diff options
Diffstat (limited to 'src/crypto/ec/simple.c')
| -rw-r--r-- | src/crypto/ec/simple.c | 1362 |
1 files changed, 1362 insertions, 0 deletions
diff --git a/src/crypto/ec/simple.c b/src/crypto/ec/simple.c new file mode 100644 index 0000000..b3f96fa --- /dev/null +++ b/src/crypto/ec/simple.c @@ -0,0 +1,1362 @@ +/* Originally written by Bodo Moeller for the OpenSSL project. + * ==================================================================== + * Copyright (c) 1998-2005 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). + * + */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * Portions of the attached software ("Contribution") are developed by + * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. + * + * The Contribution is licensed pursuant to the OpenSSL open source + * license provided above. + * + * The elliptic curve binary polynomial software is originally written by + * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems + * Laboratories. */ + +#include <openssl/ec.h> + +#include <string.h> + +#include <openssl/bn.h> +#include <openssl/err.h> +#include <openssl/mem.h> + +#include "internal.h" + + +const EC_METHOD *EC_GFp_simple_method(void) { + static const EC_METHOD ret = {EC_FLAGS_DEFAULT_OCT, + ec_GFp_simple_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_simple_group_copy, + ec_GFp_simple_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_get_affine_coordinates, + 0, + 0, + 0, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + 0 /* mul */, + 0 /* precompute_mult */, + 0 /* have_precompute_mult */, + ec_GFp_simple_field_mul, + ec_GFp_simple_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */}; + + return &ret; +} + + +/* Most method functions in this file are designed to work with non-trivial + * representations of field elements if necessary (see ecp_mont.c): while + * standard modular addition and subtraction are used, the field_mul and + * field_sqr methods will be used for multiplication, and field_encode and + * field_decode (if defined) will be used for converting between + * representations. + + * Functions ec_GFp_simple_points_make_affine() and + * ec_GFp_simple_point_get_affine_coordinates() specifically assume that if a + * non-trivial representation is used, it is a Montgomery representation (i.e. + * 'encoding' means multiplying by some factor R). */ + +int ec_GFp_simple_group_init(EC_GROUP *group) { + BN_init(&group->field); + BN_init(&group->a); + BN_init(&group->b); + group->a_is_minus3 = 0; + return 1; +} + +void ec_GFp_simple_group_finish(EC_GROUP *group) { + BN_free(&group->field); + BN_free(&group->a); + BN_free(&group->b); +} + +void ec_GFp_simple_group_clear_finish(EC_GROUP *group) { + BN_clear_free(&group->field); + BN_clear_free(&group->a); + BN_clear_free(&group->b); +} + +int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) { + if (!BN_copy(&dest->field, &src->field) || + !BN_copy(&dest->a, &src->a) || + !BN_copy(&dest->b, &src->b)) { + return 0; + } + + dest->a_is_minus3 = src->a_is_minus3; + return 1; +} + +int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, + BN_CTX *ctx) { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *tmp_a; + + /* p must be a prime > 3 */ + if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { + OPENSSL_PUT_ERROR(EC, ec_GFp_simple_group_set_curve, EC_R_INVALID_FIELD); + return 0; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + tmp_a = BN_CTX_get(ctx); + if (tmp_a == NULL) + goto err; + + /* group->field */ + if (!BN_copy(&group->field, p)) + goto err; + BN_set_negative(&group->field, 0); + + /* group->a */ + if (!BN_nnmod(tmp_a, a, p, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) + goto err; + } else if (!BN_copy(&group->a, tmp_a)) + goto err; + + /* group->b */ + if (!BN_nnmod(&group->b, b, p, ctx)) + goto err; + if (group->meth->field_encode) + if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) + goto err; + + /* group->a_is_minus3 */ + if (!BN_add_word(tmp_a, 3)) + goto err; + group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); + + ret = 1; + +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, + BIGNUM *b, BN_CTX *ctx) { + int ret = 0; + BN_CTX *new_ctx = NULL; + + if (p != NULL) { + if (!BN_copy(p, &group->field)) + return 0; + } + + if (a != NULL || b != NULL) { + if (group->meth->field_decode) { + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + if (a != NULL) { + if (!group->meth->field_decode(group, a, &group->a, ctx)) + goto err; + } + if (b != NULL) { + if (!group->meth->field_decode(group, b, &group->b, ctx)) + goto err; + } + } else { + if (a != NULL) { + if (!BN_copy(a, &group->a)) + goto err; + } + if (b != NULL) { + if (!BN_copy(b, &group->b)) + goto err; + } + } + } + + ret = 1; + +err: + if (new_ctx) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_group_get_degree(const EC_GROUP *group) { + return BN_num_bits(&group->field); +} + +int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) { + int ret = 0; + BIGNUM *a, *b, *order, *tmp_1, *tmp_2; + const BIGNUM *p = &group->field; + BN_CTX *new_ctx = NULL; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) { + OPENSSL_PUT_ERROR(EC, ec_GFp_simple_group_check_discriminant, + ERR_R_MALLOC_FAILURE); + goto err; + } + } + BN_CTX_start(ctx); + a = BN_CTX_get(ctx); + b = BN_CTX_get(ctx); + tmp_1 = BN_CTX_get(ctx); + tmp_2 = BN_CTX_get(ctx); + order = BN_CTX_get(ctx); + if (order == NULL) + goto err; + + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, a, &group->a, ctx)) + goto err; + if (!group->meth->field_decode(group, b, &group->b, ctx)) + goto err; + } else { + if (!BN_copy(a, &group->a)) + goto err; + if (!BN_copy(b, &group->b)) + goto err; + } + + /* check the discriminant: + * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) + * 0 =< a, b < p */ + if (BN_is_zero(a)) { + if (BN_is_zero(b)) + goto err; + } else if (!BN_is_zero(b)) { + if (!BN_mod_sqr(tmp_1, a, p, ctx)) + goto err; + if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) + goto err; + if (!BN_lshift(tmp_1, tmp_2, 2)) + goto err; + /* tmp_1 = 4*a^3 */ + + if (!BN_mod_sqr(tmp_2, b, p, ctx)) + goto err; + if (!BN_mul_word(tmp_2, 27)) + goto err; + /* tmp_2 = 27*b^2 */ + + if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) + goto err; + if (BN_is_zero(a)) + goto err; + } + ret = 1; + +err: + if (ctx != NULL) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_point_init(EC_POINT *point) { + BN_init(&point->X); + BN_init(&point->Y); + BN_init(&point->Z); + point->Z_is_one = 0; + + return 1; +} + +void ec_GFp_simple_point_finish(EC_POINT *point) { + BN_free(&point->X); + BN_free(&point->Y); + BN_free(&point->Z); +} + +void ec_GFp_simple_point_clear_finish(EC_POINT *point) { + BN_clear_free(&point->X); + BN_clear_free(&point->Y); + BN_clear_free(&point->Z); + point->Z_is_one = 0; +} + +int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) { + if (!BN_copy(&dest->X, &src->X)) + return 0; + if (!BN_copy(&dest->Y, &src->Y)) + return 0; + if (!BN_copy(&dest->Z, &src->Z)) + return 0; + dest->Z_is_one = src->Z_is_one; + + return 1; +} + +int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, + EC_POINT *point) { + point->Z_is_one = 0; + BN_zero(&point->Z); + return 1; +} + +int ec_GFp_simple_set_Jprojective_coordinates_GFp( + const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, + const BIGNUM *z, BN_CTX *ctx) { + BN_CTX *new_ctx = NULL; + int ret = 0; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + if (x != NULL) { + if (!BN_nnmod(&point->X, x, &group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) + goto