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 binary polynomial 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 * 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 "ec2.h" 46 #include "mplogic.h" 47 #include "mp_gf2m.h" 48 #ifndef _KERNEL 49 #include <stdlib.h> 50 #endif 51 52 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */ 53 mp_err 54 ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py) 55 { 56 57 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) { 58 return MP_YES; 59 } else { 60 return MP_NO; 61 } 62 63 } 64 65 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */ 66 mp_err 67 ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py) 68 { 69 mp_zero(px); 70 mp_zero(py); 71 return MP_OKAY; 72 } 73 74 /* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P, 75 * Q, and R can all be identical. Uses affine coordinates. */ 76 mp_err 77 ec_GF2m_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, tempx, tempy; 83 84 MP_DIGITS(&lambda) = 0; 85 MP_DIGITS(&tempx) = 0; 86 MP_DIGITS(&tempy) = 0; 87 MP_CHECKOK(mp_init(&lambda, FLAG(px))); 88 MP_CHECKOK(mp_init(&tempx, FLAG(px))); 89 MP_CHECKOK(mp_init(&tempy, FLAG(px))); 90 /* if P = inf, then R = Q */ 91 if (ec_GF2m_pt_is_inf_aff(px, py) == 0) { 92 MP_CHECKOK(mp_copy(qx, rx)); 93 MP_CHECKOK(mp_copy(qy, ry)); 94 res = MP_OKAY; 95 goto CLEANUP; 96 } 97 /* if Q = inf, then R = P */ 98 if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) { 99 MP_CHECKOK(mp_copy(px, rx)); 100 MP_CHECKOK(mp_copy(py, ry)); 101 res = MP_OKAY; 102 goto CLEANUP; 103 } 104 /* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2 105 * + lambda + px + qx */ 106 if (mp_cmp(px, qx) != 0) { 107 MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth)); 108 MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth)); 109 MP_CHECKOK(group->meth-> 110 field_div(&tempy, &tempx, &lambda, group->meth)); 111 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth)); 112 MP_CHECKOK(group->meth-> 113 field_add(&tempx, &lambda, &tempx, group->meth)); 114 MP_CHECKOK(group->meth-> 115 field_add(&tempx, &group->curvea, &tempx, group->meth)); 116 MP_CHECKOK(group->meth-> 117 field_add(&tempx, px, &tempx, group->meth)); 118 MP_CHECKOK(group->meth-> 119 field_add(&tempx, qx, &tempx, group->meth)); 120 } else { 121 /* if py != qy or qx = 0, then R = inf */ 122 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) { 123 mp_zero(rx); 124 mp_zero(ry); 125 res = MP_OKAY; 126 goto CLEANUP; 127 } 128 /* lambda = qx + qy / qx */ 129 MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth)); 130 MP_CHECKOK(group->meth-> 131 field_add(&lambda, qx, &lambda, group->meth)); 132 /* tempx = a + lambda^2 + lambda */ 133 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth)); 134 MP_CHECKOK(group->meth-> 135 field_add(&tempx, &lambda, &tempx, group->meth)); 136 MP_CHECKOK(group->meth-> 137 field_add(&tempx, &group->curvea, &tempx, group->meth)); 138 } 139 /* ry = (qx + tempx) * lambda + tempx + qy */ 140 MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth)); 141 MP_CHECKOK(group->meth-> 142 field_mul(&tempy, &lambda, &tempy, group->meth)); 143 MP_CHECKOK(group->meth-> 144 field_add(&tempy, &tempx, &tempy, group->meth)); 145 MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth)); 146 /* rx = tempx */ 147 MP_CHECKOK(mp_copy(&tempx, rx)); 148 149 CLEANUP: 150 mp_clear(&lambda); 151 mp_clear(&tempx); 152 mp_clear(&tempy); 153 return res; 154 } 155 156 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be 157 * identical. Uses affine coordinates. */ 158 mp_err 159 ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx, 160 const mp_int *qy, mp_int *rx, mp_int *ry, 161 const ECGroup *group) 162 { 163 mp_err res = MP_OKAY; 164 mp_int nqy; 165 166 MP_DIGITS(&nqy) = 0; 167 MP_CHECKOK(mp_init(&nqy, FLAG(px))); 168 /* nqy = qx+qy */ 169 MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth)); 170 MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group)); 171 CLEANUP: 172 mp_clear(&nqy); 173 return res; 174 } 175 176 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses 177 * affine coordinates. */ 178 mp_err 179 ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx, 180 mp_int *ry, const ECGroup *group) 181 { 182 return group->point_add(px, py, px, py, rx, ry, group); 183 } 184 185 /* by default, this routine is unused and thus doesn't need to be compiled */ 186 #ifdef ECL_ENABLE_GF2M_PT_MUL_AFF 187 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and 188 * R can be identical. Uses affine coordinates. */ 189 mp_err 190 ec_GF2m_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py, 191 mp_int *rx, mp_int *ry, const ECGroup *group) 192 { 193 mp_err res = MP_OKAY; 194 mp_int k, k3, qx, qy, sx, sy; 195 int b1, b3, i, l; 196 197 