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 #pragma ident "%Z%%M% %I% %E% SMI" 46 47 #include "mpi.h" 48 #include "mplogic.h" 49 #include "ecl.h" 50 #include "ecl-priv.h" 51 #ifndef _KERNEL 52 #include <stdlib.h> 53 #endif 54 55 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x, 56 * y). If x, y = NULL, then P is assumed to be the generator (base point) 57 * of the group of points on the elliptic curve. Input and output values 58 * are assumed to be NOT field-encoded. */ 59 mp_err 60 ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px, 61 const mp_int *py, mp_int *rx, mp_int *ry) 62 { 63 mp_err res = MP_OKAY; 64 mp_int kt; 65 66 ARGCHK((k != NULL) && (group != NULL), MP_BADARG); 67 MP_DIGITS(&kt) = 0; 68 69 /* want scalar to be less than or equal to group order */ 70 if (mp_cmp(k, &group->order) > 0) { 71 MP_CHECKOK(mp_init(&kt, FLAG(k))); 72 MP_CHECKOK(mp_mod(k, &group->order, &kt)); 73 } else { 74 MP_SIGN(&kt) = MP_ZPOS; 75 MP_USED(&kt) = MP_USED(k); 76 MP_ALLOC(&kt) = MP_ALLOC(k); 77 MP_DIGITS(&kt) = MP_DIGITS(k); 78 } 79 80 if ((px == NULL) || (py == NULL)) { 81 if (group->base_point_mul) { 82 MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group)); 83 } else { 84 MP_CHECKOK(group-> 85 point_mul(&kt, &group->genx, &group->geny, rx, ry, 86 group)); 87 } 88 } else { 89 if (group->meth->field_enc) { 90 MP_CHECKOK(group->meth->field_enc(px, rx, group->meth)); 91 MP_CHECKOK(group->meth->field_enc(py, ry, group->meth)); 92 MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group)); 93 } else { 94 MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group)); 95 } 96 } 97 if (group->meth->field_dec) { 98 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 99 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 100 } 101 102 CLEANUP: 103 if (MP_DIGITS(&kt) != MP_DIGITS(k)) { 104 mp_clear(&kt); 105 } 106 return res; 107 } 108 109 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 110 * k2 * P(x, y), where G is the generator (base point) of the group of 111 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 112 * Input and output values are assumed to be NOT field-encoded. */ 113 mp_err 114 ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px, 115 const mp_int *py, mp_int *rx, mp_int *ry, 116 const ECGroup *group) 117 { 118 mp_err res = MP_OKAY; 119 mp_int sx, sy; 120 121 ARGCHK(group != NULL, MP_BADARG); 122 ARGCHK(!((k1 == NULL) 123 && ((k2 == NULL) || (px == NULL) 124 || (py == NULL))), MP_BADARG); 125 126 /* if some arguments are not defined used ECPoint_mul */ 127 if (k1 == NULL) { 128 return ECPoint_mul(group, k2, px, py, rx, ry); 129 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { 130 return ECPoint_mul(group, k1, NULL, NULL, rx, ry); 131 } 132 133 MP_DIGITS(&sx) = 0; 134 MP_DIGITS(&sy) = 0; 135 MP_CHECKOK(mp_init(&sx, FLAG(k1))); 136 MP_CHECKOK(mp_init(&sy, FLAG(k1))); 137 138 MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy)); 139 MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry)); 140 141 if (group->meth->field_enc) { 142 MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth)); 143 MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth)); 144 MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth)); 145 MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth)); 146 } 147 148 MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group)); 149 150 if (group->meth->field_dec) { 151 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 152 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 153 } 154 155 CLEANUP: 156 mp_clear(&sx); 157 mp_clear(&sy); 158 return res; 159 } 160 161 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 162 * k2 * P(x, y), where G is the generator (base point) of the group of 163 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 164 * Input and output values are assumed to be NOT field-encoded. Uses 165 * algorithm 15 (simultaneous multiple point multiplication) from Brown, 166 * Hankerson, Lopez, Menezes. Software Implementation of the NIST 167 * Elliptic Curves over Prime Fields. */ 168 mp_err 169 ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px, 170 const mp_int *py, mp_int *rx, mp_int *ry, 171 const ECGroup *group) 172 { 173 mp_err res = MP_OKAY; 174 mp_int precomp[4][4][2]; 175 const mp_int *a, *b; 176 int i, j; 177 int ai, bi, d; 178 179 ARGCHK(group != NULL, MP_BADARG); 180 ARGCHK(!