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 50/* Checks if point P(px, py) is at infinity. Uses affine coordinates. */ 51mp_err 52ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py) 53{ 54 55 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) { 56 return MP_YES; 57 } else { 58 return MP_NO; 59 } 60 61} 62 63/* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */ 64mp_err 65ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py) 66{ 67 mp_zero(px); 68 mp_zero(py); 69 return MP_OKAY; 70} 71 72/* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P, 73 * Q, and R can all be identical. Uses affine coordinates. Assumes input 74 * is already field-encoded using field_enc, and returns output that is 75 * still field-encoded. */ 76mp_err 77ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx, 78 const mp_int *qy, mp_int *rx, mp_int *ry, 79 const ECGroup *group) 80{ 81 mp_err res = MP_OKAY; 82 mp_int lambda, temp, tempx, tempy; 83 84 MP_DIGITS(&lambda) = 0; 85 MP_DIGITS(&temp) = 0; 86 MP_DIGITS(&tempx) = 0; 87 MP_DIGITS(&tempy) = 0; 88 MP_CHECKOK(mp_init(&lambda, FLAG(px))); 89 MP_CHECKOK(mp_init(&temp, FLAG(px))); 90 MP_CHECKOK(mp_init(&tempx, FLAG(px))); 91 MP_CHECKOK(mp_init(&tempy, FLAG(px))); 92 /* if P = inf, then R = Q */ 93 if (ec_GFp_pt_is_inf_aff(px, py) == 0) { 94 MP_CHECKOK(mp_copy(qx, rx)); 95 MP_CHECKOK(mp_copy(qy, ry)); 96 res = MP_OKAY; 97 goto CLEANUP; 98 } 99 /* if Q = inf, then R = P */ 100 if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) { 101 MP_CHECKOK(mp_copy(px, rx)); 102 MP_CHECKOK(mp_copy(py, ry)); 103 res = MP_OKAY; 104 goto CLEANUP; 105 } 106 /* if px != qx, then lambda = (py-qy) / (px-qx) */ 107 if (mp_cmp(px, qx) != 0) { 108 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth)); 109 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth)); 110 MP_CHECKOK(group->meth-> 111 field_div(&tempy, &tempx, &lambda, group->meth)); 112 } else { 113 /* if py != qy or qy = 0, then R = inf */ 114 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) { 115 mp_zero(rx); 116 mp_zero(ry); 117 res = MP_OKAY; 118 goto CLEANUP; 119 } 120 /* lambda = (3qx^2+a) / (2qy) */ 121 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth)); 122 MP_CHECKOK(mp_set_int(&temp, 3)); 123 if (group->meth->field_enc) { 124 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); 125 } 126 MP_CHECKOK(group->meth-> 127 field_mul(&tempx, &temp, &tempx, group->meth)); 128 MP_CHECKOK(group->meth-> 129 field_add(&tempx, &group->curvea, &tempx, group->meth)); 130 MP_CHECKOK(mp_set_int(&temp, 2)); 131 if (group->meth->field_enc) { 132 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); 133 } 134 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth)); 135 MP_CHECKOK(group->meth-> 136 field_div(&tempx, &tempy, &lambda, group->meth)); 137 } 138 /* rx = lambda^2 - px - qx */ 139 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth)); 140 MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth)); 141 MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth)); 142 /* ry = (x1-x2) * lambda - y1 */ 143 MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth)); 144 MP_CHECKOK(group->meth-> 145 field_mul(&tempy, &lambda, &tempy, group->meth)); 146 MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth)); 147 MP_CHECKOK(mp_copy(&tempx, rx)); 148 MP_CHECKOK(mp_copy(&tempy, ry)); 149 150 CLEANUP: 151 mp_clear(&lambda); 152 mp_clear(&temp); 153 mp_clear(&tempx); 154 mp_clear(&tempy); 155 return res; 156} 157 158/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be 159 * identical. Uses affine coordinates. Assumes input is already 160 * field-encoded using field_enc, and returns output that is still 161 * field-encoded. */ 162mp_err 163ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx, 164 const mp_int *qy, mp_int *rx, mp_int *ry, 165 const ECGroup *group) 166{ 167 mp_err res = MP_OKAY; 168 mp_int nqy; 169 170 MP_DIGITS(&nqy) = 0; 171 MP_CHECKOK(mp_init(&nqy, FLAG(px))); 172 /* nqy = -qy */ 173 MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth)); 174 res = group->point_add(px, py, qx, &nqy, rx, ry, group); 175 CLEANUP: 176 mp_clear(&nqy); 177 return res; 178} 179 180/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses 181 * affine coordinates. Assumes input is already field-encoded using 182 * field_enc, and returns output that is still field-encoded. */ 183mp_err 184ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx, 185 mp_int *ry, const ECGroup *group) 186{ 187 return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group); 188} 189 190/* by default, this routine is unused and thus doesn't need to be compiled */ 191#ifdef ECL_ENABLE_GFP_PT_MUL_AFF 192/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and 193 * R can be identical. Uses affine coordinates. Assumes input is already 194 * field-encoded using field_enc, and returns output that is still 195 * field-encoded. */ 