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 * Douglas Stebila <douglas@stebila.ca> 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 "ecp.h" 48 #include "mpi.h" 49 #include "mplogic.h" 50 #include "mpi-priv.h" 51 #ifndef _KERNEL 52 #include <stdlib.h> 53 #endif 54 55 /* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1. a can be r. 56 * Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to 57 * Elliptic Curve Cryptography. */ 58 mp_err 59 ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth) 60 { 61 mp_err res = MP_OKAY; 62 mp_size a_used = MP_USED(a); 63 int a_bits = mpl_significant_bits(a); 64 mp_digit carry; 65 66 #ifdef ECL_THIRTY_TWO_BIT 67 mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0; 68 mp_digit r0, r1, r2, r3, r4, r5, r6, r7; 69 int r8; /* must be a signed value ! */ 70 #else 71 mp_digit a4=0, a5=0, a6=0, a7=0; 72 mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l; 73 mp_digit r0, r1, r2, r3; 74 int r4; /* must be a signed value ! */ 75 #endif 76 /* for polynomials larger than twice the field size 77 * use regular reduction */ 78 if (a_bits < 256) { 79 if (a == r) return MP_OKAY; 80 return mp_copy(a,r); 81 } 82 if (a_bits > 512) { 83 MP_CHECKOK(mp_mod(a, &meth->irr, r)); 84 } else { 85 86 #ifdef ECL_THIRTY_TWO_BIT 87 switch (a_used) { 88 case 16: 89 a15 = MP_DIGIT(a,15); 90 case 15: 91 a14 = MP_DIGIT(a,14); 92 case 14: 93 a13 = MP_DIGIT(a,13); 94 case 13: 95 a12 = MP_DIGIT(a,12); 96 case 12: 97 a11 = MP_DIGIT(a,11); 98 case 11: 99 a10 = MP_DIGIT(a,10); 100 case 10: 101 a9 = MP_DIGIT(a,9); 102 case 9: 103 a8 = MP_DIGIT(a,8); 104 } 105 106 r0 = MP_DIGIT(a,0); 107 r1 = MP_DIGIT(a,1); 108 r2 = MP_DIGIT(a,2); 109 r3 = MP_DIGIT(a,3); 110 r4 = MP_DIGIT(a,4); 111 r5 = MP_DIGIT(a,5); 112 r6 = MP_DIGIT(a,6); 113 r7 = MP_DIGIT(a,7); 114 115 /* sum 1 */ 116 MP_ADD_CARRY(r3, a11, r3, 0, carry); 117 MP_ADD_CARRY(r4, a12, r4, carry, carry); 118 MP_ADD_CARRY(r5, a13, r5, carry, carry); 119 MP_ADD_CARRY(r6, a14, r6, carry, carry); 120 MP_ADD_CARRY(r7, a15, r7, carry, carry); 121 r8 = carry; 122 MP_ADD_CARRY(r3, a11, r3, 0, carry); 123 MP_ADD_CARRY(r4, a12, r4, carry, carry); 124 MP_ADD_CARRY(r5, a13, r5, carry, carry); 125 MP_ADD_CARRY(r6, a14, r6, carry, carry); 126 MP_ADD_CARRY(r7, a15, r7, carry, carry); 127 r8 += carry; 128 /* sum 2 */ 129 MP_ADD_CARRY(r3, a12, r3, 0, carry); 130 MP_ADD_CARRY(r4, a13, r4, carry, carry); 131 MP_ADD_CARRY(r5, a14, r5, carry, carry); 132 MP_ADD_CARRY(r6, a15, r6, carry, carry); 133 MP_ADD_CARRY(r7, 0, r7, carry, carry); 134 r8 += carry; 135 /* combine last bottom of sum 3 with second sum 2 */ 136 MP_ADD_CARRY(r0, a8, r0, 0, carry); 137 MP_ADD_CARRY(r1, a9, r1, carry, carry); 138 MP_ADD_CARRY(r2, a10, r2, carry, carry); 139 MP_ADD_CARRY(r3, a12, r3, carry, carry); 140 MP_ADD_CARRY(r4, a13, r4, carry, carry); 141 MP_ADD_CARRY(r5, a14, r5, carry, carry); 142 MP_ADD_CARRY(r6, a15, r6, carry, carry); 143 MP_ADD_CARRY(r7, a15, r7, carry, carry); /* from sum 3 */ 144 r8 += carry; 145 /* sum 3 (rest of it)*/ 146 MP_ADD_CARRY(r6, a14, r6, 0, carry); 147 