| /* crypto/ec/ec2_mult.c */ |
| /* ==================================================================== |
| * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. |
| * |
| * The Elliptic Curve Public-Key Crypto Library (ECC Code) included |
| * herein is developed by SUN MICROSYSTEMS, INC., and is contributed |
| * to the OpenSSL project. |
| * |
| * The ECC Code is licensed pursuant to the OpenSSL open source |
| * license provided below. |
| * |
| * The software is originally written by Sheueling Chang Shantz and |
| * Douglas Stebila of Sun Microsystems Laboratories. |
| * |
| */ |
| /* ==================================================================== |
| * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in |
| * the documentation and/or other materials provided with the |
| * distribution. |
| * |
| * 3. All advertising materials mentioning features or use of this |
| * software must display the following acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| * |
| * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| * endorse or promote products derived from this software without |
| * prior written permission. For written permission, please contact |
| * openssl-core@openssl.org. |
| * |
| * 5. Products derived from this software may not be called "OpenSSL" |
| * nor may "OpenSSL" appear in their names without prior written |
| * permission of the OpenSSL Project. |
| * |
| * 6. Redistributions of any form whatsoever must retain the following |
| * acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| * OF THE POSSIBILITY OF SUCH DAMAGE. |
| * ==================================================================== |
| * |
| * This product includes cryptographic software written by Eric Young |
| * (eay@cryptsoft.com). This product includes software written by Tim |
| * Hudson (tjh@cryptsoft.com). |
| * |
| */ |
| |
| #include <openssl/err.h> |
| |
| #include "ec_lcl.h" |
| |
| #ifndef OPENSSL_NO_EC2M |
| |
| /*- |
| * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective |
| * coordinates. |
| * Uses algorithm Mdouble in appendix of |
| * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| * modified to not require precomputation of c=b^{2^{m-1}}. |
| */ |
| static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, |
| BN_CTX *ctx) |
| { |
| BIGNUM *t1; |
| int ret = 0; |
| |
| /* Since Mdouble is static we can guarantee that ctx != NULL. */ |
| BN_CTX_start(ctx); |
| t1 = BN_CTX_get(ctx); |
| if (t1 == NULL) |
| goto err; |
| |
| if (!group->meth->field_sqr(group, x, x, ctx)) |
| goto err; |
| if (!group->meth->field_sqr(group, t1, z, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, z, x, t1, ctx)) |
| goto err; |
| if (!group->meth->field_sqr(group, x, x, ctx)) |
| goto err; |
| if (!group->meth->field_sqr(group, t1, t1, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) |
| goto err; |
| if (!BN_GF2m_add(x, x, t1)) |
| goto err; |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| /*- |
| * Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery |
| * projective coordinates. |
| * Uses algorithm Madd in appendix of |
| * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| */ |
| static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, |
| BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2, |
| BN_CTX *ctx) |
| { |
| BIGNUM *t1, *t2; |
| int ret = 0; |
| |
| /* Since Madd is static we can guarantee that ctx != NULL. */ |
| BN_CTX_start(ctx); |
| t1 = BN_CTX_get(ctx); |
| t2 = BN_CTX_get(ctx); |
| if (t2 == NULL) |
| goto err; |
| |
| if (!BN_copy(t1, x)) |
| goto err; |
| if (!group->meth->field_mul(group, x1, x1, z2, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, z1, z1, x2, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, t2, x1, z1, ctx)) |
| goto err; |
| if (!BN_GF2m_add(z1, z1, x1)) |
