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>, 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 "ecp.h" 46 #include "mpi.h" 47 #include "mplogic.h" 48 #include "mpi-priv.h" 49 #ifndef _KERNEL 50 #include <stdlib.h> 51 #endif 52 53 #define ECP224_DIGITS ECL_CURVE_DIGITS(224) 54 55 /* Fast modular reduction for p224 = 2^224 - 2^96 + 1. a can be r. Uses 56 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software 57 * Implementation of the NIST Elliptic Curves over Prime Fields. */ 58 mp_err 59 ec_GFp_nistp224_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 64 int r3b; 65 mp_digit carry; 66 #ifdef ECL_THIRTY_TWO_BIT 67 mp_digit a6a = 0, a6b = 0, 68 a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0; 69 mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a; 70 #else 71 mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0; 72 mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0; 73 mp_digit r0, r1, r2, r3; 74 #endif 75 76 /* reduction not needed if a is not larger than field size */ 77 if (a_used < ECP224_DIGITS) { 78 if (a == r) return MP_OKAY; 79 return mp_copy(a, r); 80 } 81 /* for polynomials larger than twice the field size, use regular 82 * reduction */ 83 if (a_used > ECL_CURVE_DIGITS(224*2)) { 84 MP_CHECKOK(mp_mod(a, &meth->irr, r)); 85 } else { 86 #ifdef ECL_THIRTY_TWO_BIT 87 /* copy out upper words of a */ 88 switch (a_used) { 89 case 14: 90 a6b = MP_DIGIT(a, 13); 91 /* FALLTHROUGH */ 92 case 13: 93 a6a = MP_DIGIT(a, 12); 94 /* FALLTHROUGH */ 95 case 12: 96 a5b = MP_DIGIT(a, 11); 97 /* FALLTHROUGH */ 98 case 11: 99 a5a = MP_DIGIT(a, 10); 100 /* FALLTHROUGH */ 101 case 10: 102 a4b = MP_DIGIT(a, 9); 103 /* FALLTHROUGH */ 104 case 9: 105 a4a = MP_DIGIT(a, 8); 106 /* FALLTHROUGH */ 107 case 8: 108 a3b = MP_DIGIT(a, 7); 109 } 110 r3a = MP_DIGIT(a, 6); 111 r2b= MP_DIGIT(a, 5); 112 r2a= MP_DIGIT(a, 4); 113 r1b = MP_DIGIT(a, 3); 114 r1a = MP_DIGIT(a, 2); 115 r0b = MP_DIGIT(a, 1); 116 r0a = MP_DIGIT(a, 0); 117 118 119 /* implement r = (a3a,a2,a1,a0) 120 +(a5a, a4,a3b, 0) 121 +( 0, a6,a5b, 0) 122 -( 0 0, 0|a6b, a6a|a5b ) 123 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ 124 MP_ADD_CARRY (r1b, a3b, r1b, 0, carry); 125 MP_ADD_CARRY (r2a, a4a, r2a, carry, carry); 126 MP_ADD_CARRY (r2b, a4b, r2b, carry, carry); 127 MP_ADD_CARRY (r3a, a5a, r3a, carry, carry); 128 r3b = carry; 129 MP_ADD_CARRY (r1b, a5b, r1b, 0, carry); 130 MP_ADD_CARRY (r2a, a6a, r2a, carry, carry); 131 MP_ADD_CARRY (r2b, a6b, r2b, carry, carry); 132 MP_ADD_CARRY (r3a, 0, r3a, carry, carry); 133 r3b += carry; 134 MP_SUB_BORROW(r0a, a3b, r0a, 0, carry); 135 MP_SUB_BORROW(r0b, a4a, r0b, carry, carry); 136 MP_SUB_BORROW(r1a, a4b, r1a, carry, carry); 137 MP_SUB_BORROW(r1b, a5a, r1b, carry, carry); 138 MP_SUB_BORROW(r2a, a5b, r2a, carry, carry); 139 MP_SUB_BORROW(r2b, a6a, r2b, carry, carry); 140 MP_SUB_BORROW(r3a, a6b, r3a, carry, carry); 141 r3b -= carry; 142 MP_SUB_BORROW(r0a, a5b, r0a, 0, carry); 143 MP_SUB_BORROW(r0b, a6a, r0b, carry, carry); 144 MP_SUB_BORROW(r1a, a6b, r1a, carry, carry); 145 if (carry) { 146 MP_SUB_BORROW(r1b, 0, r1b, carry, carry); 147 MP_SUB_BORROW(r2a, 0, r2a, carry, carry); 148 MP_SUB_BORROW(r2b, 0, r2b, carry, carry); 149 MP_SUB_BORROW(r3a, 0, r3a, carry, carry); 150 r3b -= carry; 151 } 152 153 while (r3b > 0) { 154 int tmp; 155 MP_ADD_CARRY(r1b, r3b, r1b, 0, carry); 156 if (carry) { 157 MP_ADD_CARRY(r2a, 0, r2a, carry, carry); 158 MP_ADD_CARRY(r2b, 