1/* 2 * Copyright (c) 2007, 2011, 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 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories 35 * 36 *********************************************************************** */ 37 38#include "ecp.h" 39#include "mpi.h" 40#include "mplogic.h" 41#include "mpi-priv.h" 42#ifndef _KERNEL 43#include <stdlib.h> 44#endif 45 46#define ECP224_DIGITS ECL_CURVE_DIGITS(224) 47 48/* Fast modular reduction for p224 = 2^224 - 2^96 + 1. a can be r. Uses 49 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software 50 * Implementation of the NIST Elliptic Curves over Prime Fields. */ 51mp_err 52ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth) 53{ 54 mp_err res = MP_OKAY; 55 mp_size a_used = MP_USED(a); 56 57 int r3b; 58 mp_digit carry; 59#ifdef ECL_THIRTY_TWO_BIT 60 mp_digit a6a = 0, a6b = 0, 61 a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0; 62 mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a; 63#else 64 mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0; 65 mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0; 66 mp_digit r0, r1, r2, r3; 67#endif 68 69 /* reduction not needed if a is not larger than field size */ 70 if (a_used < ECP224_DIGITS) { 71 if (a == r) return MP_OKAY; 72 return mp_copy(a, r); 73 } 74 /* for polynomials larger than twice the field size, use regular 75 * reduction */ 76 if (a_used > ECL_CURVE_DIGITS(224*2)) { 77 MP_CHECKOK(mp_mod(a, &meth->irr, r)); 78 } else { 79#ifdef ECL_THIRTY_TWO_BIT 80 /* copy out upper words of a */ 81 switch (a_used) { 82 case 14: 83 a6b = MP_DIGIT(a, 13); 84 case 13: 85 a6a = MP_DIGIT(a, 12); 86 case 12: 87 a5b = MP_DIGIT(a, 11); 88 case 11: 89 a5a = MP_DIGIT(a, 10); 90 case 10: 91 a4b = MP_DIGIT(a, 9); 92 case 9: 93 a4a = MP_DIGIT(a, 8); 94 case 8: 95 a3b = MP_DIGIT(a, 7); 96 } 97 r3a = MP_DIGIT(a, 6); 98 r2b= MP_DIGIT(a, 5); 99 r2a= MP_DIGIT(a, 4); 100 r1b = MP_DIGIT(a, 3); 101 r1a = MP_DIGIT(a, 2); 102 r0b = MP_DIGIT(a, 1); 103 r0a = MP_DIGIT(a, 0); 104 105 106 /* implement r = (a3a,a2,a1,a0) 107 +(a5a, a4,a3b, 0) 108 +( 0, a6,a5b, 0) 109 -( 0 0, 0|a6b, a6a|a5b ) 110 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ 111 MP_ADD_CARRY (r1b, a3b, r1b, 0, carry); 112 MP_ADD_CARRY (r2a, a4a, r2a, carry, carry); 113 MP_ADD_CARRY (r2b, a4b, r2b, carry, carry); 114 MP_ADD_CARRY (r3a, a5a, r3a, carry, carry); 115 r3b = carry; 116 MP_ADD_CARRY (r1b, a5b, r1b, 0, carry); 117 MP_ADD_CARRY (r2a, a6a, r2a, carry, carry); 118 MP_ADD_CARRY (r2b, a6b, r2b, carry, carry); 119 MP_ADD_CARRY (r3a, 0, r3a, carry, carry); 120 r3b += carry; 121 MP_SUB_BORROW(r0a, a3b, r0a, 0, carry); 122 MP_SUB_BORROW(r0b, a4a, r0b, carry, carry); 123 MP_SUB_BORROW(r1a, a4b, r1a, carry, carry); 124 MP_SUB_BORROW(r1b, a5a, r1b, carry, carry); 125 MP_SUB_BORROW(r2a, a5b, r2a, carry, carry); 126 MP_SUB_BORROW(r2b, a6a, r2b, carry, carry); 127 MP_SUB_BORROW(r3a, a6b, r3a, carry, carry); 128 r3b -= carry; 129 MP_SUB_BORROW(r0a, a5b, r0a, 0, carry); 130 MP_SUB_BORROW(r0b, a6a, r0b, carry, carry); 131 MP_SUB_BORROW(r1a, a6b, r1a, carry, carry); 132 if (carry) { 133 MP_SUB_BORROW(r1b, 0, r1b, carry, carry); 134 MP_SUB_BORROW(r2a, 0, r2a, carry, carry); 135 MP_SUB_BORROW(r2b, 0, r2b, carry, carry); 136 MP_SUB_BORROW(r3a, 0, r3a, carry, carry); 137 r3b -= carry; 138 } 139 140 while (r3b > 0) { 141 int tmp; 142 MP_ADD_CARRY(r1b, r3b, r1b, 0, carry); 143 if (carry) { 144 MP_ADD_CARRY(r2a, 