| goto err; |
| if (!group->meth->field_sqr(group, z1, z1, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, x1, z1, t1, ctx)) |
| goto err; |
| if (!BN_GF2m_add(x1, x1, t2)) |
| goto err; |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| /*- |
| * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) |
| * using Montgomery point multiplication algorithm Mxy() in appendix of |
| * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| * Returns: |
| * 0 on error |
| * 1 if return value should be the point at infinity |
| * 2 otherwise |
| */ |
| static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, |
| BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, |
| BN_CTX *ctx) |
| { |
| BIGNUM *t3, *t4, *t5; |
| int ret = 0; |
| |
| if (BN_is_zero(z1)) { |
| BN_zero(x2); |
| BN_zero(z2); |
| return 1; |
| } |
| |
| if (BN_is_zero(z2)) { |
| if (!BN_copy(x2, x)) |
| return 0; |
| if (!BN_GF2m_add(z2, x, y)) |
| return 0; |
| return 2; |
| } |
| |
| /* Since Mxy is static we can guarantee that ctx != NULL. */ |
| BN_CTX_start(ctx); |
| t3 = BN_CTX_get(ctx); |
| t4 = BN_CTX_get(ctx); |
| t5 = BN_CTX_get(ctx); |
| if (t5 == NULL) |
| goto err; |
| |
| if (!BN_one(t5)) |
| goto err; |
| |
| if (!group->meth->field_mul(group, t3, z1, z2, ctx)) |
| goto err; |
| |
| if (!group->meth->field_mul(group, z1, z1, x, ctx)) |
| goto err; |
| if (!BN_GF2m_add(z1, z1, x1)) |
| goto err; |
| if (!group->meth->field_mul(group, z2, z2, x, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, x1, z2, x1, ctx)) |
| goto err; |
| if (!BN_GF2m_add(z2, z2, x2)) |
| goto err; |
| |
| if (!group->meth->field_mul(group, z2, z2, z1, ctx)) |
| goto err; |
| if (!group->meth->field_sqr(group, t4, x, ctx)) |
| goto err; |
| if (!BN_GF2m_add(t4, t4, y)) |
| goto err; |
| if (!group->meth->field_mul(group, t4, t4, t3, ctx)) |
| goto err; |
| if (!BN_GF2m_add(t4, t4, z2)) |
| goto err; |
| |
| if (!group->meth->field_mul(group, t3, t3, x, ctx)) |
| goto err; |
| if (!group->meth->field_div(group, t3, t5, t3, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, t4, t3, t4, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, x2, x1, t3, ctx)) |
| goto err; |
| if (!BN_GF2m_add(z2, x2, x)) |
| goto err; |
| |
| if (!group->meth->field_mul(group, z2, z2, t4, ctx)) |
| goto err; |
| if (!BN_GF2m_add(z2, z2, y)) |
| goto err; |
| |
| ret = 2; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| /*- |
| * Computes scalar*point and stores the result in r. |
| * point can not equal r. |
| * Uses a modified algorithm 2P of |
| * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| * |
| * To protect against side-channel attack the function uses constant time swap, |
| * avoiding conditional branches. |
| */ |
| static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, |
| EC_POINT *r, |
| const BIGNUM *scalar, |
| const EC_POINT *point, |
| BN_CTX *ctx) |
| { |
| BIGNUM *x1, *x2, *z1, *z2; |
| int ret = 0, i; |
| BN_ULONG mask, word; |
| |
| if (r == point) { |
| ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); |
| return 0; |
| } |
| |
| /* if result should be point at infinity */ |
| if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || |
| EC_POINT_is_at_infinity(group, point)) { |
| return EC_POINT_set_to_infinity(group, r); |
| } |
| |
| /* only support affine coordinates */ |
| if (!point->Z_is_one) |
| return 0; |
| |
| /* |
| * Since point_multiply is static we can guarantee that ctx != NULL. |
| */ |
| BN_CTX_start(ctx); |
| x1 = BN_CTX_get(ctx); |
| z1 = BN_CTX_get(ctx); |
| if (z1 == NULL) |
| goto err; |
| |
| x2 = &r->X; |
| z2 = &r->Y; |
| |
| bn_wexpand(x1, group->field.top); |
| bn_wexpand(z1, group->field.top); |
| bn_wexpand(x2, group->field.top); |
| bn_wexpand(z2, group->field.top); |
| |
| if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) |