0, r2b, carry, carry); 159 MP_ADD_CARRY(r3a, 0, r3a, carry, carry); 160 } 161 tmp = carry; 162 MP_SUB_BORROW(r0a, r3b, r0a, 0, carry); 163 if (carry) { 164 MP_SUB_BORROW(r0b, 0, r0b, carry, carry); 165 MP_SUB_BORROW(r1a, 0, r1a, carry, carry); 166 MP_SUB_BORROW(r1b, 0, r1b, carry, carry); 167 MP_SUB_BORROW(r2a, 0, r2a, carry, carry); 168 MP_SUB_BORROW(r2b, 0, r2b, carry, carry); 169 MP_SUB_BORROW(r3a, 0, r3a, carry, carry); 170 tmp -= carry; 171 } 172 r3b = tmp; 173 } 174 175 while (r3b < 0) { 176 mp_digit maxInt = MP_DIGIT_MAX; 177 MP_ADD_CARRY (r0a, 1, r0a, 0, carry); 178 MP_ADD_CARRY (r0b, 0, r0b, carry, carry); 179 MP_ADD_CARRY (r1a, 0, r1a, carry, carry); 180 MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry); 181 MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry); 182 MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry); 183 MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry); 184 r3b += carry; 185 } 186 /* check for final reduction */ 187 /* now the only way we are over is if the top 4 words are all ones */ 188 if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX) 189 && (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) && 190 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) { 191 /* one last subraction */ 192 MP_SUB_BORROW(r0a, 1, r0a, 0, carry); 193 MP_SUB_BORROW(r0b, 0, r0b, carry, carry); 194 MP_SUB_BORROW(r1a, 0, r1a, carry, carry); 195 r1b = r2a = r2b = r3a = 0; 196 } 197 198 199 if (a != r) { 200 MP_CHECKOK(s_mp_pad(r, 7)); 201 } 202 /* set the lower words of r */ 203 MP_SIGN(r) = MP_ZPOS; 204 MP_USED(r) = 7; 205 MP_DIGIT(r, 6) = r3a; 206 MP_DIGIT(r, 5) = r2b; 207 MP_DIGIT(r, 4) = r2a; 208 MP_DIGIT(r, 3) = r1b; 209 MP_DIGIT(r, 2) = r1a; 210 MP_DIGIT(r, 1) = r0b; 211 MP_DIGIT(r, 0) = r0a; 212 #else 213 /* copy out upper words of a */ 214 switch (a_used) { 215 case 7: 216 a6 = MP_DIGIT(a, 6); 217 a6b = a6 >> 32; 218 a6a_a5b = a6 << 32; 219 /* FALLTHROUGH */ 220 case 6: 221 a5 = MP_DIGIT(a, 5); 222 a5b = a5 >> 32; 223 a6a_a5b |= a5b; 224 a5b = a5b << 32; 225 a5a_a4b = a5 << 32; 226 a5a = a5 & 0xffffffff; 227 /* FALLTHROUGH */ 228 case 5: 229 a4 = MP_DIGIT(a, 4); 230 a5a_a4b |= a4 >> 32; 231 a4a_a3b = a4 << 32; 232 /* FALLTHROUGH */ 233 case 4: 234 a3b = MP_DIGIT(a, 3) >> 32; 235 a4a_a3b |= a3b; 236 a3b = a3b << 32; 237 } 238 239 r3 = MP_DIGIT(a, 3) & 0xffffffff; 240 r2 = MP_DIGIT(a, 2); 241 r1 = MP_DIGIT(a, 1); 242 r0 = MP_DIGIT(a, 0); 243 244 /* implement r = (a3a,a2,a1,a0) 245 +(a5a, a4,a3b, 0) 246 +( 0, a6,a5b, 0) 247 -( 0 0, 0|a6b, a6a|a5b ) 248 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ 249 MP_ADD_CARRY (r1, a3b, r1, 0, carry); 250 MP_ADD_CARRY (r2, a4 , r2, carry, carry); 251 MP_ADD_CARRY (r3, a5a, r3, carry, carry); 252 MP_ADD_CARRY (r1, a5b, r1, 0, carry); 253 MP_ADD_CARRY (r2, a6 , r2, carry, carry); 254 MP_ADD_CARRY (r3, 0, r3, carry, carry); 255 256 MP_SUB_BORROW(r0, a4a_a3b, r0, 0, carry); 257 MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry); 258 MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry); 259 MP_SUB_BORROW(r3, a6b , r3, carry, carry); 260 MP_SUB_BORROW(r0, a6a_a5b, r0, 0, carry); 261 MP_SUB_BORROW(r1, a6b , r1, carry, carry); 262 if (carry) { 263 MP_SUB_BORROW(r2, 0, r2, carry, carry); 264 MP_SUB_BORROW(r3, 0, r3, carry, carry); 265 } 266 267 268 /* if the value is negative, r3 has a 2's complement 269 * high value */ 270 r3b = (int)(r3 >>32); 271 while (r3b > 0) { 272 r3 &= 