kt) = MP_ALLOC(k); 75 MP_DIGITS(&kt) = MP_DIGITS(k); 76 } 77 78 if ((px == NULL) || (py == NULL)) { 79 if (group->base_point_mul) { 80 MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group)); 81 } else { 82 MP_CHECKOK(group-> 83 point_mul(&kt, &group->genx, &group->geny, rx, ry, 84 group)); 85 } 86 } else { 87 if (group->meth->field_enc) { 88 MP_CHECKOK(group->meth->field_enc(px, rx, group->meth)); 89 MP_CHECKOK(group->meth->field_enc(py, ry, group->meth)); 90 MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group)); 91 } else { 92 MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group)); 93 } 94 } 95 if (group->meth->field_dec) { 96 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 97 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 98 } 99 100 CLEANUP: 101 if (MP_DIGITS(&kt) != MP_DIGITS(k)) { 102 mp_clear(&kt); 103 } 104 return res; 105 } 106 107 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 108 * k2 * P(x, y), where G is the generator (base point) of the group of 109 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 110 * Input and output values are assumed to be NOT field-encoded. */ 111 mp_err 112 ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px, 113 const mp_int *py, mp_int *rx, mp_int *ry, 114 const ECGroup *group) 115 { 116 mp_err res = MP_OKAY; 117 mp_int sx, sy; 118 119 ARGCHK(group != NULL, MP_BADARG); 120 ARGCHK(!((k1 == NULL) 121 && ((k2 == NULL) || (px == NULL) 122 || (py == NULL))), MP_BADARG); 123 124 /* if some arguments are not defined used ECPoint_mul */ 125 if (k1 == NULL) { 126 return ECPoint_mul(group, k2, px, py, rx, ry); 127 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { 128 return ECPoint_mul(group, k1, NULL, NULL, rx, ry); 129 } 130 131 MP_DIGITS(&sx) = 0; 132 MP_DIGITS(&sy) = 0; 133 MP_CHECKOK(mp_init(&sx, FLAG(k1))); 134 MP_CHECKOK(mp_init(&sy, FLAG(k1))); 135 136 MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy)); 137 MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry)); 138 139 if (group->meth->field_enc) { 140 MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth)); 141 MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth)); 142 MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth)); 143 MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth)); 144 } 145 146 MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group)); 147 148 if (group->meth->field_dec) { 149 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 150 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 151 } 152 153 CLEANUP: 154 mp_clear(&sx); 155 mp_clear(&sy); 156 return res; 157 } 158 159 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 160 * k2 * P(x, y), where G is the generator (base point) of the group of 161 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 162 * Input and output values are assumed to be NOT field-encoded. Uses 163 * algorithm 15 (simultaneous multiple point multiplication) from Brown, 164 * Hankerson, Lopez, Menezes. Software Implementation of the NIST 165 * Elliptic Curves over Prime Fields. */ 166 mp_err 167 ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px, 168 const mp_int *py, mp_int *rx, mp_int *ry, 169 const ECGroup *group) 170 { 171 mp_err res = MP_OKAY; 172 mp_int precomp[4][4][2]; 173 const mp_int *a, *b; 174 int i, j; 175 int ai, bi, d; 176 177 ARGCHK(group != NULL, MP_BADARG); 178 ARGCHK(!((k1 == NULL) 179 && ((k2 == NULL) || (px == NULL) 180 || (py == NULL))), MP_BADARG); 181 182 /* if some arguments are not defined used ECPoint_mul */ 183 if (k1 == NULL) { 184 return ECPoint_mul(group, k2, px, py, rx, ry); 185 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { 186 return ECPoint_mul(group, k1, NULL, NULL, rx, ry); 187 } 188 189 /* initialize precomputation table */ 190 for (i = 0; i < 4; i++) { 191 for (j = 0; j < 4; j++) { 192 MP_DIGITS(&precomp[i][j][0]) = 0; 193 MP_DIGITS(&precomp[i][j][1]) = 0; 194 } 195 } 196 for (i = 0; i < 4; i++) { 197 for (j = 0; j < 4; j++) { 198 MP_CHECKOK( mp_init_size(&precomp[i][j][0], 199 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); 200 MP_CHECKOK( mp_init_size(&precomp[i][j][1], 201 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); 202 } 203 } 204 205 /* fill precomputation table */ 206 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ 207 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { 208 a = k2; 209 b = k1; 210 if (group->meth->field_enc) { 211 MP_CHECKOK(group->meth-> 212 field_enc(px, &precomp[1][0][0], group->meth)); 213 MP_CHECKOK(group->meth-> 214 