| goto err; /* x1 = x */ |
| if (!BN_one(z1)) |
| goto err; /* z1 = 1 */ |
| if (!group->meth->field_sqr(group, z2, x1, ctx)) |
| goto err; /* z2 = x1^2 = x^2 */ |
| if (!group->meth->field_sqr(group, x2, z2, ctx)) |
| goto err; |
| if (!BN_GF2m_add(x2, x2, &group->b)) |
| goto err; /* x2 = x^4 + b */ |
| |
| /* find top most bit and go one past it */ |
| i = scalar->top - 1; |
| mask = BN_TBIT; |
| word = scalar->d[i]; |
| while (!(word & mask)) |
| mask >>= 1; |
| mask >>= 1; |
| /* if top most bit was at word break, go to next word */ |
| if (!mask) { |
| i--; |
| mask = BN_TBIT; |
| } |
| |
| for (; i >= 0; i--) { |
| word = scalar->d[i]; |
| while (mask) { |
| BN_consttime_swap(word & mask, x1, x2, group->field.top); |
| BN_consttime_swap(word & mask, z1, z2, group->field.top); |
| if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) |
| goto err; |
| if (!gf2m_Mdouble(group, x1, z1, ctx)) |
| goto err; |
| BN_consttime_swap(word & mask, x1, x2, group->field.top); |
| BN_consttime_swap(word & mask, z1, z2, group->field.top); |
| mask >>= 1; |
| } |
| mask = BN_TBIT; |
| } |
| |
| /* convert out of "projective" coordinates */ |
| i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); |
| if (i == 0) |
| goto err; |
| else if (i == 1) { |
| if (!EC_POINT_set_to_infinity(group, r)) |
| goto err; |
| } else { |
| if (!BN_one(&r->Z)) |
| goto err; |
| r->Z_is_one = 1; |
| } |
| |
| /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ |
| BN_set_negative(&r->X, 0); |
| BN_set_negative(&r->Y, 0); |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| /*- |
| * Computes the sum |
| * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] |
| * gracefully ignoring NULL scalar values. |
| */ |
| int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *ctx) |
| { |
| BN_CTX *new_ctx = NULL; |
| int ret = 0; |
| size_t i; |
| EC_POINT *p = NULL; |
| EC_POINT *acc = NULL; |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return 0; |
| } |
| |
| /* |
| * This implementation is more efficient than the wNAF implementation for |
| * 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more |
| * points, or if we can perform a fast multiplication based on |
| * precomputation. |
| */ |
| if ((scalar && (num > 1)) || (num > 2) |
| || (num == 0 && EC_GROUP_have_precompute_mult(group))) { |
| ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); |
| goto err; |
| } |
| |
| if ((p = EC_POINT_new(group)) == NULL) |
| goto err; |
| if ((acc = EC_POINT_new(group)) == NULL) |
| goto err; |
| |
| if (!EC_POINT_set_to_infinity(group, acc)) |
| goto err; |
| |
| if (scalar) { |
| if (!ec_GF2m_montgomery_point_multiply |
| (group, p, scalar, group->generator, ctx)) |
| goto err; |
| if (BN_is_negative(scalar)) |
| if (!group->meth->invert(group, p, ctx)) |
| goto err; |
| if (!group->meth->add(group, acc, acc, p, ctx)) |
| goto err; |
| } |
| |
| for (i = 0; i < num; i++) { |
| if (!ec_GF2m_montgomery_point_multiply |
| (group, p, scalars[i], points[i], ctx)) |
| goto err; |
| if (BN_is_negative(scalars[i])) |
| if (!group->meth->invert(group, p, ctx)) |
| goto err; |
| if (!group->meth->add(group, acc, acc, p, ctx)) |
| goto err; |
| } |
| |
| if (!EC_POINT_copy(r, acc)) |
| goto err; |
| |
| ret = 1; |
| |
| err: |
| if (p) |
| EC_POINT_free(p); |
| if (acc) |
| EC_POINT_free(acc); |
| if (new_ctx != NULL) |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| /* |
| * Precomputation for point multiplication: fall back to wNAF methods because |
| * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate |
| */ |
| |
| int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
| { |
| return ec_wNAF_precompute_mult(group, ctx); |
| } |
| |
| int ec_GF2m_have_precompute_mult(const EC_GROUP *group) |
| { |
| return ec_wNAF_have_precompute_mult(group); |
| } |
| |
| #endif |