0xffffffff; 273 MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry); 274 if (carry) { 275 MP_ADD_CARRY(r2, 0, r2, carry, carry); 276 MP_ADD_CARRY(r3, 0, r3, carry, carry); 277 } 278 MP_SUB_BORROW(r0, r3b, r0, 0, carry); 279 if (carry) { 280 MP_SUB_BORROW(r1, 0, r1, carry, carry); 281 MP_SUB_BORROW(r2, 0, r2, carry, carry); 282 MP_SUB_BORROW(r3, 0, r3, carry, carry); 283 } 284 r3b = (int)(r3 >>32); 285 } 286 287 while (r3b < 0) { 288 MP_ADD_CARRY (r0, 1, r0, 0, carry); 289 MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry); 290 MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry); 291 MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry); 292 r3b = (int)(r3 >>32); 293 } 294 /* check for final reduction */ 295 /* now the only way we are over is if the top 4 words are all ones */ 296 if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX) 297 && ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) && 298 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) { 299 /* one last subraction */ 300 MP_SUB_BORROW(r0, 1, r0, 0, carry); 301 MP_SUB_BORROW(r1, 0, r1, carry, carry); 302 r2 = r3 = 0; 303 } 304 305 306 if (a != r) { 307 MP_CHECKOK(s_mp_pad(r, 4)); 308 } 309 /* set the lower words of r */ 310 MP_SIGN(r) = MP_ZPOS; 311 MP_USED(r) = 4; 312 MP_DIGIT(r, 3) = r3; 313 MP_DIGIT(r, 2) = r2; 314 MP_DIGIT(r, 1) = r1; 315 MP_DIGIT(r, 0) = r0; 316 #endif 317 } 318 319 CLEANUP: 320 return res; 321 } 322 323 /* Compute the square of polynomial a, reduce modulo p224. Store the 324 * result in r. r could be a. Uses optimized modular reduction for p224. 325 */ 326 mp_err 327 ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) 328 { 329 mp_err res = MP_OKAY; 330 331 MP_CHECKOK(mp_sqr(a, r)); 332 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 333 CLEANUP: 334 return res; 335 } 336 337 /* Compute the product of two polynomials a and b, reduce modulo p224. 338 * Store the result in r. r could be a or b; a could be b. Uses 339 * optimized modular reduction for p224. */ 340 mp_err 341 ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r, 342 const GFMethod *meth) 343 { 344 mp_err res = MP_OKAY; 345 346 MP_CHECKOK(mp_mul(a, b, r)); 347 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 348 CLEANUP: 349 return res; 350 } 351 352 /* Divides two field elements. If a is NULL, then returns the inverse of 353 * b. */ 354 mp_err 355 ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r, 356 const GFMethod *meth) 357 { 358 mp_err res = MP_OKAY; 359 mp_int t; 360 361 /* If a is NULL, then return the inverse of b, otherwise return a/b. */ 362 if (a == NULL) { 363 return mp_invmod(b, &meth->irr, r); 364 } else { 365 /* MPI doesn't support divmod, so we implement it using invmod and 366 * mulmod. */ 367 MP_CHECKOK(mp_init(&t, FLAG(b))); 368 MP_CHECKOK(mp_invmod(b, &meth->irr, &t)); 369 MP_CHECKOK(mp_mul(a, &t, r)); 370 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 371 CLEANUP: 372 mp_clear(&t); 373 return res; 374 } 375 } 376 377 /* Wire in fast field arithmetic and precomputation of base point for 378 * named curves. */ 379 mp_err 380 ec_group_set_gfp224(ECGroup *group, ECCurveName name) 381 { 382 if (name == ECCurve_NIST_P224) { 383 group->meth->field_mod = &ec_GFp_nistp224_mod; 384 group->meth->field_mul = &ec_GFp_nistp224_mul; 385 group->meth->field_sqr = &ec_GFp_nistp224_sqr; 386 group->meth->field_div = &ec_GFp_nistp224_div; 387 } 388 return MP_OKAY; 389 } 390