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 #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 #define ECP224_DIGITS ECL_CURVE_DIGITS(224) 56 57 /* Fast modular reduction for p224 = 2^224 - 2^96 + 1. a can be r. Uses 58 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software 59 * Implementation of the NIST Elliptic Curves over Prime Fields. */ 60 mp_err 61 ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth) 62 { 63 mp_err res = MP_OKAY; 64 mp_size a_used = MP_USED(a); 65 66 int r3b; 67 mp_digit carry; 68 #ifdef ECL_THIRTY_TWO_BIT 69 mp_digit a6a = 0, a6b = 0, 70 a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0; 71 mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a; 72 #else 73 mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0; 74 mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0; 75 mp_digit r0, r1, r2, r3; 76 #endif 77 78 /* reduction not needed if a is not larger than field size */ 79 if (a_used < ECP224_DIGITS) { 80 if (a == r) return MP_OKAY; 81 return mp_copy(a, r); 82 } 83 /* for polynomials larger than twice the field size, use regular 84 * reduction */ 85 if (a_used > ECL_CURVE_DIGITS(224*2)) { 86 MP_CHECKOK(mp_mod(a, &meth->irr, r)); 87 } else { 88 #ifdef ECL_THIRTY_TWO_BIT 89 /* copy out upper words of a */ 90 switch (a_used) { 91 case 14: 92 a6b = MP_DIGIT(a, 13); 93 case 13: 94 a6a = MP_DIGIT(a, 12); 95 case 12: 96 a5b = MP_DIGIT(a, 11); 97 case 11: 98 a5a = MP_DIGIT(a, 10); 99 case 10: 100 a4b = MP_DIGIT(a, 9); 101 case 9: 102 a4a = MP_DIGIT(a, 8); 103 case 8: 104 a3b = MP_DIGIT(a, 7); 105 } 106 r3a = MP_DIGIT(a, 6); 107 r2b= MP_DIGIT(a, 5); 108 r2a= MP_DIGIT(a, 4); 109 r1b = MP_DIGIT(a, 3); 110 r1a = MP_DIGIT(a, 2); 111 r0b = MP_DIGIT(a, 1); 112 r0a = MP_DIGIT(a, 0); 113 114 115 /* implement r = (a3a,a2,a1,a0) 116 +(a5a, a4,a3b, 0) 117 +( 0, a6,a5b, 0) 118 -( 0 0, 0|a6b, a6a|a5b ) 119 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ 120 MP_ADD_CARRY (r1b, a3b, r1b, 0, carry); 121 MP_ADD_CARRY (r2a, a4a, r2a, carry, carry); 122 MP_ADD_CARRY (r2b, a4b, r2b, carry, carry); 123 MP_ADD_CARRY (r3a, a5a, r3a, carry, carry); 124 r3b = carry; 125 MP_ADD_CARRY (r1b, a5b, r1b, 0, carry); 126 MP_ADD_CARRY (r2a, a6a, r2a, carry, carry); 127 MP_ADD_CARRY (r2b, a6b, r2b, carry, carry); 128 MP_ADD_CARRY (r3a, 0, r3a, carry, carry); 129 r3b += carry; 130 MP_SUB_BORROW(r0a, a3b, r0a, 0, carry); 131 MP_SUB_BORROW(r0b, a4a, r0b, carry, carry); 132 MP_SUB_BORROW(r1a, a4b, r1a, carry, carry); 133 MP_SUB_BORROW(r1b, a5a, r1b, carry, carry); 134 MP_SUB_BORROW(r2a, a5b, r2a, carry, carry); 135 MP_SUB_BORROW(r2b, a6a, r2b, carry, carry); 136 MP_SUB_BORROW(r3a, a6b, r3a, carry, carry); 137 r3b -= carry; 138 MP_SUB_BORROW(r0a, a5b, r0a, 0, carry); 139 MP_SUB_BORROW(r0b, a6a, r0b, carry, carry); 140 MP_SUB_BORROW(r1a, a6b, r1a, carry, carry); 141 if (carry) { 142 MP_SUB_BORROW(r1b, 0, r1b, carry, carry); 143 MP_SUB_BORROW(r2a, 0, r2a, carry, carry); 144 MP_SUB_BORROW(r2b, 0, r2b, carry, carry); 145 MP_SUB_BORROW(r3a, 0, r3a, carry, carry); 146 r3b -= carry; 147 } 148 149 while (r3b > 0) { 150 int tmp; 151 MP_ADD_CARRY(r1b, r3b, r1b, 0, carry); 152 if (carry) { 153 MP_ADD_CARRY(r2a, 0, r2a, carry, carry); 154 MP_ADD_CARRY(r2b, 0, r2b, carry, carry); 155 MP_ADD_CARRY(r3a, 0, r3a, carry, carry); 156 } 157 tmp = carry; 158 MP_SUB_BORROW(r0a, r3b, r0a, 