MP_DIGITS(&k) = 0; 198 MP_DIGITS(&k3) = 0; 199 MP_DIGITS(&qx) = 0; 200 MP_DIGITS(&qy) = 0; 201 MP_DIGITS(&sx) = 0; 202 MP_DIGITS(&sy) = 0; 203 MP_CHECKOK(mp_init(&k)); 204 MP_CHECKOK(mp_init(&k3)); 205 MP_CHECKOK(mp_init(&qx)); 206 MP_CHECKOK(mp_init(&qy)); 207 MP_CHECKOK(mp_init(&sx)); 208 MP_CHECKOK(mp_init(&sy)); 209 210 /* if n = 0 then r = inf */ 211 if (mp_cmp_z(n) == 0) { 212 mp_zero(rx); 213 mp_zero(ry); 214 res = MP_OKAY; 215 goto CLEANUP; 216 } 217 /* Q = P, k = n */ 218 MP_CHECKOK(mp_copy(px, &qx)); 219 MP_CHECKOK(mp_copy(py, &qy)); 220 MP_CHECKOK(mp_copy(n, &k)); 221 /* if n < 0 then Q = -Q, k = -k */ 222 if (mp_cmp_z(n) < 0) { 223 MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth)); 224 MP_CHECKOK(mp_neg(&k, &k)); 225 } 226 #ifdef ECL_DEBUG /* basic double and add method */ 227 l = mpl_significant_bits(&k) - 1; 228 MP_CHECKOK(mp_copy(&qx, &sx)); 229 MP_CHECKOK(mp_copy(&qy, &sy)); 230 for (i = l - 1; i >= 0; i--) { 231 /* S = 2S */ 232 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); 233 /* if k_i = 1, then S = S + Q */ 234 if (mpl_get_bit(&k, i) != 0) { 235 MP_CHECKOK(group-> 236 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); 237 } 238 } 239 #else /* double and add/subtract method from 240 * standard */ 241 /* k3 = 3 * k */ 242 MP_CHECKOK(mp_set_int(&k3, 3)); 243 MP_CHECKOK(mp_mul(&k, &k3, &k3)); 244 /* S = Q */ 245 MP_CHECKOK(mp_copy(&qx, &sx)); 246 MP_CHECKOK(mp_copy(&qy, &sy)); 247 /* l = index of high order bit in binary representation of 3*k */ 248 l = mpl_significant_bits(&k3) - 1; 249 /* for i = l-1 downto 1 */ 250 for (i = l - 1; i >= 1; i--) { 251 /* S = 2S */ 252 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); 253 b3 = MP_GET_BIT(&k3, i); 254 b1 = MP_GET_BIT(&k, i); 255 /* if k3_i = 1 and k_i = 0, then S = S + Q */ 256 if ((b3 == 1) && (b1 == 0)) { 257 MP_CHECKOK(group-> 258 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); 259 /* if k3_i = 0 and k_i = 1, then S = S - Q */ 260 } else if ((b3 == 0) && (b1 == 1)) { 261 MP_CHECKOK(group-> 262 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group)); 263 } 264 } 265 #endif 266 /* output S */ 267 MP_CHECKOK(mp_copy(&sx, rx)); 268 MP_CHECKOK(mp_copy(&sy, ry)); 269 270 CLEANUP: 271 mp_clear(&k); 272 mp_clear(&k3); 273 mp_clear(&qx); 274 mp_clear(&qy); 275 mp_clear(&sx); 276 mp_clear(&sy); 277 return res; 278 } 279 #endif 280 281 /* Validates a point on a GF2m curve. */ 282 mp_err 283 ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group) 284 { 285 mp_err res = MP_NO; 286 mp_int accl, accr, tmp, pxt, pyt; 287 288 MP_DIGITS(&accl) = 0; 289 MP_DIGITS(&accr) = 0; 290 MP_DIGITS(&tmp) = 0; 291 MP_DIGITS(&pxt) = 0; 292 MP_DIGITS(&pyt) = 0; 293 MP_CHECKOK(mp_init(&accl, FLAG(px))); 294 MP_CHECKOK(mp_init(&accr, FLAG(px))); 295 MP_CHECKOK(mp_init(&tmp, FLAG(px))); 296 MP_CHECKOK(mp_init(&pxt, FLAG(px))); 297 MP_CHECKOK(mp_init(&pyt, FLAG(px))); 298 299 /* 1: Verify that publicValue is not the point at infinity */ 300 if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) { 301 res = MP_NO; 302 goto CLEANUP; 303 } 304 /* 2: Verify that the coordinates of publicValue are elements 305 * of the field. 306 */ 307 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) || 308 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) { 309 res = MP_NO; 310 goto CLEANUP; 311 } 312 /* 3: Verify that publicValue is on the curve. */ 313 if (group->meth->field_enc) { 314 group->meth->field_enc(px, &pxt, group->meth); 315 group->meth->field_enc(py, &pyt, group->meth); 316 } else { 317 mp_copy(px, &pxt); 318 mp_copy(py, &pyt); 319 } 320 /* left-hand side: y^2 + x*y */ 321 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) ); 322 MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) ); 323 MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) ); 324 /* right-hand side: x^3 + a*x^2 + b */ 325 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) ); 326 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) ); 327 MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) ); 328 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) ); 329 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) ); 330 /* check LHS - RHS == 0 */ 331 MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) ); 332 if (mp_cmp_z(&accr) != 0) { 333 res = MP_NO; 334 goto CLEANUP; 335 } 336 /* 4: Verify that the order of the curve times the publicValue 337 * is the point at infinity. 338 */ 339 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) ); 340 if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) { 341 res = MP_NO; 342 goto CLEANUP; 343 } 344 345 res = MP_YES; 346 347 CLEANUP: 348 mp_clear(&accl); 349 mp_clear(&accr); 350 mp_clear(&tmp); 351 mp_clear(&pxt); 352 mp_clear(&pyt); 353 return res; 354 } 355