err; + } + } + + if (y != NULL) { + if (!BN_nnmod(&point->Y, y, &group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) + goto err; + } + } + + if (z != NULL) { + int Z_is_one; + + if (!BN_nnmod(&point->Z, z, &group->field, ctx)) + goto err; + Z_is_one = BN_is_one(&point->Z); + if (group->meth->field_encode) { + if (Z_is_one && (group->meth->field_set_to_one != 0)) { + if (!group->meth->field_set_to_one(group, &point->Z, ctx)) + goto err; + } else { + if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) + goto err; + } + } + point->Z_is_one = Z_is_one; + } + + ret = 1; + +err: + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BIGNUM *z, BN_CTX *ctx) { + BN_CTX *new_ctx = NULL; + int ret = 0; + + if (group->meth->field_decode != 0) { + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + if (x != NULL) { + if (!group->meth->field_decode(group, x, &point->X, ctx)) + goto err; + } + if (y != NULL) { + if (!group->meth->field_decode(group, y, &point->Y, ctx)) + goto err; + } + if (z != NULL) { + if (!group->meth->field_decode(group, z, &point->Z, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; + } + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; + } + if (z != NULL) { + if (!BN_copy(z, &point->Z)) + goto err; + } + } + + ret = 1; + +err: + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, + EC_POINT *point, const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) { + if (x == NULL || y == NULL) { + /* unlike for projective coordinates, we do not tolerate this */ + OPENSSL_PUT_ERROR(EC, ec_GFp_simple_point_set_affine_coordinates, + ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + return ec_point_set_Jprojective_coordinates_GFp(group, point, x, y, + BN_value_one(), ctx); +} + +int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, + BIGNUM *y, BN_CTX *ctx) { + BN_CTX *new_ctx = NULL; + BIGNUM *Z, *Z_1, *Z_2, *Z_3; + const BIGNUM *Z_; + int ret = 0; + + if (EC_POINT_is_at_infinity(group, point)) { + OPENSSL_PUT_ERROR(EC, ec_GFp_simple_point_get_affine_coordinates, + EC_R_POINT_AT_INFINITY); + return 0; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + Z = BN_CTX_get(ctx); + Z_1 = BN_CTX_get(ctx); + Z_2 = BN_CTX_get(ctx); + Z_3 = BN_CTX_get(ctx); + if (Z_3 == NULL) + goto err; + + /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ + + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, Z, &point->Z, ctx)) + goto err; + Z_ = Z; + } else { + Z_ = &point->Z; + } + + if (BN_is_one(Z_)) { + if (group->meth->field_decode) { + if (x != NULL) { + if (!group->meth->field_decode(group, x, &point->X, ctx)) + goto err; + } + if (y != NULL) { + if (!group->meth->field_decode(group, y, &point->Y, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; + } + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; + } + } + } else { + if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) { + OPENSSL_PUT_ERROR(EC, ec_GFp_simple_point_get_affine_coordinates, + ERR_R_BN_LIB); + goto err; + } + + if (group->meth->field_encode == 0) { + /* field_sqr works on standard representation */ + if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) + goto err; + } + + if (x != NULL) { + /* in the Montgomery case, field_mul will cancel out Montgomery factor in + * X: */ + if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) + goto err; + } + + if (y != NULL) { + if (group->meth->field_encode == 0) { + /* field_mul works on standard representation */ + if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) + goto err; + } + + /* in the Montgomery case, field_mul will cancel out Montgomery factor in + * Y: */ + if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) + goto err; + } + } + + ret = 