ec2_mult.c revision 160815
1321369Sdim/* crypto/ec/ec2_mult.c */ 2193323Sed/* ==================================================================== 3353358Sdim * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 4353358Sdim * 5353358Sdim * The Elliptic Curve Public-Key Crypto Library (ECC Code) included 6193323Sed * herein is developed by SUN MICROSYSTEMS, INC., and is contributed 7193323Sed * to the OpenSSL project. 8193323Sed * 9309124Sdim * The ECC Code is licensed pursuant to the OpenSSL open source 10309124Sdim * license provided below. 11309124Sdim * 12309124Sdim * The software is originally written by Sheueling Chang Shantz and 13309124Sdim * Douglas Stebila of Sun Microsystems Laboratories. 14193323Sed * 15193323Sed */ 16193323Sed/* ==================================================================== 17193323Sed * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. 18327952Sdim * 19321369Sdim * Redistribution and use in source and binary forms, with or without 20321369Sdim * modification, are permitted provided that the following conditions 21321369Sdim * are met: 22327952Sdim * 23249423Sdim * 1. Redistributions of source code must retain the above copyright 24198090Srdivacky * notice, this list of conditions and the following disclaimer. 25193323Sed * 26327952Sdim * 2. Redistributions in binary form must reproduce the above copyright 27193323Sed * notice, this list of conditions and the following disclaimer in 28321369Sdim * the documentation and/or other materials provided with the 29193323Sed * distribution. 30327952Sdim * 31327952Sdim * 3. All advertising materials mentioning features or use of this 32327952Sdim * software must display the following acknowledgment: 33327952Sdim * "This product includes software developed by the OpenSSL Project 34360784Sdim * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 35321369Sdim * 36327952Sdim * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 37212904Sdim * endorse or promote products derived from this software without 38198090Srdivacky * prior written permission. For written permission, please contact 39212904Sdim * openssl-core@openssl.org. 40321369Sdim * 41321369Sdim * 5. Products derived from this software may not be called "OpenSSL" 42321369Sdim * nor may "OpenSSL" appear in their names without prior written 43321369Sdim * permission of the OpenSSL Project. 44321369Sdim * 45327952Sdim * 6. Redistributions of any form whatsoever must retain the following 46321369Sdim * acknowledgment: 47193323Sed * "This product includes software developed by the OpenSSL Project 48193323Sed * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 49276479Sdim * 50276479Sdim * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 51321369Sdim * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 52321369Sdim * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 53360784Sdim * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 54321369Sdim * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 55193323Sed * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 56193323Sed * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 57314564Sdim * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 58309124Sdim * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 59280031Sdim * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 60280031Sdim * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 61193323Sed * OF THE POSSIBILITY OF SUCH DAMAGE. 62321369Sdim * ==================================================================== 63193323Sed * 64280031Sdim * This product includes cryptographic software written by Eric Young 65193323Sed * (eay@cryptsoft.com). This product includes software written by Tim 66193323Sed * Hudson (tjh@cryptsoft.com). 67198090Srdivacky * 68309124Sdim */ 69280031Sdim 70280031Sdim#include <openssl/err.h> 71280031Sdim 72280031Sdim#include "ec_lcl.h" 73193323Sed 74309124Sdim 75193323Sed/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective 76321369Sdim * coordinates. 