diff options
Diffstat (limited to 'openssl/crypto/ec/ec2_mult.c')
| -rw-r--r-- | openssl/crypto/ec/ec2_mult.c | 380 |
1 files changed, 380 insertions, 0 deletions
diff --git a/openssl/crypto/ec/ec2_mult.c b/openssl/crypto/ec/ec2_mult.c new file mode 100644 index 000000000..ff368fd7d --- /dev/null +++ b/openssl/crypto/ec/ec2_mult.c @@ -0,0 +1,380 @@ +/* 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" + + +/* 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". + * 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 + * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation". + */ +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 + * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation". + * 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 algorithm 2P of + * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation". + */ +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, j; + BN_ULONG mask; + + 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; + + 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; j = BN_BITS2 - 1; + mask = BN_TBIT; + while (!(scalar->d[i] & mask)) { mask >>= 1; j--; } + mask >>= 1; j--; + /* if top most bit was at word break, go to next word */ + if (!mask) + { + i--; j = BN_BITS2 - 1; + mask = BN_TBIT; + } + + for (; i >= 0; i--) + { + for (; j >= 0; j--) + { + if (scalar->d[i] & mask) + { + if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err; + if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err; + } + else + { + if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; + if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; + } + mask >>= 1; + } + j = BN_BITS2 - 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; + + 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 (!EC_POINT_set_to_infinity(group, r)) 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, r, r, 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, r, r, p, ctx)) goto err; + } + + ret = 1; + + err: + if (p) EC_POINT_free(p); + 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); + } |