196mp_err 197ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py, 198 mp_int *rx, mp_int *ry, const ECGroup *group) 199{ 200 mp_err res = MP_OKAY; 201 mp_int k, k3, qx, qy, sx, sy; 202 int b1, b3, i, l; 203 204 MP_DIGITS(&k) = 0; 205 MP_DIGITS(&k3) = 0; 206 MP_DIGITS(&qx) = 0; 207 MP_DIGITS(&qy) = 0; 208 MP_DIGITS(&sx) = 0; 209 MP_DIGITS(&sy) = 0; 210 MP_CHECKOK(mp_init(&k)); 211 MP_CHECKOK(mp_init(&k3)); 212 MP_CHECKOK(mp_init(&qx)); 213 MP_CHECKOK(mp_init(&qy)); 214 MP_CHECKOK(mp_init(&sx)); 215 MP_CHECKOK(mp_init(&sy)); 216 217 /* if n = 0 then r = inf */ 218 if (mp_cmp_z(n) == 0) { 219 mp_zero(rx); 220 mp_zero(ry); 221 res = MP_OKAY; 222 goto CLEANUP; 223 } 224 /* Q = P, k = n */ 225 MP_CHECKOK(mp_copy(px, &qx)); 226 MP_CHECKOK(mp_copy(py, &qy)); 227 MP_CHECKOK(mp_copy(n, &k)); 228 /* if n < 0 then Q = -Q, k = -k */ 229 if (mp_cmp_z(n) < 0) { 230 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth)); 231 MP_CHECKOK(mp_neg(&k, &k)); 232 } 233#ifdef ECL_DEBUG /* basic double and add method */ 234 l = mpl_significant_bits(&k) - 1; 235 MP_CHECKOK(mp_copy(&qx, &sx)); 236 MP_CHECKOK(mp_copy(&qy, &sy)); 237 for (i = l - 1; i >= 0; i--) { 238 /* S = 2S */ 239 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); 240 /* if k_i = 1, then S = S + Q */ 241 if (mpl_get_bit(&k, i) != 0) { 242 MP_CHECKOK(group-> 243 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); 244 } 245 } 246#else /* double and add/subtract method from 247 * standard */ 248 /* k3 = 3 * k */ 249 MP_CHECKOK(mp_set_int(&k3, 3)); 250 MP_CHECKOK(mp_mul(&k, &k3, &k3)); 251 /* S = Q */ 252 MP_CHECKOK(mp_copy(&qx, &sx)); 253 MP_CHECKOK(mp_copy(&qy, &sy)); 254 /* l = index of high order bit in binary representation of 3*k */ 255 l = mpl_significant_bits(&k3) - 1; 256 /* for i = l-1 downto 1 */ 257 for (i = l - 1; i >= 1; i--) { 258 /* S = 2S */ 259 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); 260 b3 = MP_GET_BIT(&k3, i); 261 b1 = MP_GET_BIT(&k, i); 262 /* if k3_i = 1 and k_i = 0, then S = S + Q */ 263 if ((b3 == 1) && (b1 == 0)) { 264 MP_CHECKOK(group-> 265 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); 266 /* if k3_i = 0 and k_i = 1, then S = S - Q */ 267 } else if ((b3 == 0) && (b1 == 1)) { 268 MP_CHECKOK(group-> 269 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group)); 270 } 271 } 272#endif 273 /* output S */ 274 MP_CHECKOK(mp_copy(&sx, rx)); 275 MP_CHECKOK(mp_copy(&sy, ry)); 276 277 CLEANUP: 278 mp_clear(&k); 279 mp_clear(&k3); 280 mp_clear(&qx); 281 mp_clear(&qy); 282 mp_clear(&sx); 283 mp_clear(&sy); 284 return res; 285} 286#endif 287 288/* Validates a point on a GFp curve. */ 289mp_err 290ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group) 291{ 292 mp_err res = MP_NO; 293 mp_int accl, accr, tmp, pxt, pyt; 294 295 MP_DIGITS(&accl) = 0; 296 MP_DIGITS(&accr) = 0; 297 MP_DIGITS(&tmp) = 0; 298 MP_DIGITS(&pxt) = 0; 299 MP_DIGITS(&pyt) = 0; 300 MP_CHECKOK(mp_init(&accl, FLAG(px))); 301 MP_CHECKOK(mp_init(&accr, FLAG(px))); 302 MP_CHECKOK(mp_init(&tmp, FLAG(px))); 303 MP_CHECKOK(mp_init(&pxt, FLAG(px))); 304 MP_CHECKOK(mp_init(&pyt, FLAG(px))); 305 306 /* 1: Verify that publicValue is not the point at infinity */ 307 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { 308 res = MP_NO; 309 goto CLEANUP; 310 } 311 /* 2: Verify that the coordinates of publicValue are elements 312 * of the field. 313 */ 314 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) || 315 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) { 316 res = MP_NO; 317 goto CLEANUP; 318 } 319 /* 3: Verify that publicValue is on the curve. */ 320 if (group->meth->field_enc) { 321 group->meth->field_enc(px, &pxt, group->meth); 322 group->meth->field_enc(py, &pyt, group->meth); 323 } else { 324 mp_copy(px, &pxt); 325 mp_copy(py, &pyt); 326 } 327 /* left-hand side: y^2 */ 328 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) ); 329 /* right-hand side: x^3 + a*x + b */ 330 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) ); 331 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) ); 332 MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) ); 333 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) ); 334 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) ); 335 /* check LHS - RHS == 0 */ 336 MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) ); 337 if (mp_cmp_z(&accr) != 0) { 338 res = MP_NO; 339 goto CLEANUP; 340 } 341 /* 4: Verify that the order of the curve times the publicValue 342 * is the point at infinity. 343 */ 344 /* timing mitigation is not supported */ 345 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt, /*timing*/ 0) ); 346 if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) { 347 res = MP_NO; 348 goto CLEANUP; 349 } 350 351 res = MP_YES; 352 353CLEANUP: 354 mp_clear(&accl); 355 mp_clear(&accr); 356 mp_clear(&tmp); 357 mp_clear(&pxt); 358 mp_clear(&pyt); 359 return res; 360} 361