((k1 == NULL) 181 && ((k2 == NULL) || (px == NULL) 182 || (py == NULL))), MP_BADARG); 183 184 /* if some arguments are not defined used ECPoint_mul */ 185 if (k1 == NULL) { 186 return ECPoint_mul(group, k2, px, py, rx, ry); 187 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { 188 return ECPoint_mul(group, k1, NULL, NULL, rx, ry); 189 } 190 191 /* initialize precomputation table */ 192 for (i = 0; i < 4; i++) { 193 for (j = 0; j < 4; j++) { 194 MP_DIGITS(&precomp[i][j][0]) = 0; 195 MP_DIGITS(&precomp[i][j][1]) = 0; 196 } 197 } 198 for (i = 0; i < 4; i++) { 199 for (j = 0; j < 4; j++) { 200 MP_CHECKOK( mp_init_size(&precomp[i][j][0], 201 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); 202 MP_CHECKOK( mp_init_size(&precomp[i][j][1], 203 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) ); 204 } 205 } 206 207 /* fill precomputation table */ 208 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ 209 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { 210 a = k2; 211 b = k1; 212 if (group->meth->field_enc) { 213 MP_CHECKOK(group->meth-> 214 field_enc(px, &precomp[1][0][0], group->meth)); 215 MP_CHECKOK(group->meth-> 216 field_enc(py, &precomp[1][0][1], group->meth)); 217 } else { 218 MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); 219 MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); 220 } 221 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); 222 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); 223 } else { 224 a = k1; 225 b = k2; 226 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); 227 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); 228 if (group->meth->field_enc) { 229 MP_CHECKOK(group->meth-> 230 field_enc(px, &precomp[0][1][0], group->meth)); 231 MP_CHECKOK(group->meth-> 232 field_enc(py, &precomp[0][1][1], group->meth)); 233 } else { 234 MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); 235 MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); 236 } 237 } 238 /* precompute [*][0][*] */ 239 mp_zero(&precomp[0][0][0]); 240 mp_zero(&precomp[0][0][1]); 241 MP_CHECKOK(group-> 242 point_dbl(&precomp[1][0][0], &precomp[1][0][1], 243 &precomp[2][0][0], &precomp[2][0][1], group)); 244 MP_CHECKOK(group-> 245 point_add(&precomp[1][0][0], &precomp[1][0][1], 246 &precomp[2][0][0], &precomp[2][0][1], 247 &precomp[3][0][0], &precomp[3][0][1], group)); 248 /* precompute [*][1][*] */ 249 for (i = 1; i < 4; i++) { 250 MP_CHECKOK(group-> 251 point_add(&precomp[0][1][0], &precomp[0][1][1], 252 &precomp[i][0][0], &precomp[i][0][1], 253 &precomp[i][1][0], &precomp[i][1][1], group)); 254 } 255 /* precompute [*][2][*] */ 256 MP_CHECKOK(group-> 257 point_dbl(&precomp[0][1][0], &precomp[0][1][1], 258 &precomp[0][2][0], &precomp[0][2][1], group)); 259 for (i = 1; i < 4; i++) { 260 MP_CHECKOK(group-> 261 point_add(&precomp[0][2][0], &precomp[0][2][1], 262 &precomp[i][0][0], &precomp[i][0][1], 263 &precomp[i][2][0], &precomp[i][2][1], group)); 264 } 265 /* precompute [*][3][*] */ 266 MP_CHECKOK(group-> 267 point_add(&precomp[0][1][0], &precomp[0][1][1], 268 &precomp[0][2][0], &precomp[0][2][1], 269 &precomp[0][3][0], &precomp[0][3][1], group)); 270 for (i = 1; i < 4; i++) { 271 MP_CHECKOK(group-> 272 point_add(&precomp[0][3][0], &precomp[0][3][1], 273 &precomp[i][0][0], &precomp[i][0][1], 274 &precomp[i][3][0], &precomp[i][3][1], group)); 275 } 276 277 d = (mpl_significant_bits(a) + 1) / 2; 278 279 /* R = inf */ 280 mp_zero(rx); 281 mp_zero(ry); 282 283 for (i = d - 1; i >= 0; i--) { 284 ai = MP_GET_BIT(a, 2 * i + 1); 285 ai <<= 1; 286 ai |= MP_GET_BIT(a, 2 * i); 287 bi = MP_GET_BIT(b, 2 * i + 1); 288 bi <<= 1; 289 bi |= MP_GET_BIT(b, 2 * i); 290 /* R = 2^2 * R */ 291 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); 292 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); 293 /* R = R + (ai * A + bi * B) */ 294 MP_CHECKOK(group-> 295 point_add(rx, ry, &precomp[ai][bi][0], 296 &precomp[ai][bi][1], rx, ry, group)); 297 } 298 299 if (group->meth->field_dec) { 300 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); 301 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); 302 } 303 304 CLEANUP: 305 for (i = 0; i < 4; i++) { 306 for (j = 0; j < 4; j++) { 307 mp_clear(&precomp[i][j][0]); 308 mp_clear(&precomp[i][j][1]); 309 } 310 } 311 return res; 312 } 313 314 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 315 * k2 * P(x, y), where G is the generator (base point) of the group of 316 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. 317 * Input and output values are assumed to be NOT field-encoded. */ 318 mp_err 319 ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2, 320 const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry) 321 { 322 mp_err res = MP_OKAY; 323 mp_int k1t, k2t; 324 const mp_int *k1p, *k2p; 325 326 MP_DIGITS(&k1t) = 0; 327 MP_DIGITS(&k2t) = 0; 328 329 ARGCHK(group != NULL, MP_BADARG); 330 331 /* want scalar to be less than or equal to group order */ 332 if (k1 != NULL) { 333 if (mp_cmp(k1, &group->order) >= 0) { 334 MP_CHECKOK(mp_init(&k1t, FLAG(k1))); 335 MP_CHECKOK(mp_mod(k1, &group->order, &k1t)); 336 k1p = &k1t; 337 } else { 338 k1p = k1; 339 } 340 } else { 341 k1p = k1; 342 } 343 if (k2 != NULL) { 344 if (mp_cmp(k2, &group->order) >= 0) { 345 MP_CHECKOK(mp_init(&k2t, FLAG(k2))); 346 MP_CHECKOK(mp_mod(k2, &group->order, &k2t)); 347 k2p = &k2t; 348 } else { 349 k2p = k2; 350 } 351 } else { 352 k2p = k2; 353 } 354 355 /* if points_mul is defined, then use it */ 356 if (group->points_mul) { 357 res = group->points_mul(k1p, k2p, px, py, rx, ry, group); 358 } else { 359 res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group); 360 } 361 362 CLEANUP: 363 mp_clear(&k1t); 364 mp_clear(&k2t); 365 return res; 366 } 367