ec2_mult.c revision 656d9c7f52f88b3a3daccafa7655dec086c4756e
1/* crypto/ec/ec2_mult.c */ 2/* ==================================================================== 3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 4 * 5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included 6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed 7 * to the OpenSSL project. 8 * 9 * The ECC Code is licensed pursuant to the OpenSSL open source 10 * license provided below. 11 * 12 * The software is originally written by Sheueling Chang Shantz and 13 * Douglas Stebila of Sun Microsystems Laboratories. 14 * 15 */ 16/* ==================================================================== 17 * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. 18 * 19 * Redistribution and use in source and binary forms, with or without 20 * modification, are permitted provided that the following conditions 21 * are met: 22 * 23 * 1. Redistributions of source code must retain the above copyright 24 * notice, this list of conditions and the following disclaimer. 25 * 26 * 2. Redistributions in binary form must reproduce the above copyright 27 * notice, this list of conditions and the following disclaimer in 28 * the documentation and/or other materials provided with the 29 * distribution. 30 * 31 * 3. All advertising materials mentioning features or use of this 32 * software must display the following acknowledgment: 33 * "This product includes software developed by the OpenSSL Project 34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 35 * 36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 37 * endorse or promote products derived from this software without 38 * prior written permission. For written permission, please contact 39 * openssl-core@openssl.org. 40 * 41 * 5. Products derived from this software may not be called "OpenSSL" 42 * nor may "OpenSSL" appear in their names without prior written 43 * permission of the OpenSSL Project. 44 * 45 * 6. Redistributions of any form whatsoever must retain the following 46 * acknowledgment: 47 * "This product includes software developed by the OpenSSL Project 48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 49 * 50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 61 * OF THE POSSIBILITY OF SUCH DAMAGE. 62 * ==================================================================== 63 * 64 * This product includes cryptographic software written by Eric Young 65 * (eay@cryptsoft.com). This product includes software written by Tim 66 * Hudson (tjh@cryptsoft.com). 67 * 68 */ 69 70#include <openssl/err.h> 71 72#include "ec_lcl.h" 73 74 75/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective 76 * coordinates. 77 * Uses algorithm Mdouble in appendix of 78 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over 79 * GF(2^m) without precomputation". 80 * modified to not require precomputation of c=b^{2^{m-1}}. 81 */ 82static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) 83 { 84 BIGNUM *t1; 85 int ret = 0; 86 87 /* Since Mdouble is static we can guarantee that ctx != NULL. */ 88 BN_CTX_start(ctx); 89 t1 = BN_CTX_get(ctx); 90 if (t1 == NULL) goto err; 91 92 if (!group->meth->field_sqr(group, x, x, ctx)) goto err; 93 if (!group->meth->field_sqr(group, t1, z, ctx)) goto err; 94 if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err; 95 if (!group->meth->field_sqr(group, x, x, ctx)) goto err; 96 if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err; 97 if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err; 98 if (!BN_GF2m_add(x, x, t1)) goto err; 99 100 ret = 1; 101 102 err: 103 BN_CTX_end(ctx); 104 return ret; 105 } 106 107/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery 108 * projective coordinates. 109 * Uses algorithm Madd in appendix of 110 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 111 * GF(2^m) without precomputation". 112 */ 113static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, 114 const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) 115 { 116 BIGNUM *t1, *t2; 117 int ret = 0; 118 119 /* Since Madd is static we can guarantee that ctx != NULL. */ 120 BN_CTX_start(ctx); 121 t1 = BN_CTX_get(ctx); 122 t2 = BN_CTX_get(ctx); 123 if (t2 == NULL) goto err; 124 125 if (!BN_copy(t1, x)) goto err; 126 if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err; 127 if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err; 128 if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err; 129 if (!BN_GF2m_add(z1, z1, x1)) goto err; 130 if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err; 131 if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err; 132 if (!BN_GF2m_add(x1, x1, t2)) goto err; 133 134 ret = 1; 135 136 err: 137 BN_CTX_end(ctx); 138 return ret; 139 } 140 141/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) 142 * using Montgomery point multiplication algorithm Mxy() in appendix of 143 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 144 * GF(2^m) without precomputation". 