0, carry); 159 if (carry) { 160 MP_SUB_BORROW(r0b, 0, r0b, carry, carry); 161 MP_SUB_BORROW(r1a, 0, r1a, carry, carry); 162 MP_SUB_BORROW(r1b, 0, r1b, carry, carry); 163 MP_SUB_BORROW(r2a, 0, r2a, carry, carry); 164 MP_SUB_BORROW(r2b, 0, r2b, carry, carry); 165 MP_SUB_BORROW(r3a, 0, r3a, carry, carry); 166 tmp -= carry; 167 } 168 r3b = tmp; 169 } 170 171 while (r3b < 0) { 172 mp_digit maxInt = MP_DIGIT_MAX; 173 MP_ADD_CARRY (r0a, 1, r0a, 0, carry); 174 MP_ADD_CARRY (r0b, 0, r0b, carry, carry); 175 MP_ADD_CARRY (r1a, 0, r1a, carry, carry); 176 MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry); 177 MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry); 178 MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry); 179 MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry); 180 r3b += carry; 181 } 182 /* check for final reduction */ 183 /* now the only way we are over is if the top 4 words are all ones */ 184 if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX) 185 && (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) && 186 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) { 187 /* one last subraction */ 188 MP_SUB_BORROW(r0a, 1, r0a, 0, carry); 189 MP_SUB_BORROW(r0b, 0, r0b, carry, carry); 190 MP_SUB_BORROW(r1a, 0, r1a, carry, carry); 191 r1b = r2a = r2b = r3a = 0; 192 } 193 194 195 if (a != r) { 196 MP_CHECKOK(s_mp_pad(r, 7)); 197 } 198 /* set the lower words of r */ 199 MP_SIGN(r) = MP_ZPOS; 200 MP_USED(r) = 7; 201 MP_DIGIT(r, 6) = r3a; 202 MP_DIGIT(r, 5) = r2b; 203 MP_DIGIT(r, 4) = r2a; 204 MP_DIGIT(r, 3) = r1b; 205 MP_DIGIT(r, 2) = r1a; 206 MP_DIGIT(r, 1) = r0b; 207 MP_DIGIT(r, 0) = r0a; 208 #else 209 /* copy out upper words of a */ 210 switch (a_used) { 211 case 7: 212 a6 = MP_DIGIT(a, 6); 213 a6b = a6 >> 32; 214 a6a_a5b = a6 << 32; 215 case 6: 216 a5 = MP_DIGIT(a, 5); 217 a5b = a5 >> 32; 218 a6a_a5b |= a5b; 219 a5b = a5b << 32; 220 a5a_a4b = a5 << 32; 221 a5a = a5 & 0xffffffff; 222 case 5: 223 a4 = MP_DIGIT(a, 4); 224 a5a_a4b |= a4 >> 32; 225 a4a_a3b = a4 << 32; 226 case 4: 227 a3b = MP_DIGIT(a, 3) >> 32; 228 a4a_a3b |= a3b; 229 a3b = a3b << 32; 230 } 231 232 r3 = MP_DIGIT(a, 3) & 0xffffffff; 233 r2 = MP_DIGIT(a, 2); 234 r1 = MP_DIGIT(a, 1); 235 r0 = MP_DIGIT(a, 0); 236 237 /* implement r = (a3a,a2,a1,a0) 238 +(a5a, a4,a3b, 0) 239 +( 0, a6,a5b, 0) 240 -( 0 0, 0|a6b, a6a|a5b ) 241 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ 242 MP_ADD_CARRY (r1, a3b, r1, 0, carry); 243 MP_ADD_CARRY (r2, a4 , r2, carry, carry); 244 MP_ADD_CARRY (r3, a5a, r3, carry, carry); 245 MP_ADD_CARRY (r1, a5b, r1, 0, carry); 246 MP_ADD_CARRY (r2, a6 , r2, carry, carry); 247 MP_ADD_CARRY (r3, 0, r3, carry, carry); 248 249 MP_SUB_BORROW(r0, a4a_a3b, r0, 0, carry); 250 MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry); 251 MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry); 252 MP_SUB_BORROW(r3, a6b , r3, carry, carry); 253 MP_SUB_BORROW(r0, a6a_a5b, r0, 0, carry); 254 MP_SUB_BORROW(r1, a6b , r1, carry, carry); 255 if (carry) { 256 MP_SUB_BORROW(r2, 0, r2, carry, carry); 257 MP_SUB_BORROW(r3, 0, r3, carry, carry); 258 } 259 260 261 /* if the value is negative, r3 has a 2's complement 262 * high value */ 263 r3b = (int)(r3 >>32); 264 while (r3b > 0) { 265 r3 &= 0xffffffff; 266 MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry); 267 if (carry) { 268 