77321369Sdim * Uses algorithm Mdouble in appendix of 78321369Sdim * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over 79314564Sdim * GF(2^m) without precomputation". 80193323Sed * modified to not require precomputation of c=b^{2^{m-1}}. 81193323Sed */ 82193323Sedstatic int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) 83193323Sed { 84314564Sdim BIGNUM *t1; 85314564Sdim int ret = 0; 86321369Sdim 87314564Sdim /* Since Mdouble is static we can guarantee that ctx != NULL. */ 88314564Sdim BN_CTX_start(ctx); 89314564Sdim t1 = BN_CTX_get(ctx); 90314564Sdim if (t1 == NULL) goto err; 91321369Sdim 92314564Sdim if (!group->meth->field_sqr(group, x, x, ctx)) goto err; 93314564Sdim if (!group->meth->field_sqr(group, t1, z, ctx)) goto err; 94314564Sdim if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err; 95314564Sdim if (!group->meth->field_sqr(group, x, x, ctx)) goto err; 96314564Sdim if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err; 97314564Sdim if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err; 98314564Sdim if (!BN_GF2m_add(x, x, t1)) goto err; 99314564Sdim 100360784Sdim ret = 1; 101280031Sdim 102280031Sdim err: 103193323Sed BN_CTX_end(ctx); 104193323Sed return ret; 105360784Sdim } 106314564Sdim 107314564Sdim/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery 108314564Sdim * projective coordinates. 109314564Sdim * Uses algorithm Madd in appendix of 110249423Sdim * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 111249423Sdim * GF(2^m) without precomputation". 112193323Sed */ 113309124Sdimstatic int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, 114341825Sdim const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) 115193323Sed { 116198090Srdivacky BIGNUM *t1, *t2; 117198090Srdivacky int ret = 0; 118280031Sdim 119280031Sdim /* Since Madd is static we can guarantee that ctx != NULL. */ 120309124Sdim BN_CTX_start(ctx); 121280031Sdim t1 = BN_CTX_get(ctx); 122280031Sdim t2 = BN_CTX_get(ctx); 123280031Sdim if (t2 == NULL) goto err; 124280031Sdim 125280031Sdim if (!BN_copy(t1, x)) goto err; 126280031Sdim if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err; 127280031Sdim if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err; 128280031Sdim if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err; 129280031Sdim if (!BN_GF2m_add(z1, z1, x1)) goto err; 130280031Sdim if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err; 131309124Sdim if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err; 132280031Sdim if (!BN_GF2m_add(x1, x1, t2)) goto err; 133288943Sdim 134280031Sdim ret = 1; 135223017Sdim 136193323Sed err: 137360784Sdim BN_CTX_end(ctx); 138360784Sdim return ret; 139195340Sed } 140193323Sed 141198090Srdivacky/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) 142223017Sdim * using Montgomery point multiplication algorithm Mxy() in appendix of 143223017Sdim * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 144223017Sdim * GF(2^m) without precomputation". 145288943Sdim * Returns: 146280031Sdim * 0 on error 147198090Srdivacky * 1 if return value should be the point at infinity 148198090Srdivacky * 2 otherwise 149288943Sdim */ 150280031Sdimstatic int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, 151198090Srdivacky BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) 152280031Sdim { 153193323Sed BIGNUM *t3, *t4, *t5; 154193323Sed int ret = 0; 155249423Sdim 156193323Sed if (BN_is_zero(z1)) 157249423Sdim { 158249423Sdim BN_zero(x2); 159249423Sdim BN_zero(z2); 160309124Sdim return 1; 161341825Sdim } 162251662Sdim 163249423Sdim if (BN_is_zero(z2)) 164251662Sdim { 165341825Sdim if (!BN_copy(x2, x)) return 0; 166280031Sdim if (!BN_GF2m_add(z2, x, y)) return 0; 167251662Sdim return 2; 168249423Sdim } 169249423Sdim 170276479Sdim /* Since Mxy is static we can guarantee that ctx != NULL. */ 171249423Sdim BN_CTX_start(ctx); 172249423Sdim t3 = BN_CTX_get(ctx); 173249423Sdim t4 = BN_CTX_get(ctx); 174249423Sdim t5 = BN_CTX_get(ctx); 175249423Sdim if (t5 == NULL) goto err; 176249423Sdim 177249423Sdim if (!BN_one(t5)) goto err; 