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 binary polynomial 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 * Sheueling Chang-Shantz <sheueling.chang@sun.com>, 35 * Stephen Fung <fungstep@hotmail.com>, and 36 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories. 37 * 38 *********************************************************************** */ 39 40#include "ec2.h" 41#include "mp_gf2m.h" 42#include "mp_gf2m-priv.h" 43#include "mpi.h" 44#include "mpi-priv.h" 45#ifndef _KERNEL 46#include <stdlib.h> 47#endif 48 49/* Fast reduction for polynomials over a 233-bit curve. Assumes reduction 50 * polynomial with terms {233, 74, 0}. */ 51mp_err 52ec_GF2m_233_mod(const mp_int *a, mp_int *r, const GFMethod *meth) 53{ 54 mp_err res = MP_OKAY; 55 mp_digit *u, z; 56 57 if (a != r) { 58 MP_CHECKOK(mp_copy(a, r)); 59 } 60#ifdef ECL_SIXTY_FOUR_BIT 61 if (MP_USED(r) < 8) { 62 MP_CHECKOK(s_mp_pad(r, 8)); 63 } 64 u = MP_DIGITS(r); 65 MP_USED(r) = 8; 66 67 /* u[7] only has 18 significant bits */ 68 z = u[7]; 69 u[4] ^= (z << 33) ^ (z >> 41); 70 u[3] ^= (z << 23); 71 z = u[6]; 72 u[4] ^= (z >> 31); 73 u[3] ^= (z << 33) ^ (z >> 41); 74 u[2] ^= (z << 23); 75 z = u[5]; 76 u[3] ^= (z >> 31); 77 u[2] ^= (z << 33) ^ (z >> 41); 78 u[1] ^= (z << 23); 79 z = u[4]; 80 u[2] ^= (z >> 31); 81 u[1] ^= (z << 33) ^ (z >> 41); 82 u[0] ^= (z << 23); 83 z = u[3] >> 41; /* z only has 23 significant bits */ 84 u[1] ^= (z << 10); 85 u[0] ^= z; 86 /* clear bits above 233 */ 87 u[7] = u[6] = u[5] = u[4] = 0; 88 u[3] ^= z << 41; 89#else 90 if (MP_USED(r) < 15) { 91 MP_CHECKOK(s_mp_pad(r, 15)); 92 } 93 u = MP_DIGITS(r); 94 MP_USED(r) = 15; 95 96 /* u[14] only has 18 significant bits */ 97 z = u[14]; 98 u[9] ^= (z << 1); 99 u[7] ^= (z >> 9); 100 u[6] ^= (z << 23); 101 z = u[13]; 102 u[9] ^= (z >> 31); 103 u[8] ^= (z << 1); 104 u[6] ^= (z >> 9); 105 u[5] ^= (z << 23); 106 z = u[12]; 107 u[8] ^= (z >> 31); 108 u[7] ^= (z << 1); 109 u[5] ^= (z >> 9); 110 u[4] ^= (z << 23); 111 z = u[11]; 112 u[7] ^= (z >> 31); 113 u[6] ^= (z << 1); 114 u[4] ^= (z >> 9); 115 u[3] ^= (z << 23); 116 z = u[10]; 117 u[6] ^= (z >> 31); 118 u[5] ^= (z << 1); 119 u[3] ^= (z >> 9); 120 u[2] ^= (z << 23); 121 z = u[9]; 122 u[5] ^= (z >> 31); 123 u[4] ^= (z << 1); 124 u[2] ^= (z >> 9); 125 u[1] ^= (z << 23); 126 z = u[8]; 127 u[4] ^= (z >> 31); 128 u[3] ^= (z << 1); 129 u[1] ^= (z >> 9); 130 u[0] ^= (z << 23); 131 z = u[7] >> 9; /* z only has 23 significant bits */ 132 u[3] ^= (z >> 22); 133 u[2] ^= (z << 10); 134 u[0] ^= z; 135 /* clear bits above 233 */ 136 u[14] = u[13] = u[12] = u[11] = u[10] = u[9] = u[8] = 0; 137 u[7] ^= z << 9; 138#endif 139 s_mp_clamp(r); 140 141 CLEANUP: 142 return res; 143} 144 145/* Fast squaring for polynomials over a 233-bit curve. Assumes reduction 146 * polynomial with terms {233, 74, 0}. */ 147mp_err 148ec_GF2m_233_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) 149{ 150 mp_err res = MP_OKAY; 151 mp_digit *u, *v; 152 153 v = MP_DIGITS(a); 154 155#ifdef ECL_SIXTY_FOUR_BIT 156 if (MP_USED(a) < 4) { 157 return mp_bsqrmod(a, meth->irr_arr, r); 158 } 159 if (MP_USED(r) < 8) { 160 MP_CHECKOK(s_mp_pad(r, 8)); 161 } 162 MP_USED(r) = 8; 163#else 164 if (MP_USED(a) < 8) { 165 return mp_bsqrmod(a, meth->irr_arr, r); 166 } 167 if (MP_USED(r) < 15) { 168 MP_CHECKOK(s_mp_pad(r, 15)); 169 } 170 MP_USED(r) = 