MP_ADD_CARRY(r2, 0, r2, carry, carry); 269 MP_ADD_CARRY(r3, 0, r3, carry, carry); 270 } 271 MP_SUB_BORROW(r0, r3b, r0, 0, carry); 272 if (carry) { 273 MP_SUB_BORROW(r1, 0, r1, carry, carry); 274 MP_SUB_BORROW(r2, 0, r2, carry, carry); 275 MP_SUB_BORROW(r3, 0, r3, carry, carry); 276 } 277 r3b = (int)(r3 >>32); 278 } 279 280 while (r3b < 0) { 281 MP_ADD_CARRY (r0, 1, r0, 0, carry); 282 MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry); 283 MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry); 284 MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry); 285 r3b = (int)(r3 >>32); 286 } 287 /* check for final reduction */ 288 /* now the only way we are over is if the top 4 words are all ones */ 289 if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX) 290 && ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) && 291 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) { 292 /* one last subraction */ 293 MP_SUB_BORROW(r0, 1, r0, 0, carry); 294 MP_SUB_BORROW(r1, 0, r1, carry, carry); 295 r2 = r3 = 0; 296 } 297 298 299 if (a != r) { 300 MP_CHECKOK(s_mp_pad(r, 4)); 301 } 302 /* set the lower words of r */ 303 MP_SIGN(r) = MP_ZPOS; 304 MP_USED(r) = 4; 305 MP_DIGIT(r, 3) = r3; 306 MP_DIGIT(r, 2) = r2; 307 MP_DIGIT(r, 1) = r1; 308 MP_DIGIT(r, 0) = r0; 309 #endif 310 } 311 312 CLEANUP: 313 return res; 314 } 315 316 /* Compute the square of polynomial a, reduce modulo p224. Store the 317 * result in r. r could be a. Uses optimized modular reduction for p224. 318 */ 319 mp_err 320 ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) 321 { 322 mp_err res = MP_OKAY; 323 324 MP_CHECKOK(mp_sqr(a, r)); 325 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 326 CLEANUP: 327 return res; 328 } 329 330 /* Compute the product of two polynomials a and b, reduce modulo p224. 331 * Store the result in r. r could be a or b; a could be b. Uses 332 * optimized modular reduction for p224. */ 333 mp_err 334 ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r, 335 const GFMethod *meth) 336 { 337 mp_err res = MP_OKAY; 338 339 MP_CHECKOK(mp_mul(a, b, r)); 340 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 341 CLEANUP: 342 return res; 343 } 344 345 /* Divides two field elements. If a is NULL, then returns the inverse of 346 * b. */ 347 mp_err 348 ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r, 349 const GFMethod *meth) 350 { 351 mp_err res = MP_OKAY; 352 mp_int t; 353 354 /* If a is NULL, then return the inverse of b, otherwise return a/b. */ 355 if (a == NULL) { 356 return mp_invmod(b, &meth->irr, r); 357 } else { 358 /* MPI doesn't support divmod, so we implement it using invmod and 359 * mulmod. */ 360 MP_CHECKOK(mp_init(&t, FLAG(b))); 361 MP_CHECKOK(mp_invmod(b, &meth->irr, &t)); 362 MP_CHECKOK(mp_mul(a, &t, r)); 363 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 364 CLEANUP: 365 mp_clear(&t); 366 return res; 367 } 368 } 369 370 /* Wire in fast field arithmetic and precomputation of base point for 371 * named curves. */ 372 mp_err 373 ec_group_set_gfp224(ECGroup *group, ECCurveName name) 374 { 375 if (name == ECCurve_NIST_P224) { 376 group->meth->field_mod = &ec_GFp_nistp224_mod; 377 group->meth->field_mul = &ec_GFp_nistp224_mul; 378 group->meth->field_sqr = &ec_GFp_nistp224_sqr; 379 group->meth->field_div = &ec_GFp_nistp224_div; 380 } 381 return MP_OKAY; 382 } 383