0, r2a, carry, carry); 145 MP_ADD_CARRY(r2b, 0, r2b, carry, carry); 146 MP_ADD_CARRY(r3a, 0, r3a, carry, carry); 147 } 148 tmp = carry; 149 MP_SUB_BORROW(r0a, r3b, r0a, 0, carry); 150 if (carry) { 151 MP_SUB_BORROW(r0b, 0, r0b, carry, carry); 152 MP_SUB_BORROW(r1a, 0, r1a, carry, carry); 153 MP_SUB_BORROW(r1b, 0, r1b, carry, carry); 154 MP_SUB_BORROW(r2a, 0, r2a, carry, carry); 155 MP_SUB_BORROW(r2b, 0, r2b, carry, carry); 156 MP_SUB_BORROW(r3a, 0, r3a, carry, carry); 157 tmp -= carry; 158 } 159 r3b = tmp; 160 } 161 162 while (r3b < 0) { 163 mp_digit maxInt = MP_DIGIT_MAX; 164 MP_ADD_CARRY (r0a, 1, r0a, 0, carry); 165 MP_ADD_CARRY (r0b, 0, r0b, carry, carry); 166 MP_ADD_CARRY (r1a, 0, r1a, carry, carry); 167 MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry); 168 MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry); 169 MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry); 170 MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry); 171 r3b += carry; 172 } 173 /* check for final reduction */ 174 /* now the only way we are over is if the top 4 words are all ones */ 175 if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX) 176 && (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) && 177 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) { 178 /* one last subraction */ 179 MP_SUB_BORROW(r0a, 1, r0a, 0, carry); 180 MP_SUB_BORROW(r0b, 0, r0b, carry, carry); 181 MP_SUB_BORROW(r1a, 0, r1a, carry, carry); 182 r1b = r2a = r2b = r3a = 0; 183 } 184 185 186 if (a != r) { 187 MP_CHECKOK(s_mp_pad(r, 7)); 188 } 189 /* set the lower words of r */ 190 MP_SIGN(r) = MP_ZPOS; 191 MP_USED(r) = 7; 192 MP_DIGIT(r, 6) = r3a; 193 MP_DIGIT(r, 5) = r2b; 194 MP_DIGIT(r, 4) = r2a; 195 MP_DIGIT(r, 3) = r1b; 196 MP_DIGIT(r, 2) = r1a; 197 MP_DIGIT(r, 1) = r0b; 198 MP_DIGIT(r, 0) = r0a; 199#else 200 /* copy out upper words of a */ 201 switch (a_used) { 202 case 7: 203 a6 = MP_DIGIT(a, 6); 204 a6b = a6 >> 32; 205 a6a_a5b = a6 << 32; 206 case 6: 207 a5 = MP_DIGIT(a, 5); 208 a5b = a5 >> 32; 209 a6a_a5b |= a5b; 210 a5b = a5b << 32; 211 a5a_a4b = a5 << 32; 212 a5a = a5 & 0xffffffff; 213 case 5: 214 a4 = MP_DIGIT(a, 4); 215 a5a_a4b |= a4 >> 32; 216 a4a_a3b = a4 << 32; 217 case 4: 218 a3b = MP_DIGIT(a, 3) >> 32; 219 a4a_a3b |= a3b; 220 a3b = a3b << 32; 221 } 222 223 r3 = MP_DIGIT(a, 3) & 0xffffffff; 224 r2 = MP_DIGIT(a, 2); 225 r1 = MP_DIGIT(a, 1); 226 r0 = MP_DIGIT(a, 0); 227 228 /* implement r = (a3a,a2,a1,a0) 229 +(a5a, a4,a3b, 0) 230 +( 0, a6,a5b, 0) 231 -( 0 0, 0|a6b, a6a|a5b ) 232 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ 233 MP_ADD_CARRY_ZERO (r1, a3b, r1, carry); 234 MP_ADD_CARRY (r2, a4 , r2, carry, carry); 235 MP_ADD_CARRY (r3, a5a, r3, carry, carry); 236 MP_ADD_CARRY_ZERO (r1, a5b, r1, carry); 237 MP_ADD_CARRY (r2, a6 , r2, carry, carry); 238 MP_ADD_CARRY (r3, 0, r3, carry, carry); 239 240 MP_SUB_BORROW(r0, a4a_a3b, r0, 0, carry); 241 MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry); 242 MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry); 243 MP_SUB_BORROW(r3, a6b , r3, carry, carry); 244 MP_SUB_BORROW(r0, a6a_a5b, r0, 0, carry); 245 MP_SUB_BORROW(r1, a6b , r1, carry, carry); 246 if (carry) { 247 MP_SUB_BORROW(r2, 0, r2, carry, carry); 248 MP_SUB_BORROW(r3, 0, r3, carry, carry); 249 } 250 251 252 /* if the value is negative, r3 has a 2's complement 253 * high value */ 254 r3b = (int)(r3 >>32); 255 while (r3b > 0) { 256 r3 &= 