MP_ADD_CARRY(r7, 0, r7, carry, carry); 148 r8 += carry; 149 /* sum 4 (rest of it)*/ 150 MP_ADD_CARRY(r0, a9, r0, 0, carry); 151 MP_ADD_CARRY(r1, a10, r1, carry, carry); 152 MP_ADD_CARRY(r2, a11, r2, carry, carry); 153 MP_ADD_CARRY(r3, a13, r3, carry, carry); 154 MP_ADD_CARRY(r4, a14, r4, carry, carry); 155 MP_ADD_CARRY(r5, a15, r5, carry, carry); 156 MP_ADD_CARRY(r6, a13, r6, carry, carry); 157 MP_ADD_CARRY(r7, a8, r7, carry, carry); 158 r8 += carry; 159 /* diff 5 */ 160 MP_SUB_BORROW(r0, a11, r0, 0, carry); 161 MP_SUB_BORROW(r1, a12, r1, carry, carry); 162 MP_SUB_BORROW(r2, a13, r2, carry, carry); 163 MP_SUB_BORROW(r3, 0, r3, carry, carry); 164 MP_SUB_BORROW(r4, 0, r4, carry, carry); 165 MP_SUB_BORROW(r5, 0, r5, carry, carry); 166 MP_SUB_BORROW(r6, a8, r6, carry, carry); 167 MP_SUB_BORROW(r7, a10, r7, carry, carry); 168 r8 -= carry; 169 /* diff 6 */ 170 MP_SUB_BORROW(r0, a12, r0, 0, carry); 171 MP_SUB_BORROW(r1, a13, r1, carry, carry); 172 MP_SUB_BORROW(r2, a14, r2, carry, carry); 173 MP_SUB_BORROW(r3, a15, r3, carry, carry); 174 MP_SUB_BORROW(r4, 0, r4, carry, carry); 175 MP_SUB_BORROW(r5, 0, r5, carry, carry); 176 MP_SUB_BORROW(r6, a9, r6, carry, carry); 177 MP_SUB_BORROW(r7, a11, r7, carry, carry); 178 r8 -= carry; 179 /* diff 7 */ 180 MP_SUB_BORROW(r0, a13, r0, 0, carry); 181 MP_SUB_BORROW(r1, a14, r1, carry, carry); 182 MP_SUB_BORROW(r2, a15, r2, carry, carry); 183 MP_SUB_BORROW(r3, a8, r3, carry, carry); 184 MP_SUB_BORROW(r4, a9, r4, carry, carry); 185 MP_SUB_BORROW(r5, a10, r5, carry, carry); 186 MP_SUB_BORROW(r6, 0, r6, carry, carry); 187 MP_SUB_BORROW(r7, a12, r7, carry, carry); 188 r8 -= carry; 189 /* diff 8 */ 190 MP_SUB_BORROW(r0, a14, r0, 0, carry); 191 MP_SUB_BORROW(r1, a15, r1, carry, carry); 192 MP_SUB_BORROW(r2, 0, r2, carry, carry); 193 MP_SUB_BORROW(r3, a9, r3, carry, carry); 194 MP_SUB_BORROW(r4, a10, r4, carry, carry); 195 MP_SUB_BORROW(r5, a11, r5, carry, carry); 196 MP_SUB_BORROW(r6, 0, r6, carry, carry); 197 MP_SUB_BORROW(r7, a13, r7, carry, carry); 198 r8 -= carry; 199 200 /* reduce the overflows */ 201 while (r8 > 0) { 202 mp_digit r8_d = r8; 203 MP_ADD_CARRY(r0, r8_d, r0, 0, carry); 204 MP_ADD_CARRY(r1, 0, r1, carry, carry); 205 MP_ADD_CARRY(r2, 0, r2, carry, carry); 206 MP_ADD_CARRY(r3, -r8_d, r3, carry, carry); 207 MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry, carry); 208 MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry, carry); 209 MP_ADD_CARRY(r6, -(r8_d+1), r6, carry, carry); 210 MP_ADD_CARRY(r7, (r8_d-1), r7, carry, carry); 211 r8 = carry; 212 } 213 214 /* reduce the underflows */ 215 while (r8 < 0) { 216 mp_digit r8_d = -r8; 217 MP_SUB_BORROW(r0, r8_d, r0, 0, carry); 218 MP_SUB_BORROW(r1, 0, r1, carry, carry); 219 MP_SUB_BORROW(r2, 0, r2, carry, carry); 220 MP_SUB_BORROW(r3, -r8_d, r3, carry, carry); 221 MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry, carry); 222 MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry, carry); 223 MP_SUB_BORROW(r6, -(r8_d+1), r6, carry, carry); 224 MP_SUB_BORROW(r7, (r8_d-1), r7, carry, carry); 225 r8 = -carry; 226 } 