178249423Sdim 179249423Sdim if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err; 180249423Sdim 181249423Sdim if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err; 182249423Sdim if (!BN_GF2m_add(z1, z1, x1)) goto err; 183276479Sdim if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err; 184249423Sdim if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err; 185249423Sdim if (!BN_GF2m_add(z2, z2, x2)) goto err; 186249423Sdim 187309124Sdim if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err; 188249423Sdim if (!group->meth->field_sqr(group, t4, x, ctx)) goto err; 189261991Sdim if (!BN_GF2m_add(t4, t4, y)) goto err; 190261991Sdim if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err; 191309124Sdim if (!BN_GF2m_add(t4, t4, z2)) goto err; 192249423Sdim 193249423Sdim if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err; 194249423Sdim if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err; 195276479Sdim if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err; 196249423Sdim if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err; 197249423Sdim if (!BN_GF2m_add(z2, x2, x)) goto err; 198341825Sdim 199249423Sdim if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err; 200249423Sdim if (!BN_GF2m_add(z2, z2, y)) goto err; 201249423Sdim 202249423Sdim ret = 2; 203198090Srdivacky 204234353Sdim err: 205309124Sdim BN_CTX_end(ctx); 206223017Sdim return ret; 207193323Sed } 208360784Sdim 209360784Sdim/* Computes scalar*point and stores the result in r. 210195340Sed * point can not equal r. 211198090Srdivacky * Uses algorithm 2P of 212223017Sdim * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over 213223017Sdim * GF(2^m) without precomputation". 214280031Sdim */ 215198892Srdivackystatic int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 216327952Sdim const EC_POINT *point, BN_CTX *ctx) 217198892Srdivacky { 218198892Srdivacky BIGNUM *x1, *x2, *z1, *z2; 219198892Srdivacky int ret = 0, i, j; 220198892Srdivacky BN_ULONG mask; 221198892Srdivacky 222198892Srdivacky if (r == point) 223198892Srdivacky { 224360784Sdim ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); 225360784Sdim return 0; 226198892Srdivacky } 227198892Srdivacky 228198892Srdivacky /* if result should be point at infinity */ 229280031Sdim if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || 230280031Sdim EC_POINT_is_at_infinity(group, point)) 231280031Sdim { 232280031Sdim return EC_POINT_set_to_infinity(group, r); 233280031Sdim } 234280031Sdim 235280031Sdim /* only support affine coordinates */ 236280031Sdim if (!point->Z_is_one) return 0; 237276479Sdim 238234353Sdim /* Since point_multiply is static we can guarantee that ctx != NULL. */ 239234353Sdim BN_CTX_start(ctx); 240226633Sdim x1 = BN_CTX_get(ctx); 241280031Sdim z1 = BN_CTX_get(ctx); 242198892Srdivacky if (z1 == NULL) goto err; 243198090Srdivacky 244198090Srdivacky x2 = &r->X; 245198090Srdivacky z2 = &r->Y; 246198090Srdivacky 247198090Srdivacky if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */ 248198090Srdivacky if (!BN_one(z1)) goto err; /* z1 = 1 */ 249198090Srdivacky if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */ 250198090Srdivacky if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err; 251198090Srdivacky if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ 252198090Srdivacky 253193323Sed /* find top most bit and go one past it */ 254234353Sdim i = scalar->top - 1; j = BN_BITS2 - 1; 255193323Sed mask = BN_TBIT; 256198090Srdivacky while (!