15; 171#endif 172 u = MP_DIGITS(r); 173 174#ifdef ECL_THIRTY_TWO_BIT 175 u[14] = gf2m_SQR0(v[7]); 176 u[13] = gf2m_SQR1(v[6]); 177 u[12] = gf2m_SQR0(v[6]); 178 u[11] = gf2m_SQR1(v[5]); 179 u[10] = gf2m_SQR0(v[5]); 180 u[9] = gf2m_SQR1(v[4]); 181 u[8] = gf2m_SQR0(v[4]); 182#endif 183 u[7] = gf2m_SQR1(v[3]); 184 u[6] = gf2m_SQR0(v[3]); 185 u[5] = gf2m_SQR1(v[2]); 186 u[4] = gf2m_SQR0(v[2]); 187 u[3] = gf2m_SQR1(v[1]); 188 u[2] = gf2m_SQR0(v[1]); 189 u[1] = gf2m_SQR1(v[0]); 190 u[0] = gf2m_SQR0(v[0]); 191 return ec_GF2m_233_mod(r, r, meth); 192 193 CLEANUP: 194 return res; 195} 196 197/* Fast multiplication for polynomials over a 233-bit curve. Assumes 198 * reduction polynomial with terms {233, 74, 0}. */ 199mp_err 200ec_GF2m_233_mul(const mp_int *a, const mp_int *b, mp_int *r, 201 const GFMethod *meth) 202{ 203 mp_err res = MP_OKAY; 204 mp_digit a3 = 0, a2 = 0, a1 = 0, a0, b3 = 0, b2 = 0, b1 = 0, b0; 205 206#ifdef ECL_THIRTY_TWO_BIT 207 mp_digit a7 = 0, a6 = 0, a5 = 0, a4 = 0, b7 = 0, b6 = 0, b5 = 0, b4 = 208 0; 209 mp_digit rm[8]; 210#endif 211 212 if (a == b) { 213 return ec_GF2m_233_sqr(a, r, meth); 214 } else { 215 switch (MP_USED(a)) { 216#ifdef ECL_THIRTY_TWO_BIT 217 case 8: 218 a7 = MP_DIGIT(a, 7); 219 case 7: 220 a6 = MP_DIGIT(a, 6); 221 case 6: 222 a5 = MP_DIGIT(a, 5); 223 case 5: 224 a4 = MP_DIGIT(a, 4); 225#endif 226 case 4: 227 a3 = MP_DIGIT(a, 3); 228 case 3: 229 a2 = MP_DIGIT(a, 2); 230 case 2: 231 a1 = MP_DIGIT(a, 1); 232 default: 233 a0 = MP_DIGIT(a, 0); 234 } 235 switch (MP_USED(b)) { 236#ifdef ECL_THIRTY_TWO_BIT 237 case 8: 238 b7 = MP_DIGIT(b, 7); 239 case 7: 240 b6 = MP_DIGIT(b, 6); 241 case 6: 242 b5 = MP_DIGIT(b, 5); 243 case 5: 244 b4 = MP_DIGIT(b, 4); 245#endif 246 case 4: 247 b3 = MP_DIGIT(b, 3); 248 case 3: 249 b2 = MP_DIGIT(b, 2); 250 case 2: 251 b1 = MP_DIGIT(b, 1); 252 default: 253 b0 = MP_DIGIT(b, 0); 254 } 255#ifdef ECL_SIXTY_FOUR_BIT 256 MP_CHECKOK(s_mp_pad(r, 8)); 257 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0); 258 MP_USED(r) = 8; 259 s_mp_clamp(r); 260#else 261 MP_CHECKOK(s_mp_pad(r, 16)); 262 s_bmul_4x4(MP_DIGITS(r) + 8, a7, a6, a5, a4, b7, b6, b5, b4); 263 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0); 264 s_bmul_4x4(rm, a7 ^ a3, a6 ^ a2, a5 ^ a1, a4 ^ a0, b7 ^ b3, 265 b6 ^ b2, b5 ^ b1, b4 ^ b0); 266 rm[7] ^= MP_DIGIT(r, 7) ^ MP_DIGIT(r, 15); 267 rm[6] ^= MP_DIGIT(r, 6) ^ MP_DIGIT(r, 14); 268 rm[5] ^= MP_DIGIT(r, 5) ^ MP_DIGIT(r, 13); 269 rm[4] ^= MP_DIGIT(r, 4) ^ MP_DIGIT(r, 12); 270 rm[3] ^= MP_DIGIT(r, 3) ^ MP_DIGIT(r, 11); 271 rm[2] ^= MP_DIGIT(r, 2) ^ MP_DIGIT(r, 10); 272 rm[1] ^= MP_DIGIT(r, 1) ^ MP_DIGIT(r, 9); 273 rm[0] ^= MP_DIGIT(r, 0) ^ MP_DIGIT(r, 8); 274 MP_DIGIT(r, 11) ^= rm[7]; 275 MP_DIGIT(r, 10) ^= rm[6]; 276 MP_DIGIT(r, 9) ^= rm[5]; 277 MP_DIGIT(r, 8) ^= rm[4]; 278 MP_DIGIT(r, 7) ^= rm[3]; 279 MP_DIGIT(r, 6) ^= rm[2]; 280 MP_DIGIT(r, 5) ^= rm[1]; 281 MP_DIGIT(r, 4) ^= rm[0]; 282 MP_USED(r) = 16; 283 s_mp_clamp(r); 284#endif 285 return ec_GF2m_233_mod(r, r, meth); 286 } 287 288 CLEANUP: 289 return res; 290} 291 292/* Wire in fast field arithmetic for 233-bit curves. */ 293mp_err 294ec_group_set_gf2m233(ECGroup *group, ECCurveName name) 295{ 296 group->meth->field_mod = &ec_GF2m_233_mod; 297 group->meth->field_mul = &ec_GF2m_233_mul; 298 group->meth->field_sqr = &ec_GF2m_233_sqr; 299 return MP_OKAY; 300} 301