227 if (a != r) { 228 MP_CHECKOK(s_mp_pad(r,8)); 229 } 230 MP_SIGN(r) = MP_ZPOS; 231 MP_USED(r) = 8; 232 233 MP_DIGIT(r,7) = r7; 234 MP_DIGIT(r,6) = r6; 235 MP_DIGIT(r,5) = r5; 236 MP_DIGIT(r,4) = r4; 237 MP_DIGIT(r,3) = r3; 238 MP_DIGIT(r,2) = r2; 239 MP_DIGIT(r,1) = r1; 240 MP_DIGIT(r,0) = r0; 241 242 /* final reduction if necessary */ 243 if ((r7 == MP_DIGIT_MAX) && 244 ((r6 > 1) || ((r6 == 1) && 245 (r5 || r4 || r3 || 246 ((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX) 247 && (r0 == MP_DIGIT_MAX)))))) { 248 MP_CHECKOK(mp_sub(r, &meth->irr, r)); 249 } 250 #ifdef notdef 251 252 253 /* smooth the negatives */ 254 while (MP_SIGN(r) != MP_ZPOS) { 255 MP_CHECKOK(mp_add(r, &meth->irr, r)); 256 } 257 while (MP_USED(r) > 8) { 258 MP_CHECKOK(mp_sub(r, &meth->irr, r)); 259 } 260 261 /* final reduction if necessary */ 262 if (MP_DIGIT(r,7) >= MP_DIGIT(&meth->irr,7)) { 263 if (mp_cmp(r,&meth->irr) != MP_LT) { 264 MP_CHECKOK(mp_sub(r, &meth->irr, r)); 265 } 266 } 267 #endif 268 s_mp_clamp(r); 269 #else 270 switch (a_used) { 271 case 8: 272 a7 = MP_DIGIT(a,7); 273 case 7: 274 a6 = MP_DIGIT(a,6); 275 case 6: 276 a5 = MP_DIGIT(a,5); 277 case 5: 278 a4 = MP_DIGIT(a,4); 279 } 280 a7l = a7 << 32; 281 a7h = a7 >> 32; 282 a6l = a6 << 32; 283 a6h = a6 >> 32; 284 a5l = a5 << 32; 285 a5h = a5 >> 32; 286 a4l = a4 << 32; 287 a4h = a4 >> 32; 288 r3 = MP_DIGIT(a,3); 289 r2 = MP_DIGIT(a,2); 290 r1 = MP_DIGIT(a,1); 291 r0 = MP_DIGIT(a,0); 292 293 /* sum 1 */ 294 MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry); 295 MP_ADD_CARRY(r2, a6, r2, carry, carry); 296 MP_ADD_CARRY(r3, a7, r3, carry, carry); 297 r4 = carry; 298 MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry); 299 MP_ADD_CARRY(r2, a6, r2, carry, carry); 300 MP_ADD_CARRY(r3, a7, r3, carry, carry); 301 r4 += carry; 302 /* sum 2 */ 303 MP_ADD_CARRY(r1, a6l, r1, 0, carry); 304 MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry); 305 MP_ADD_CARRY(r3, a7h, r3, carry, carry); 306 r4 += carry; 307 MP_ADD_CARRY(r1, a6l, r1, 0, carry); 308 MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry); 309 MP_ADD_CARRY(r3, a7h, r3, carry, carry); 310 r4 += carry; 311 312 /* sum 3 */ 313 MP_ADD_CARRY(r0, a4, r0, 0, carry); 314 MP_ADD_CARRY(r1, a5l >> 32, r1, carry, carry); 315 MP_ADD_CARRY(r2, 0, r2, carry, carry); 316 MP_ADD_CARRY(r3, a7, r3, carry, carry); 317 r4 += carry; 318 /* sum 4 */ 319 MP_ADD_CARRY(r0, a4h | a5l, r0, 0, carry); 320 MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry, carry); 321 MP_ADD_CARRY(r2, a7, r2, carry, carry); 322 MP_ADD_CARRY(r3, a6h | a4l, r3, carry, carry); 323 r4 += carry; 324 /* diff 5 */ 325 MP_SUB_BORROW(r0, a5h | a6l, r0, 0, carry); 326 MP_SUB_BORROW(r1, a6h, r1, carry, carry); 327 MP_SUB_BORROW(r2, 0, r2, carry, carry); 328 MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry, carry); 329 r4 -= carry; 330 /* diff 6 */ 331 MP_SUB_BORROW(r0, a6, r0, 0, carry); 332 MP_SUB_BORROW(r1, a7, r1, carry, carry); 333 MP_SUB_BORROW(r2, 0, r2, carry, carry); 334 MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry, carry); 