1; + +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) { + int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, + BN_CTX *); + int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; + int ret = 0; + + if (a == b) + return EC_POINT_dbl(group, r, a, ctx); + if (EC_POINT_is_at_infinity(group, a)) + return EC_POINT_copy(r, b); + if (EC_POINT_is_at_infinity(group, b)) + return EC_POINT_copy(r, a); + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = &group->field; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + n0 = BN_CTX_get(ctx); + n1 = BN_CTX_get(ctx); + n2 = BN_CTX_get(ctx); + n3 = BN_CTX_get(ctx); + n4 = BN_CTX_get(ctx); + n5 = BN_CTX_get(ctx); + n6 = BN_CTX_get(ctx); + if (n6 == NULL) + goto end; + + /* Note that in this function we must not read components of 'a' or 'b' + * once we have written the corresponding components of 'r'. + * ('r' might be one of 'a' or 'b'.) + */ + + /* n1, n2 */ + if (b->Z_is_one) { + if (!BN_copy(n1, &a->X)) + goto end; + if (!BN_copy(n2, &a->Y)) + goto end; + /* n1 = X_a */ + /* n2 = Y_a */ + } else { + if (!field_sqr(group, n0, &b->Z, ctx)) + goto end; + if (!field_mul(group, n1, &a->X, n0, ctx)) + goto end; + /* n1 = X_a * Z_b^2 */ + + if (!field_mul(group, n0, n0, &b->Z, ctx)) + goto end; + if (!field_mul(group, n2, &a->Y, n0, ctx)) + goto end; + /* n2 = Y_a * Z_b^3 */ + } + + /* n3, n4 */ + if (a->Z_is_one) { + if (!BN_copy(n3, &b->X)) + goto end; + if (!BN_copy(n4, &b->Y)) + goto end; + /* n3 = X_b */ + /* n4 = Y_b */ + } else { + if (!field_sqr(group, n0, &a->Z, ctx)) + goto end; + if (!field_mul(group, n3, &b->X, n0, ctx)) + goto end; + /* n3 = X_b * Z_a^2 */ + + if (!field_mul(group, n0, n0, &a->Z, ctx)) + goto end; + if (!field_mul(group, n4, &b->Y, n0, ctx)) + goto end; + /* n4 = Y_b * Z_a^3 */ + } + + /* n5, n6 */ + if (!BN_mod_sub_quick(n5, n1, n3, p)) + goto end; + if (!BN_mod_sub_quick(n6, n2, n4, p)) + goto end; + /* n5 = n1 - n3 */ + /* n6 = n2 - n4 */ + + if (BN_is_zero(n5)) { + if (BN_is_zero(n6)) { + /* a is the same point as b */ + BN_CTX_end(ctx); + ret = EC_POINT_dbl(group, r, a, ctx); + ctx = NULL; + goto end; + } else { + /* a is the inverse of b */ + BN_zero(&r->Z); + r->Z_is_one = 0; + ret = 1; + goto end; + } + } + + /* 'n7', 'n8' */ + if (!BN_mod_add_quick(n1, n1, n3, p)) + goto end; + if (!BN_mod_add_quick(n2, n2, n4, p)) + goto end; + /* 'n7' = n1 + n3 */ + /* 'n8' = n2 + n4 */ + + /* Z_r */ + if (a->Z_is_one && b->Z_is_one) { + if (!BN_copy(&r->Z, n5)) + goto end; + } else { + if (a->Z_is_one) { + if (!BN_copy(n0, &b->Z)) + goto end; + } else if (b->Z_is_one) { + if (!BN_copy(n0, &a->Z)) + goto end; + } else { + if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) + goto end; + } + if (!field_mul(group, &r->Z, n0, n5, ctx)) + goto end; + } + r->Z_is_one = 0; + /* Z_r = Z_a * Z_b * n5 */ + + /* X_r */ + if (!field_sqr(group, n0, n6, ctx)) + goto end; + if (!field_sqr(group, n4, n5, ctx)) + goto end; + if (!field_mul(group, n3, n1, n4, ctx)) + goto end; + if (!BN_mod_sub_quick(&r->X, n0, n3, p)) + goto end; + /* X_r = n6^2 - n5^2 * 'n7' */ + + /* 'n9' */ + if (!BN_mod_lshift1_quick(n0, &r->X, p)) + goto end; + if (!BN_mod_sub_quick(n0, n3, n0, p)) + goto end; + /* n9 = n5^2 * 'n7' - 2 * X_r */ + + /* Y_r */ + if (!field_mul(group, n0, n0, n6, ctx)) + goto end; + if (!field_mul(group, n5, n4, n5, ctx)) + goto end; /* now n5 is n5^3 */ + if (!field_mul(group, n1, n2, n5, ctx)) + goto end; + if (!BN_mod_sub_quick(n0, n0, n1, p)) + goto end; + if (BN_is_odd(n0)) + if (!BN_add(n0, n0, p)) + goto end; + /* now 0 <= n0 < 2*p, and n0 is even */ + if (!BN_rshift1(&r->Y, n0)) + goto end; + /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ + + ret = 1; + +end: + if (ctx) /* otherwise we already called BN_CTX_end */ + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + BN_CTX *ctx) { + int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, + BN_CTX *); + int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *n0, *n1, *n2, *n3; + int ret = 0; + + if (EC_POINT_is_at_infinity(group, a)) { + BN_zero(&r->Z); + r->Z_is_one = 0; + return 1; + } + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = &group->field; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + n0 = BN_CTX_get(ctx); + n1 = BN_CTX_get(ctx); + n2 = BN_CTX_get(ctx); + n3 = BN_CTX_get(ctx); + if (n3 == NULL) + goto err; + + /* Note that in this function we must not read components of 'a' + * once we have written the corresponding components of 'r'. + * ('r' might the same as 'a'.) + */ + + /* n1 */ + if (a->Z_is_one) { + if (!field_sqr(group, n0, &a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, &group->a, p)) + goto err; + /* n1 = 3 * X_a^2 + a_curve */ + } else if (group->a_is_minus3) { + if (!field_sqr(group, n1, &a->Z, ctx)) + goto err; + if (!BN_mod_add_quick(n0, &a->X, n1, p)) + goto err; + if (!BN_mod_sub_quick(n2, &a->X, n1, p)) + goto err; + if (!field_mul(group, n1, n0, n2, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, n1, p)) + goto err; + /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) + * = 3 * X_a^2 - 3 * Z_a^4 */ + } else { + if (!field_sqr(group, n0, &a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!field_sqr(group, n1, &a->Z, ctx)) + goto err; + if (!field_sqr(group, n1, n1, ctx)) + goto err; + if (!field_mul(group, n1, n1, &group->a, ctx)) + goto err; + if (!BN_mod_add_quick(n1, n1, n0, p)) + goto err; + /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ + } + + /* Z_r */ + if (a->Z_is_one) { + if (!BN_copy(n0, &a->Y)) + goto err; + } else { + if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) + goto err; + } + if (!BN_mod_lshift1_quick(&r->Z, n0, p)) + goto err; + r->Z_is_one = 0; + /* Z_r = 2 * Y_a * Z_a */ + + /* n2 */ + if (!field_sqr(group, n3, &a->Y, ctx)) + goto err; + if (!field_mul(group, n2, &a->X, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n2, n2, 2, p)) + goto err; + /* n2 = 4 * X_a * Y_a^2 */ + + /* X_r */ + if (!BN_mod_lshift1_quick(n0, n2, p)) + goto err; + if (!field_sqr(group, &r->X, n1, ctx)) + goto err; + if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) + goto err; + /* X_r = n1^2 - 2 * n2 */ + + /* n3 */ + if (!field_sqr(group, n0, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n3, n0, 3, p)) + goto err; + /* n3 = 8 * Y_a^4 */ + + /* Y_r */ + if (!BN_mod_sub_quick(n0, n2, &r->X, p)) + goto err; + if (!field_mul(group, n0, n1, n0, ctx)) + goto err; + if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) + goto err; + /* Y_r = n1 * (n2 - X_r) - n3 */ + + ret = 1; + +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) { + if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) + /* point is its own inverse */ + return 1; + + return BN_usub(&point->Y, &group->field, &point->Y); +} + +int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) { + return !point->Z_is_one && BN_is_zero(&point->Z); +} + +int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, + BN_CTX *ctx) { + int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, + BN_CTX *); + int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *rh, *tmp, *Z4, *Z6; + int ret = -1; + + if (EC_POINT_is_at_infinity(group, point)) + return 1; + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = &group->field; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + rh = BN_CTX_get(ctx); + tmp = BN_CTX_get(ctx); + Z4 = BN_CTX_get(ctx); + Z6 = BN_CTX_get(ctx); + if (Z6 == NULL) + goto err; + + /* We have a curve defined by a Weierstrass equation + * y^2 = x^3 + a*x + b. + * The point to consider is given in Jacobian projective coordinates + * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). + * Substituting this and multiplying by Z^6 transforms the above equation + * into + * Y^2 = X^3 + a*X*Z^4 + b*Z^6. + * To test this, we add up the right-hand side in 'rh'. + */ + + /* rh := X^2 */ + if (!field_sqr(group, rh, &point->X, ctx)) + goto err; + + if (!point->Z_is_one) { + if (!field_sqr(group, tmp, &point->Z, ctx)) + goto err; + if (!field_sqr(group, Z4, tmp, ctx)) + goto err; + if (!field_mul(group, Z6, Z4, tmp, ctx)) + goto err; + + /* rh := (rh + a*Z^4)*X */ + if (group->a_is_minus3) { + if (!BN_mod_lshift1_quick(tmp, Z4, p)) + goto err; + if (!BN_mod_add_quick(tmp, tmp, Z4, p)) + goto err; + if (!BN_mod_sub_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; + } else { + if (!field_mul(group, tmp, Z4, &group->a, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; + } + + /* rh := rh + b*Z^6 */ + if (!field_mul(group, tmp, &group->b, Z6, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + } else { + /* point->Z_is_one */ + + /* rh := (rh + a)*X */ + if (!BN_mod_add_quick(rh, rh, &group->a, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; + /* rh := rh + b */ + if (!BN_mod_add_quick(rh, rh, &group->b, p)) + goto err; + } + + /* 'lh' := Y^2 */ + if (!field_sqr(group, tmp, &point->Y, ctx)) + goto err; + + ret = (0 == BN_ucmp(tmp, rh)); + +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) { + /* return values: + * -1 error + * 0 equal (in affine coordinates) + * 1 not equal + */ + + int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, + BN_CTX *); + int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + BN_CTX *new_ctx = NULL; + BIGNUM *tmp1, *tmp2, *Za23, *Zb23; + const BIGNUM *tmp1_, *tmp2_; + int ret = -1; + + if (EC_POINT_is_at_infinity(group, a)) { + return EC_POINT_is_at_infinity(group, b) ? 0 : 1; + } + + if (EC_POINT_is_at_infinity(group, b)) + return 1; + + if (a->Z_is_one && b->Z_is_one) { + return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; + } + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + tmp1 = BN_CTX_get(ctx); + tmp2 = BN_CTX_get(ctx); + Za23 = BN_CTX_get(ctx); + Zb23 = BN_CTX_get(ctx); + if (Zb23 == NULL) + goto end; + + /* We have to decide whether + * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), + * or equivalently, whether + * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). + */ + + if (!b->Z_is_one) { + if (!field_sqr(group, Zb23, &b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) + goto end; + tmp1_ = tmp1; + } else + tmp1_ = &a->X; + if (!a->Z_is_one) { + if (!field_sqr(group, Za23, &a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, &b->X, Za23, ctx)) + goto end; + tmp2_ = tmp2; + } else + tmp2_ = &b->X; + + /* compare X_a*Z_b^2 with X_b*Z_a^2 */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ + goto end; + } + + + if (!b->Z_is_one) { + if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) + goto end; + /* tmp1_ = tmp1 */ + } else + tmp1_ = &a->Y; + if (!a->Z_is_one) { + if (!field_mul(group, Za23, Za23, &a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) + goto end; + /* tmp2_ = tmp2 */ + } else + tmp2_ = &b->Y; + + /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ + goto end; + } + + /* points are equal */ + ret = 0; + +end: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, + BN_CTX *ctx) { + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + int ret = 0; + + if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) + return 1; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!point->Z_is_one) { + OPENSSL_PUT_ERROR(EC, ec_GFp_simple_make_affine, ERR_R_INTERNAL_ERROR); + goto err; + } + + ret = 1; + +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, + EC_POINT *points[], BN_CTX *ctx) { + BN_CTX *new_ctx = NULL; + BIGNUM *tmp, *tmp_Z; + BIGNUM **prod_Z = NULL; + size_t i; + int ret = 0; + + if (num == 0) { + return 1; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) { + return 0; + } + } + + BN_CTX_start(ctx); + tmp = BN_CTX_get(ctx); + tmp_Z = BN_CTX_get(ctx); + if (tmp == NULL || tmp_Z == NULL) { + goto err; + } + + prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0])); + if (prod_Z == NULL) { + goto err; + } + memset(prod_Z, 0, num * sizeof(prod_Z[0])); + for (i = 0; i < num; i++) { + prod_Z[i] = BN_new(); + if (prod_Z[i] == NULL) { + goto err; + } + } + + /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, + * skipping any zero-valued inputs (pretend that they're 1). */ + + if (!BN_is_zero(&points[0]->Z)) { + if (!BN_copy(prod_Z[0], &points[0]->Z)) { + goto err; + } + } else { + if (group->meth->field_set_to_one != 0) { + if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) { + goto err; + } + } else { + if (!BN_one(prod_Z[0])) { + goto err; + } + } + } + + for (i = 1; i < num; i++) { + if (!BN_is_zero(&points[i]->Z)) { + if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], + &points[i]->Z, ctx)) { + goto err; + } + } else { + if (!BN_copy(prod_Z[i], prod_Z[i - 1])) { + goto err; + } + } + } + + /* Now use a single explicit inversion to replace every + * non-zero points[i]->Z by its inverse. */ + + if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx)) { + OPENSSL_PUT_ERROR(EC, ec_GFp_simple_points_make_affine, ERR_R_BN_LIB); + goto err; + } + + if (group->meth->field_encode != NULL) { + /* In the Montgomery case, we just turned R*H (representing H) + * into 1/(R*H), but we need R*(1/H) (representing 1/H); + * i.e. we need to multiply by the Montgomery factor twice. */ + if (!group->meth->field_encode(group, tmp, tmp, ctx) || + !group->meth->field_encode(group, tmp, tmp, ctx)) { + goto err; + } + } + + for (i = num - 1; i > 0; --i) { + /* Loop invariant: tmp is the product of the inverses of + * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */ + if (BN_is_zero(&points[i]->Z)) { + continue; + } + + /* Set tmp_Z to the inverse of points[i]->Z (as product + * of Z inverses 0 .. i, Z values 0 .. i - 1). */ + if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx) || + /* Update tmp to satisfy the loop invariant for i - 1. */ + !group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx) || + /* Replace points[i]->Z by its inverse. */ + !BN_copy(&points[i]->Z, tmp_Z)) { + goto err; + } + } + + /* Replace points[0]->Z by its inverse. */ + if (!BN_is_zero(&points[0]->Z) && !BN_copy(&points[0]->Z, tmp)) { + goto err; + } + + /* Finally, fix up the X and Y coordinates for all points. */ + for (i = 0; i < num; i++) { + EC_POINT *p = points[i]; + + if (!BN_is_zero(&p->Z)) { + /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1). */ + if (!group->meth->field_sqr(group, tmp, &p->Z, ctx) || + !group->meth->field_mul(group, &p->X, &p->X, tmp, ctx) || + !group->meth->field_mul(group, tmp, tmp, &p->Z, ctx) || + !group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) { + goto err; + } + + if (group->meth->field_set_to_one != NULL) { + if (!group->meth->field_set_to_one(group, &p->Z, ctx)) { + goto err; + } + } else { + if (!BN_one(&p->Z)) { + goto err; + } + } + p->Z_is_one = 1; + } + } + + ret = 1; + +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) { + BN_CTX_free(new_ctx); + } + if (prod_Z != NULL) { + for (i = 0; i < num; i++) { + if (prod_Z[i] == NULL) { + break; + } + BN_clear_free(prod_Z[i]); + } + OPENSSL_free(prod_Z); + } + + return ret; +} + +int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) { + return BN_mod_mul(r, a, b, &group->field, ctx); +} + +int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) { + return BN_mod_sqr(r, a, &group->field, ctx); +} |