145 * Returns: 146 * 0 on error 147 * 1 if return value should be the point at infinity 148 * 2 otherwise 149 */ 150static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, 151 BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) 152 { 153 BIGNUM *t3, *t4, *t5; 154 int ret = 0; 155 156 if (BN_is_zero(z1)) 157 { 158 BN_zero(x2); 159 BN_zero(z2); 160 return 1; 161 } 162 163 if (BN_is_zero(z2)) 164 { 165 if (!BN_copy(x2, x)) return 0; 166 if (!BN_GF2m_add(z2, x, y)) return 0; 167 return 2; 168 } 169 170 /* Since Mxy is static we can guarantee that ctx != NULL. */ 171 BN_CTX_start(ctx); 172 t3 = BN_CTX_get(ctx); 173 t4 = BN_CTX_get(ctx); 174 t5 = BN_CTX_get(ctx); 175 if (t5 == NULL) goto err; 176 177 if (!BN_one(t5)) goto err; 178 179 if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err; 180 181 if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err; 182 if (!BN_GF2m_add(z1, z1, x1)) goto err; 183 if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err; 184 if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err; 185 if (!BN_GF2m_add(z2, z2, x2)) goto err; 186 187 if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err; 188 if (!group->meth->field_sqr(group, t4, x, ctx)) goto err; 189 if (!BN_GF2m_add(t4, t4, y)) goto err; 190 if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err; 191 if (!BN_GF2m_add(t4, t4, z2)) goto err; 192 193 if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err; 194 if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err; 195 if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err; 196 if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err; 197 if (!BN_GF2m_add(z2, x2, x)) goto err; 198 199 if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err; 200 if (!BN_GF2m_add(z2, z2, y)) goto err; 201 202 ret = 2; 203 204 err: 205 BN_CTX_end(ctx); 206 return ret; 207 } 208 209/* Computes scalar*point and stores the result in r. 210 * point can not equal r. 211 * Uses algorithm 2P of 212 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 213 * GF(2^m) without precomputation". 214 */ 215static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 216 const EC_POINT *point, BN_CTX *ctx) 217 { 218 BIGNUM *x1, *x2, *z1, *z2; 219 int ret = 0, i, j; 220 BN_ULONG mask; 221 222 if (r == point) 223 { 224 ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); 225 return 0; 226 } 227 228 /* if result should be point at infinity */ 229 if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || 230 EC_POINT_is_at_infinity(group, point)) 231 { 232 return EC_POINT_set_to_infinity(group, r); 233 } 234 235 /* only support affine coordinates */ 236 if (!point->Z_is_one) return 0; 237 238 /* Since point_multiply is static we can guarantee that ctx != NULL. */ 239 BN_CTX_start(ctx); 240 x1 = BN_CTX_get(ctx); 241 z1 = BN_CTX_get(ctx); 242 if (z1 == NULL) goto err; 243 244 x2 = &r->X; 245 z2 = &r->Y; 246 247 if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */ 248 if (!BN_one(z1)) goto err; /* z1 = 1 */ 249 if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */ 250 if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err; 251 if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ 252 253 /* find top most bit and go one past it */ 254 i = scalar->top - 1; j = BN_BITS2 - 1; 255 mask = BN_TBIT; 256 while (!(scalar->d[i] & mask)) { mask >>= 1; j--; } 257 mask >>= 1; j--; 258 /* if top most bit was at word break, go to next word */ 259 if (!mask) 260 { 261 i--; j = BN_BITS2 - 1; 262 mask = BN_TBIT; 263 } 264 265 for (; i >= 0; i--) 266 { 267 for (; j >= 0; j--) 268 { 269 if (scalar->d[i] & mask) 270 { 271 if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err; 272 if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err; 273 } 274 else 275 { 276 if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; 277 if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; 278 } 279 mask >>= 1; 280 } 281 j = BN_BITS2 - 1; 282 mask = BN_TBIT; 283 } 284 285 /* convert out of "projective" coordinates */ 286 i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); 287 if (i == 0) goto err; 288 else if (i == 1) 289 { 290 if (!EC_POINT_set_to_infinity(group, r)) goto err; 291 } 292 else 293 { 294 if (!BN_one(&r->Z)) goto err; 295 r->Z_is_one = 1; 296 } 297 298 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ 299 BN_set_negative(&r->X, 0); 300 BN_set_negative(&r->Y, 0); 301 302 ret = 1; 303 304 err: 305 BN_CTX_end(ctx); 306 return ret; 307 } 308 309 310/* Computes the sum 311 * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] 312 * gracefully ignoring NULL scalar values. 313 */ 314int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 315 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) 316 { 317 BN_CTX *new_ctx = NULL; 318 int ret = 0; 319 size_t i; 320 EC_POINT *p=NULL; 321 322 if (ctx == NULL) 323 { 324 ctx = new_ctx = BN_CTX_new(); 325 if (ctx == NULL) 326 return 0; 327 } 328 329 /* This implementation is more efficient than the wNAF implementation for 2 330 * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points, 331 * or if we can perform a fast multiplication based on precomputation. 332 */ 333 if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group))) 334 { 335 ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); 336 goto err; 337 } 338 339 if ((p = EC_POINT_new(group)) == NULL) goto err; 340 341 if (!EC_POINT_set_to_infinity(group, r)) goto err; 342 343 if (scalar) 344 { 345 if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err; 346 if (BN_is_negative(scalar)) 347 if (!group->meth->invert(group, p, ctx)) goto err; 348 if (!group->meth->add(group, r, r, p, ctx)) goto err; 349 } 350 351 for (i = 0; i < num; i++) 352 { 353 if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err; 354 if (BN_is_negative(scalars[i])) 355 if (!group->meth->invert(group, p, ctx)) goto err; 356 if (!group->meth->add(group, r, r, p, ctx)) goto err; 357 } 358 359 ret = 1; 360 361 err: 362 if (p) EC_POINT_free(p); 363 if (new_ctx != NULL) 364 BN_CTX_free(new_ctx); 365 return ret; 366 } 367 368 369/* Precomputation for point multiplication: fall back to wNAF methods 370 * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */ 371 372int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 373 { 374 return ec_wNAF_precompute_mult(group, ctx); 375 } 376 377int ec_GF2m_have_precompute_mult(const EC_GROUP *group) 378 { 379 return ec_wNAF_have_precompute_mult(group); 380 } 381