field_enc(py, &precomp[1][0][1], group->meth)); 215 } else { 216 MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); 217 MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); 218 } 219 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); 220 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); 221 } else { 222 a = k1; 223 b = k2; 224 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); 225 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); 226 if (group->meth->field_enc) { 227 MP_CHECKOK(group->meth-> 228 field_enc(px, &precomp[0][1][0], group->meth)); 229 MP_CHECKOK(group->meth-> 230 field_enc(py, &precomp[0][1][1], group->meth)); 231 } else { 232 MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); 233 MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); 234 } 235 } 236 /* precompute [*][0][*] */ 237 mp_zero(&precomp[0][0][0]); 238 mp_zero(&precomp[0][0][1]); 239 MP_CHECKOK(group-> 240 point_dbl(&precomp[1][0][0], &precomp[1][0][1], 241 &precomp[2][0][0], &precomp[2][0][1], group)); 242 MP_CHECKOK(group-> 243 point_add(&precomp[1][0][0], &precomp[1][0][1], 244 &precomp[2][0][0], &precomp[2][0][1], 245 &precomp[3][0][0], &precomp[3][0][1], group)); 246 /* precompute [*][1][*] */ 247 for (i = 1; i < 4; i++) { 248 MP_CHECKOK(group-> 249 point_add(&precomp[0][1][0], &precomp[0][1][1], 250 &precomp[i][0][0], &precomp[i][0][1], 251 &precomp[i][1][0], &precomp[i][1][1], group)); 252 } 253 /* precompute [*][2][*] */ 254 MP_CHECKOK(group-> 255 point_dbl(&precomp[0][1][0], &precomp[0][1][1], 256 &precomp[0][2][0], &precomp[0][2][1], group)); 257 for (i = 1; i < 4; i++) { 258 MP_CHECKOK(group-> 259 point_add(&precomp[0][2][0], &precomp[0][2][1], 260 &precomp[i][0][0], &precomp[i][0][1], 261 &precomp[i][2][0], &precomp[i][2][1], group)); 262 } 263 /* precompute [*][3][*] */ 264 MP_CHECKOK(group-> 265 point_add(&precomp[0][1][0], &precomp[0][1][1], 266 &precomp[0][2][0], &precomp[0][2][1], 267 &precomp[0][3][0], &precomp[0][3][1], group)); 268 for (i = 1; i < 4; i++) { 269 MP_CHECKOK(group-> 270 point_add(&precomp[0][3][0], &precomp[0][3][1], 271 &precomp[i][0][0], &precomp[i][0][1], 272 &precomp[i][3][0], &precomp[i][3][1], group)); 273 } 274 275 d = (mpl_significant_bits(a) + 1) / 2; 276 277 /* R = inf */ 278 mp_zero(rx); 279 mp_zero(ry); 280 281 for (i = d - 1; i >= 0; i--) { 282 ai = MP_GET_BIT(a, 2 * i + 1); 283 ai <<= 1; 284 ai |= MP_GET_BIT(a, 2 * i); 285 bi = MP_GET_BIT(b, 2 * i + 1); 286 bi <<= 1; 287 bi |= MP_GET_BIT(b, 2 * i); 288 /* R = 2^2 * R */ 289 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); 290 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); 291 /* R = R + (ai * A + bi * B) */ 292 MP_CHECKOK(group-> 293 point_add(rx, ry, &precomp[ai][bi][0], 294 &precomp[ai][bi][1], rx, ry, group)); 295 } 296 297 if (group->meth->field_dec) { 298 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 299 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 300 } 301 302 CLEANUP: 303 for (i = 0; i < 4; i++) { 304 for (j = 0; j < 4; j++) { 305 mp_clear(&precomp[i][j][0]); 306 mp_clear(&precomp[i][j][1]); 307 } 308 } 309 return res; 310 } 311 312 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 313 * k2 * P(x, y), where G is the generator (base point) of the group of 314 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 315 * Input and output values are assumed to be NOT field-encoded. */ 316 mp_err 317 ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2, 318 const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry) 319 { 320 mp_err res = MP_OKAY; 321 mp_int k1t, k2t; 322 const mp_int *k1p, *k2p; 323 324 MP_DIGITS(&k1t) = 0; 325 MP_DIGITS(&k2t) = 0; 326 327 ARGCHK(group != NULL, MP_BADARG); 328 329 /* want scalar to be less than or equal to group order */ 330 if (k1 != NULL) { 331 if (mp_cmp(k1, &group->order) >= 0) { 332 MP_CHECKOK(mp_init(&k1t, FLAG(k1))); 333 MP_CHECKOK(mp_mod(k1, &group->order, &k1t)); 334 k1p = &k1t; 335 } else { 336 k1p = k1; 337 } 338 } else { 339 k1p = k1; 340 } 341 if (k2 != NULL) { 342 if (mp_cmp(k2, &group->order) >= 0) { 343 MP_CHECKOK(mp_init(&k2t, FLAG(k2))); 344 MP_CHECKOK(mp_mod(k2, &group->order, &k2t)); 345 k2p = &k2t; 346 } else { 347 k2p = k2; 348 } 349 } else { 350 k2p = k2; 351 } 352 353 /* if points_mul is defined, then use it */ 354 if (group->points_mul) { 355 res = group->points_mul(k1p, k2p, px, py, rx, ry, group); 356 } else { 357 res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group); 358 } 359 360 CLEANUP: 361 mp_clear(&k1t); 362 mp_clear(&k2t); 363 return res; 364 } 365