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 56 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */ 57 mp_err 58 ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py) 59 { 60 61 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) { 62 return MP_YES; 63 } else { 64 return MP_NO; 65 } 66 67 } 68 69 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */ 70 mp_err 71 ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py) 72 { 73 mp_zero(px); 74 mp_zero(py); 75 return MP_OKAY; 76 } 77 78 /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P, 79 * Q, and R can all be identical. Uses affine coordinates. Assumes input 80 * is already field-encoded using field_enc, and returns output that is 81 * still field-encoded. */ 82 mp_err 83 ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx, 84 const mp_int *qy, mp_int *rx, mp_int *ry, 85 const ECGroup *group) 86 { 87 mp_err res = MP_OKAY; 88 mp_int lambda, temp, tempx, tempy; 89 90 MP_DIGITS(&lambda) = 0; 91 MP_DIGITS(&temp) = 0; 92 MP_DIGITS(&tempx) = 0; 93 MP_DIGITS(&tempy) = 0; 94 MP_CHECKOK(mp_init(&lambda, FLAG(px))); 95 MP_CHECKOK(mp_init(&temp, FLAG(px))); 96 MP_CHECKOK(mp_init(&tempx, FLAG(px))); 97 MP_CHECKOK(mp_init(&tempy, FLAG(px))); 98 /* if P = inf, then R = Q */ 99 if (ec_GFp_pt_is_inf_aff(px, py) == 0) { 100 MP_CHECKOK(mp_copy(qx, rx)); 101 MP_CHECKOK(mp_copy(qy, ry)); 102 res = MP_OKAY; 103 goto CLEANUP; 104 } 105 /* if Q = inf, then R = P */ 106 if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) { 107 MP_CHECKOK(mp_copy(px, rx)); 108 MP_CHECKOK(mp_copy(py, ry)); 109 res = MP_OKAY; 110 goto CLEANUP; 111 } 112 /* if px != qx, then lambda = (py-qy) / (px-qx) */ 113 if (mp_cmp(px, qx) != 0) { 114 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth)); 115 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth)); 116 MP_CHECKOK(group->meth-> 117 field_div(&tempy, &tempx, &lambda, group->meth)); 118 } else { 119 /* if py != qy or qy = 0, then R = inf */ 120 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) { 121 mp_zero(rx); 122 mp_zero(ry); 123 res = MP_OKAY; 124 goto CLEANUP; 125 } 126 /* lambda = (3qx^2+a) / (2qy) */ 127 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth)); 128 MP_CHECKOK(mp_set_int(&temp, 3)); 129 if (group->meth->field_enc) { 130 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); 131 } 132 MP_CHECKOK(group->meth-> 133 field_mul(&tempx, &temp, &tempx, group->meth)); 134 MP_CHECKOK(group->meth-> 135 field_add(&tempx, &group->curvea, &tempx, group->meth)); 136 MP_CHECKOK(mp_set_int(&temp, 2)); 137 if (group->meth->field_enc) { 138 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); 139 } 140 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth)); 141 MP_CHECKOK(group->meth-> 142 field_div(&tempx, &tempy, &lambda, group->meth)); 143 } 144 /* rx = lambda^2 - px - qx */ 145 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth)); 146 MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth)); 147 MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth)); 148 /* ry = (x1-x2) * lambda - y1 */ 149 MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth)); 150 MP_CHECKOK(group->meth-> 151 field_mul(&tempy, &lambda, &tempy, group->meth)); 152 MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth)); 153 MP_CHECKOK(mp_copy(&tempx, rx)); 154 MP_CHECKOK(mp_copy(&tempy, ry)); 155 156 CLEANUP: 157 mp_clear(&lambda); 158 mp_clear(&temp); 159 mp_clear(&tempx); 160 mp_clear(&tempy); 161 return res; 162 } 163 164 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be 165 * identical. Uses affine coordinates. Assumes input is already 166 * field-encoded using field_enc, and returns output that is still 167 * field-encoded. */ 168 mp_err 169 ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx, 170 const mp_int *qy, mp_int *rx, mp_int *ry, 171 const ECGroup *group) 172 { 173 mp_err res = MP_OKAY; 174 mp_int nqy; 175 176 MP_DIGITS(&nqy) = 0; 177 MP_CHECKOK(mp_init(&nqy, FLAG(px))); 178 /* nqy = -qy */ 179 MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth)); 180 res = group->point_add(px, py, qx, &nqy, rx, ry, group); 181 CLEANUP: 182 mp_clear(&nqy); 183 return res; 184 } 185 186 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses 187 * affine coordinates. Assumes input is already field-encoded using 188 * field_enc, and returns output that is still field-encoded. */ 189 mp_err 190 ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx, 191 mp_int *ry, const ECGroup *group) 192 { 193 return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group); 194 } 195 196 /* by default, this routine is unused and thus doesn't need to be compiled */ 197 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF 198 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and 199 * R can be identical. Uses affine coordinates. Assumes input is already 200 * field-encoded using field_enc, and returns