(scalar->d[i] & mask)) { mask >>= 1; j--; } 257280031Sdim mask >>= 1; j--; 258280031Sdim /* if top most bit was at word break, go to next word */ 259193323Sed if (!mask) 260193323Sed { 261314564Sdim i--; j = BN_BITS2 - 1; 262314564Sdim mask = BN_TBIT; 263314564Sdim } 264314564Sdim 265321369Sdim for (; i >= 0; i--) 266321369Sdim { 267321369Sdim for (; j >= 0; j--) 268321369Sdim { 269321369Sdim if (scalar->d[i] & mask) 270321369Sdim { 271321369Sdim if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err; 272314564Sdim if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err; 273314564Sdim } 274314564Sdim else 275314564Sdim { 276314564Sdim if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; 277314564Sdim if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; 278314564Sdim } 279314564Sdim mask >>= 1; 280314564Sdim } 281314564Sdim j = BN_BITS2 - 1; 282360784Sdim mask = BN_TBIT; 283321369Sdim } 284321369Sdim 285321369Sdim /* convert out of "projective" coordinates */ 286193323Sed i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); 287193323Sed if (i == 0) goto err; 288360784Sdim else if (i == 1) 289360784Sdim { 290309124Sdim if (!EC_POINT_set_to_infinity(group, r)) goto err; 291341825Sdim } 292341825Sdim else 293309124Sdim { 294212904Sdim if (!BN_one(&r->Z)) goto err; 295309124Sdim r->Z_is_one = 1; 296198090Srdivacky } 297198090Srdivacky 298193323Sed /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ 299221345Sdim BN_set_negative(&r->X, 0); 300221345Sdim BN_set_negative(&r->Y, 0); 301360784Sdim 302309124Sdim ret = 1; 303309124Sdim 304221345Sdim err: 305210299Sed BN_CTX_end(ctx); 306210299Sed return ret; 307360784Sdim } 308198090Srdivacky 309198090Srdivacky 310198090Srdivacky/* Computes the sum 311198090Srdivacky * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] 312198090Srdivacky * gracefully ignoring NULL scalar values. 313193323Sed */ 314198090Srdivackyint ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 315198892Srdivacky size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) 316198892Srdivacky { 317198892Srdivacky BN_CTX *new_ctx = NULL; 318193323Sed int ret = 0; 319198892Srdivacky size_t i; 320198090Srdivacky EC_POINT *p=NULL; 321341825Sdim 322210299Sed if (ctx == NULL) 323210299Sed { 324210299Sed ctx = new_ctx = BN_CTX_new(); 325198892Srdivacky if (ctx == NULL) 326198892Srdivacky return 0; 327198090Srdivacky } 328309124Sdim 329234353Sdim /* This implementation is more efficient than the wNAF implementation for 2 330234353Sdim * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points, 331198892Srdivacky * or if we can perform a fast multiplication based on precomputation. 332198090Srdivacky */ 333360784Sdim if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group))) 334198892Srdivacky { 335198892Srdivacky ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); 336198892Srdivacky goto err; 337198892Srdivacky } 338198892Srdivacky 339198892Srdivacky if ((p = EC_POINT_new(group)) == NULL) goto err; 340239462Sdim 341239462Sdim if (!EC_POINT_set_to_infinity(group, r)) goto err; 342198090Srdivacky 343198892Srdivacky if (scalar) 344198892Srdivacky { 345198892Srdivacky if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err; 346193323Sed if (BN_is_negative(scalar)) 347198892Srdivacky if (!group->meth->invert(group, p, ctx)) goto err; 348198892Srdivacky if (!group->meth->add(group, r, r, p, ctx)) goto err; 349198892Srdivacky } 350198892Srdivacky 351198090Srdivacky for (i = 0; i < num; i++) 352198090Srdivacky { 353198090Srdivacky if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err; 354193323Sed if (BN_is_negative(scalars[i])) 355198090Srdivacky if (!group->meth->invert(group, p, ctx)) goto err; 356198090Srdivacky if (!group->meth->add(group, r, r, p, ctx)) goto err; 357198090Srdivacky } 358193323Sed 359198090Srdivacky ret = 1; 360193323Sed 361198892Srdivacky err: 362198892Srdivacky if (p) EC_POINT_free(p); 363309124Sdim if (new_ctx != NULL) 364309124Sdim BN_CTX_free(new_ctx); 365198090Srdivacky return ret; 366198090Srdivacky } 367198892Srdivacky 368198090Srdivacky 369193323Sed/* Precomputation for point multiplication: fall back to wNAF methods 370193323Sed * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */ 371321369Sdim 372321369Sdimint ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 373321369Sdim { 374321369Sdim return ec_wNAF_precompute_mult(group, ctx); 375321369Sdim } 376321369Sdim 377321369Sdimint ec_GF2m_have_precompute_mult(const EC_GROUP *group) 378321369Sdim { 379321369Sdim return ec_wNAF_have_precompute_mult(group); 380321369Sdim } 381321369Sdim