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 binary polynomial 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 * Sheueling Chang-Shantz <sheueling.chang@sun.com>, 24 * Stephen Fung <fungstep@hotmail.com>, and 25 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories. 26 * 27 * Alternatively, the contents of this file may be used under the terms of 28 * either the GNU General Public License Version 2 or later (the "GPL"), or 29 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), 30 * in which case the provisions of the GPL or the LGPL are applicable instead 31 * of those above. If you wish to allow use of your version of this file only 32 * under the terms of either the GPL or the LGPL, and not to allow others to 33 * use your version of this file under the terms of the MPL, indicate your 34 * decision by deleting the provisions above and replace them with the notice 35 * and other provisions required by the GPL or the LGPL. If you do not delete 36 * the provisions above, a recipient may use your version of this file under 37 * the terms of any one of the MPL, the GPL or the LGPL. 38 * 39 * ***** END LICENSE BLOCK ***** */ 40/* 41 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. 42 * Use is subject to license terms. 43 * 44 * Sun elects to use this software under the MPL license. 45 */ 46 47#pragma ident "%Z%%M% %I% %E% SMI" 48 49#include "ec2.h" 50#include "mplogic.h" 51#include "mp_gf2m.h" 52#ifndef _KERNEL 53#include <stdlib.h> 54#endif 55 56/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery 57 * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J. 58 * and Dahab, R. "Fast multiplication on elliptic curves over GF(2^m) 59 * without precomputation". modified to not require precomputation of 60 * c=b^{2^{m-1}}. */ 61static mp_err 62gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag) 63{ 64 mp_err res = MP_OKAY; 65 mp_int t1; 66 67 MP_DIGITS(&t1) = 0; 68 MP_CHECKOK(mp_init(&t1, kmflag)); 69 70 MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); 71 MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth)); 72 MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth)); 73 MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); 74 MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth)); 75 MP_CHECKOK(group->meth-> 76 field_mul(&group->curveb, &t1, &t1, group->meth)); 77 MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth)); 78 79 CLEANUP: 80 mp_clear(&t1); 81 return res; 82} 83 84/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in 85 * Montgomery projective coordinates. Uses algorithm Madd in appendix of 86 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 87 * GF(2^m) without precomputation". */ 88static mp_err 89gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2, 90 const ECGroup *group, int kmflag) 91{ 92 mp_err res = MP_OKAY; 93 mp_int t1, t2; 94 95 MP_DIGITS(&t1) = 0; 96 MP_DIGITS(&t2) = 0; 97 MP_CHECKOK(mp_init(&t1, kmflag)); 98 MP_CHECKOK(mp_init(&t2, kmflag)); 99 100 MP_CHECKOK(mp_copy(x, &t1)); 101 MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth)); 102 MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth)); 103 MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth)); 104 MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); 105 MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth)); 106 MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth)); 107 MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth)); 108 109 CLEANUP: 110 mp_clear(&t1); 111 mp_clear(&t2); 112 return res; 113} 114 115/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) 116 * using Montgomery point multiplication algorithm Mxy() in appendix of 117 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 118 * GF(2^m) without precomputation". Returns: 0 on error 1 if return value 119 * should be the point at infinity 2 otherwise */ 120static int 121gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1, 122 mp_int *x2, mp_int *z2, const ECGroup *group) 123{ 124 mp_err res = MP_OKAY; 125 int ret = 0; 126 mp_int t3, t4, t5; 127 128 MP_DIGITS(&t3) = 0; 129 MP_DIGITS(&t4) = 0; 130 MP_DIGITS(&t5) = 0; 131 MP_CHECKOK(mp_init(&t3, FLAG(x2))); 132 MP_CHECKOK(mp_init(&t4, FLAG(x2))); 133 MP_CHECKOK(mp_init(&t5, FLAG(x2))); 134 135 if (mp_cmp_z(z1) == 0) { 136 mp_zero(x2); 137 mp_zero(z2); 