output that is still 201 * field-encoded. */ 202 mp_err 203 ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py, 204 mp_int *rx, mp_int *ry, const ECGroup *group) 205 { 206 mp_err res = MP_OKAY; 207 mp_int k, k3, qx, qy, sx, sy; 208 int b1, b3, i, l; 209 210 MP_DIGITS(&k) = 0; 211 MP_DIGITS(&k3) = 0; 212 MP_DIGITS(&qx) = 0; 213 MP_DIGITS(&qy) = 0; 214 MP_DIGITS(&sx) = 0; 215 MP_DIGITS(&sy) = 0; 216 MP_CHECKOK(mp_init(&k)); 217 MP_CHECKOK(mp_init(&k3)); 218 MP_CHECKOK(mp_init(&qx)); 219 MP_CHECKOK(mp_init(&qy)); 220 MP_CHECKOK(mp_init(&sx)); 221 MP_CHECKOK(mp_init(&sy)); 222 223 /* if n = 0 then r = inf */ 224 if (mp_cmp_z(n) == 0) { 225 mp_zero(rx); 226 mp_zero(ry); 227 res = MP_OKAY; 228 goto CLEANUP; 229 } 230 /* Q = P, k = n */ 231 MP_CHECKOK(mp_copy(px, &qx)); 232 MP_CHECKOK(mp_copy(py, &qy)); 233 MP_CHECKOK(mp_copy(n, &k)); 234 /* if n < 0 then Q = -Q, k = -k */ 235 if (mp_cmp_z(n) < 0) { 236 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth)); 237 MP_CHECKOK(mp_neg(&k, &k)); 238 } 239 #ifdef ECL_DEBUG /* basic double and add method */ 240 l = mpl_significant_bits(&k) - 1; 241 MP_CHECKOK(mp_copy(&qx, &sx)); 242 MP_CHECKOK(mp_copy(&qy, &sy)); 243 for (i = l - 1; i >= 0; i--) { 244 /* S = 2S */ 245 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); 246 /* if k_i = 1, then S = S + Q */ 247 if (mpl_get_bit(&k, i) != 0) { 248 MP_CHECKOK(group-> 249 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); 250 } 251 } 252 #else /* double and add/subtract method from 253 * standard */ 254 /* k3 = 3 * k */ 255 MP_CHECKOK(mp_set_int(&k3, 3)); 256 MP_CHECKOK(mp_mul(&k, &k3, &k3)); 257 /* S = Q */ 258 MP_CHECKOK(mp_copy(&qx, &sx)); 259 MP_CHECKOK(mp_copy(&qy, &sy)); 260 /* l = index of high order bit in binary representation of 3*k */ 261 l = mpl_significant_bits(&k3) - 1; 262 /* for i = l-1 downto 1 */ 263 for (i = l - 1; i >= 1; i--) { 264 /* S = 2S */ 265 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); 266 b3 = MP_GET_BIT(&k3, i); 267 b1 = MP_GET_BIT(&k, i); 268 /* if k3_i = 1 and k_i = 0, then S = S + Q */ 269 if ((b3 == 1) && (b1 == 0)) { 270 MP_CHECKOK(group-> 271 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); 272 /* if k3_i = 0 and k_i = 1, then S = S - Q */ 273 } else if ((b3 == 0) && (b1 == 1)) { 274 MP_CHECKOK(group-> 275 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group)); 276 } 277 } 278 #endif 279 /* output S */ 280 MP_CHECKOK(mp_copy(&sx, rx)); 281 MP_CHECKOK(mp_copy(&sy, ry)); 282 283 CLEANUP: 284 mp_clear(&k); 285 mp_clear(&k3); 286 mp_clear(&qx); 287 mp_clear(&qy); 288 mp_clear(&sx); 289 mp_clear(&sy); 290 return res; 291 } 292 #endif 293 294 /* Validates a point on a GFp curve. */ 295 mp_err 296 ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group) 297 { 298 mp_err res = MP_NO; 299 mp_int accl, accr, tmp, pxt, pyt; 300 301 MP_DIGITS(&accl) = 0; 302 MP_DIGITS(&accr) = 0; 303 MP_DIGITS(&tmp) = 0; 304 MP_DIGITS(&pxt) = 0; 305 MP_DIGITS(&pyt) = 0; 306 MP_CHECKOK(mp_init(&accl, FLAG(px))); 307 MP_CHECKOK(mp_init(&accr, FLAG(px))); 308 MP_CHECKOK(mp_init(&tmp, FLAG(px))); 309 MP_CHECKOK(mp_init(&pxt, FLAG(px))); 310 MP_CHECKOK(mp_init(&pyt, FLAG(px))); 311 312 /* 1: Verify that publicValue is not the point at infinity */ 313 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { 314 res = MP_NO; 315 goto CLEANUP; 316 } 317 /* 2: Verify that the coordinates of publicValue are elements 318 * of the field. 319 */ 320 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) || 321 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) { 322 res = MP_NO; 323 goto CLEANUP; 324 } 325 /* 3: Verify that publicValue is on the curve. */ 326 if (group->meth->field_enc) { 327 group->meth->field_enc(px, &pxt, group->meth); 328 group->meth->field_enc(py, &pyt, group->meth); 329 } else { 330 mp_copy(px, &pxt); 331 mp_copy(py, &pyt); 332 } 333 /* left-hand side: y^2 */ 334 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) ); 335 /* right-hand side: x^3 + a*x + b */ 336 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) ); 337 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) ); 338 MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) ); 339 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) ); 340 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) ); 341 /* check LHS - RHS == 0 */ 342 MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) ); 343 if (mp_cmp_z(&accr) != 0) { 344 res = MP_NO; 345 goto CLEANUP; 346 } 347 /* 4: Verify that the order of the curve times the publicValue 348 * is the point at infinity. 349 */ 350 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) ); 351 if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) { 352 res = MP_NO; 353 goto CLEANUP; 354 } 355 356 res = MP_YES; 357 358 CLEANUP: 359 mp_clear(&accl); 360 mp_clear(&accr); 361 mp_clear(&tmp); 362 mp_clear(&pxt); 363 mp_clear(&pyt); 364 return res; 365 } 366