335 r4 -= carry; 336 /* diff 7 */ 337 MP_SUB_BORROW(r0, a6h|a7l, r0, 0, carry); 338 MP_SUB_BORROW(r1, a7h|a4l, r1, carry, carry); 339 MP_SUB_BORROW(r2, a4h|a5l, r2, carry, carry); 340 MP_SUB_BORROW(r3, a6l, r3, carry, carry); 341 r4 -= carry; 342 /* diff 8 */ 343 MP_SUB_BORROW(r0, a7, r0, 0, carry); 344 MP_SUB_BORROW(r1, a4h<<32, r1, carry, carry); 345 MP_SUB_BORROW(r2, a5, r2, carry, carry); 346 MP_SUB_BORROW(r3, a6h<<32, r3, carry, carry); 347 r4 -= carry; 348 349 /* reduce the overflows */ 350 while (r4 > 0) { 351 mp_digit r4_long = r4; 352 mp_digit r4l = (r4_long << 32); 353 MP_ADD_CARRY(r0, r4_long, r0, 0, carry); 354 MP_ADD_CARRY(r1, -r4l, r1, carry, carry); 355 MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry, carry); 356 MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry, carry); 357 r4 = carry; 358 } 359 360 /* reduce the underflows */ 361 while (r4 < 0) { 362 mp_digit r4_long = -r4; 363 mp_digit r4l = (r4_long << 32); 364 MP_SUB_BORROW(r0, r4_long, r0, 0, carry); 365 MP_SUB_BORROW(r1, -r4l, r1, carry, carry); 366 MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry, carry); 367 MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry, carry); 368 r4 = -carry; 369 } 370 371 if (a != r) { 372 MP_CHECKOK(s_mp_pad(r,4)); 373 } 374 MP_SIGN(r) = MP_ZPOS; 375 MP_USED(r) = 4; 376 377 MP_DIGIT(r,3) = r3; 378 MP_DIGIT(r,2) = r2; 379 MP_DIGIT(r,1) = r1; 380 MP_DIGIT(r,0) = r0; 381 382 /* final reduction if necessary */ 383 if ((r3 > 0xFFFFFFFF00000001ULL) || 384 ((r3 == 0xFFFFFFFF00000001ULL) && 385 (r2 || (r1 >> 32)|| 386 (r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) { 387 /* very rare, just use mp_sub */ 388 MP_CHECKOK(mp_sub(r, &meth->irr, r)); 389 } 390 391 s_mp_clamp(r); 392 #endif 393 } 394 395 CLEANUP: 396 return res; 397 } 398 399 /* Compute the square of polynomial a, reduce modulo p256. Store the 400 * result in r. r could be a. Uses optimized modular reduction for p256. 401 */ 402 mp_err 403 ec_GFp_nistp256_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) 404 { 405 mp_err res = MP_OKAY; 406 407 MP_CHECKOK(mp_sqr(a, r)); 408 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth)); 409 CLEANUP: 410 return res; 411 } 412 413 /* Compute the product of two polynomials a and b, reduce modulo p256. 414 * Store the result in r. r could be a or b; a could be b. Uses 415 * optimized modular reduction for p256. */ 416 mp_err 417 ec_GFp_nistp256_mul(const mp_int *a, const mp_int *b, mp_int *r, 418 const GFMethod *meth) 419 { 420 mp_err res = MP_OKAY; 421 422 MP_CHECKOK(mp_mul(a, b, r)); 423 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth)); 424 CLEANUP: 425 return res; 426 } 427 428 /* Wire in fast field arithmetic and precomputation of base point for 429 * named curves. */ 430 mp_err 431 ec_group_set_gfp256(ECGroup *group, ECCurveName name) 432 { 433 if (name == ECCurve_NIST_P256) { 434 group->meth->field_mod = &ec_GFp_nistp256_mod; 435 group->meth->field_mul = &ec_GFp_nistp256_mul; 436 group->meth->field_sqr = &ec_GFp_nistp256_sqr; 437 } 438 return MP_OKAY; 439 } 440