138 ret = 1; 139 goto CLEANUP; 140 } 141 142 if (mp_cmp_z(z2) == 0) { 143 MP_CHECKOK(mp_copy(x, x2)); 144 MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth)); 145 ret = 2; 146 goto CLEANUP; 147 } 148 149 MP_CHECKOK(mp_set_int(&t5, 1)); 150 if (group->meth->field_enc) { 151 MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth)); 152 } 153 154 MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth)); 155 156 MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth)); 157 MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); 158 MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth)); 159 MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth)); 160 MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth)); 161 162 MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth)); 163 MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth)); 164 MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth)); 165 MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth)); 166 MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth)); 167 168 MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth)); 169 MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth)); 170 MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth)); 171 MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth)); 172 MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth)); 173 174 MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth)); 175 MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth)); 176 177 ret = 2; 178 179 CLEANUP: 180 mp_clear(&t3); 181 mp_clear(&t4); 182 mp_clear(&t5); 183 if (res == MP_OKAY) { 184 return ret; 185 } else { 186 return 0; 187 } 188} 189 190/* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R. "Fast 191 * multiplication on elliptic curves over GF(2^m) without 192 * precomputation". Elliptic curve points P and R can be identical. Uses 193 * Montgomery projective coordinates. */ 194mp_err 195ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py, 196 mp_int *rx, mp_int *ry, const ECGroup *group) 197{ 198 mp_err res = MP_OKAY; 199 mp_int x1, x2, z1, z2; 200 int i, j; 201 mp_digit top_bit, mask; 202 203 MP_DIGITS(&x1) = 0; 204 MP_DIGITS(&x2) = 0; 205 MP_DIGITS(&z1) = 0; 206 MP_DIGITS(&z2) = 0; 207 MP_CHECKOK(mp_init(&x1, FLAG(n))); 208 MP_CHECKOK(mp_init(&x2, FLAG(n))); 209 MP_CHECKOK(mp_init(&z1, FLAG(n))); 210 MP_CHECKOK(mp_init(&z2, FLAG(n))); 211 212 /* if result should be point at infinity */ 213 if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) { 214 MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); 215 goto CLEANUP; 216 } 217 218 MP_CHECKOK(mp_copy(px, &x1)); /* x1 = px */ 219 MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */ 220 MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth)); /* z2 = 221 * x1^2 = 222 * px^2 */ 223 MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth)); 224 MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth)); /* x2 225 * = 226 * px^4 227 * + 228 * b 229 */ 230 231 /* find top-most bit and go one past it */ 232 i = MP_USED(n) - 1; 233 j = MP_DIGIT_BIT - 1; 234 top_bit = 1; 235 top_bit <<= MP_DIGIT_BIT - 1; 236 mask = top_bit; 237 while (!(MP_DIGITS(n)[i] & mask)) { 238 mask >>= 1; 239 j--; 240 } 241 mask >>= 1; 242 j--; 243 244 /* if top most bit was at word break, go to next word */ 245 if (!mask) { 246 i--; 247 j = MP_DIGIT_BIT - 1; 248 mask = top_bit; 249 } 250 251 for (; i >= 0; i--) { 252 for (; j >= 0; j--) { 253 if (MP_DIGITS(n)[i] & mask) { 254 MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n))); 255 MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n))); 256 } else { 257 MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n))); 258 MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n))); 259 } 260 mask >>= 1; 261 } 262 j = MP_DIGIT_BIT - 1; 263 mask = top_bit; 264 } 265 266 /* convert out of "projective" coordinates */ 267 i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group); 268 if (i == 0) { 269 res = MP_BADARG; 270 goto CLEANUP; 271 } else if (i == 1) { 272 MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); 273 } else { 274 MP_CHECKOK(mp_copy(&x2, rx)); 275 MP_CHECKOK(mp_copy(&z2, ry)); 276 } 277 278 CLEANUP: 279 mp_clear(&x1); 280 mp_clear(&x2); 281 mp_clear(&z1); 282 mp_clear(&z2); 283 return res; 284} 285