0xffffffff; 257 MP_ADD_CARRY_ZERO(r1,((mp_digit)r3b) << 32, r1, carry); 258 if (carry) { 259 MP_ADD_CARRY(r2, 0, r2, carry, carry); 260 MP_ADD_CARRY(r3, 0, r3, carry, carry); 261 } 262 MP_SUB_BORROW(r0, r3b, r0, 0, carry); 263 if (carry) { 264 MP_SUB_BORROW(r1, 0, r1, carry, carry); 265 MP_SUB_BORROW(r2, 0, r2, carry, carry); 266 MP_SUB_BORROW(r3, 0, r3, carry, carry); 267 } 268 r3b = (int)(r3 >>32); 269 } 270 271 while (r3b < 0) { 272 MP_ADD_CARRY_ZERO (r0, 1, r0, carry); 273 MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry); 274 MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry); 275 MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry); 276 r3b = (int)(r3 >>32); 277 } 278 /* check for final reduction */ 279 /* now the only way we are over is if the top 4 words are all ones */ 280 if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX) 281 && ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) && 282 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) { 283 /* one last subraction */ 284 MP_SUB_BORROW(r0, 1, r0, 0, carry); 285 MP_SUB_BORROW(r1, 0, r1, carry, carry); 286 r2 = r3 = 0; 287 } 288 289 290 if (a != r) { 291 MP_CHECKOK(s_mp_pad(r, 4)); 292 } 293 /* set the lower words of r */ 294 MP_SIGN(r) = MP_ZPOS; 295 MP_USED(r) = 4; 296 MP_DIGIT(r, 3) = r3; 297 MP_DIGIT(r, 2) = r2; 298 MP_DIGIT(r, 1) = r1; 299 MP_DIGIT(r, 0) = r0; 300#endif 301 } 302 303 CLEANUP: 304 return res; 305} 306 307/* Compute the square of polynomial a, reduce modulo p224. Store the 308 * result in r. r could be a. Uses optimized modular reduction for p224. 309 */ 310mp_err 311ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) 312{ 313 mp_err res = MP_OKAY; 314 315 MP_CHECKOK(mp_sqr(a, r)); 316 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 317 CLEANUP: 318 return res; 319} 320 321/* Compute the product of two polynomials a and b, reduce modulo p224. 322 * Store the result in r. r could be a or b; a could be b. Uses 323 * optimized modular reduction for p224. */ 324mp_err 325ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r, 326 const GFMethod *meth) 327{ 328 mp_err res = MP_OKAY; 329 330 MP_CHECKOK(mp_mul(a, b, r)); 331 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 332 CLEANUP: 333 return res; 334} 335 336/* Divides two field elements. If a is NULL, then returns the inverse of 337 * b. */ 338mp_err 339ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r, 340 const GFMethod *meth) 341{ 342 mp_err res = MP_OKAY; 343 mp_int t; 344 345 /* If a is NULL, then return the inverse of b, otherwise return a/b. */ 346 if (a == NULL) { 347 return mp_invmod(b, &meth->irr, r); 348 } else { 349 /* MPI doesn't support divmod, so we implement it using invmod and 350 * mulmod. */ 351 MP_CHECKOK(mp_init(&t, FLAG(b))); 352 MP_CHECKOK(mp_invmod(b, &meth->irr, &t)); 353 MP_CHECKOK(mp_mul(a, &t, r)); 354 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); 355 CLEANUP: 356 mp_clear(&t); 357 return res; 358 } 359} 360 361/* Wire in fast field arithmetic and precomputation of base point for 362 * named curves. */ 363mp_err 364ec_group_set_gfp224(ECGroup *group, ECCurveName name) 365{ 366 if (name == ECCurve_NIST_P224) { 367 group->meth->field_mod = &ec_GFp_nistp224_mod; 368 group->meth->field_mul = &ec_GFp_nistp224_mul; 369 group->meth->field_sqr = &ec_GFp_nistp224_sqr; 370 group->meth->field_div = &ec_GFp_nistp224_div; 371 } 372 return MP_OKAY; 373} 374