--- /dev/null
+/* 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"
+#include "../../internal.h"
+
+
+// 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 here 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);
+ BN_init(&group->one);
+ 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);
+ BN_free(&group->one);
+}
+
+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_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);
+ // Store the field in minimal form, so it can be used with |BN_ULONG| arrays.
+ bn_set_minimal_width(&group->field);
+
+ // group->a
+ if (!BN_nnmod(tmp_a, a, &group->field, 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, &group->field, ctx)) {
+ goto err;
+ }
+ if (group->meth->field_encode &&
+ !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));
+
+ if (group->meth->field_encode != NULL) {
+ if (!group->meth->field_encode(group, &group->one, BN_value_one(), ctx)) {
+ goto err;
+ }
+ } else if (!BN_copy(&group->one, BN_value_one())) {
+ goto err;
+ }
+
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ 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 && !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 && !group->meth->field_decode(group, a, &group->a, ctx)) {
+ goto err;
+ }
+ if (b != NULL && !group->meth->field_decode(group, b, &group->b, ctx)) {
+ goto err;
+ }
+ } else {
+ if (a != NULL && !BN_copy(a, &group->a)) {
+ goto err;
+ }
+ if (b != NULL && !BN_copy(b, &group->b)) {
+ goto err;
+ }
+ }
+ }
+
+ ret = 1;
+
+err:
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *group) {
+ return BN_num_bits(&group->field);
+}
+
+int ec_GFp_simple_point_init(EC_POINT *point) {
+ BN_init(&point->X);
+ BN_init(&point->Y);
+ BN_init(&point->Z);
+
+ return 1;
+}
+
+void ec_GFp_simple_point_finish(EC_POINT *point) {
+ BN_free(&point->X);
+ BN_free(&point->Y);
+ BN_free(&point->Z);
+}
+
+int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) {
+ if (!BN_copy(&dest->X, &src->X) ||
+ !BN_copy(&dest->Y, &src->Y) ||
+ !BN_copy(&dest->Z, &src->Z)) {
+ return 0;
+ }
+
+ return 1;
+}
+
+int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
+ EC_POINT *point) {
+ BN_zero(&point->Z);
+ return 1;
+}
+
+static int set_Jprojective_coordinate_GFp(const EC_GROUP *group, BIGNUM *out,
+ const BIGNUM *in, BN_CTX *ctx) {
+ if (in == NULL) {
+ return 1;
+ }
+ if (BN_is_negative(in) ||
+ BN_cmp(in, &group->field) >= 0) {
+ OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
+ return 0;
+ }
+ if (group->meth->field_encode) {
+ return group->meth->field_encode(group, out, in, ctx);
+ }
+ return BN_copy(out, in) != NULL;
+}
+
+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) {
+ OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER);
+ return 0;
+ }
+
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL) {
+ return 0;
+ }
+ }
+
+ if (!set_Jprojective_coordinate_GFp(group, &point->X, x, ctx) ||
+ !set_Jprojective_coordinate_GFp(group, &point->Y, y, ctx) ||
+ !BN_copy(&point->Z, &group->one)) {
+ goto err;
+ }
+
+ ret = 1;
+
+err:
+ 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
+ int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0;
+
+ if (b_Z_is_one) {
+ if (!BN_copy(n1, &a->X) || !BN_copy(n2, &a->Y)) {
+ goto end;
+ }
+ // n1 = X_a
+ // n2 = Y_a
+ } else {
+ if (!field_sqr(group, n0, &b->Z, ctx) ||
+ !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) ||
+ !field_mul(group, n2, &a->Y, n0, ctx)) {
+ goto end;
+ }
+ // n2 = Y_a * Z_b^3
+ }
+
+ // n3, n4
+ int a_Z_is_one = BN_cmp(&a->Z, &group->one) == 0;
+ if (a_Z_is_one) {
+ if (!BN_copy(n3, &b->X) || !BN_copy(n4, &b->Y)) {
+ goto end;
+ }
+ // n3 = X_b
+ // n4 = Y_b
+ } else {
+ if (!field_sqr(group, n0, &a->Z, ctx) ||
+ !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) ||
+ !field_mul(group, n4, &b->Y, n0, ctx)) {
+ goto end;
+ }
+ // n4 = Y_b * Z_a^3
+ }
+
+ // n5, n6
+ if (!bn_mod_sub_consttime(n5, n1, n3, p, ctx) ||
+ !bn_mod_sub_consttime(n6, n2, n4, p, ctx)) {
+ 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);
+ ret = 1;
+ goto end;
+ }
+ }
+
+ // 'n7', 'n8'
+ if (!bn_mod_add_consttime(n1, n1, n3, p, ctx) ||
+ !bn_mod_add_consttime(n2, n2, n4, p, ctx)) {
+ 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;
+ }
+ }
+
+ // Z_r = Z_a * Z_b * n5
+
+ // X_r
+ if (!field_sqr(group, n0, n6, ctx) ||
+ !field_sqr(group, n4, n5, ctx) ||
+ !field_mul(group, n3, n1, n4, ctx) ||
+ !bn_mod_sub_consttime(&r->X, n0, n3, p, ctx)) {
+ goto end;
+ }
+ // X_r = n6^2 - n5^2 * 'n7'
+
+ // 'n9'
+ if (!bn_mod_lshift1_consttime(n0, &r->X, p, ctx) ||
+ !bn_mod_sub_consttime(n0, n3, n0, p, ctx)) {
+ goto end;
+ }
+ // n9 = n5^2 * 'n7' - 2 * X_r
+
+ // Y_r
+ if (!field_mul(group, n0, n0, n6, ctx) ||
+ !field_mul(group, n5, n4, n5, ctx)) {
+ goto end; // now n5 is n5^3
+ }
+ if (!field_mul(group, n1, n2, n5, ctx) ||
+ !bn_mod_sub_consttime(n0, n0, n1, p, ctx)) {
+ goto end;
+ }
+ if (BN_is_odd(n0) && !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);
+ }
+ 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);
+ 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 (BN_cmp(&a->Z, &group->one) == 0) {
+ if (!field_sqr(group, n0, &a->X, ctx) ||
+ !bn_mod_lshift1_consttime(n1, n0, p, ctx) ||
+ !bn_mod_add_consttime(n0, n0, n1, p, ctx) ||
+ !bn_mod_add_consttime(n1, n0, &group->a, p, ctx)) {
+ goto err;
+ }
+ // n1 = 3 * X_a^2 + a_curve
+ } else if (group->a_is_minus3) {
+ if (!field_sqr(group, n1, &a->Z, ctx) ||
+ !bn_mod_add_consttime(n0, &a->X, n1, p, ctx) ||
+ !bn_mod_sub_consttime(n2, &a->X, n1, p, ctx) ||
+ !field_mul(group, n1, n0, n2, ctx) ||
+ !bn_mod_lshift1_consttime(n0, n1, p, ctx) ||
+ !bn_mod_add_consttime(n1, n0, n1, p, ctx)) {
+ 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) ||
+ !bn_mod_lshift1_consttime(n1, n0, p, ctx) ||
+ !bn_mod_add_consttime(n0, n0, n1, p, ctx) ||
+ !field_sqr(group, n1, &a->Z, ctx) ||
+ !field_sqr(group, n1, n1, ctx) ||
+ !field_mul(group, n1, n1, &group->a, ctx) ||
+ !bn_mod_add_consttime(n1, n1, n0, p, ctx)) {
+ goto err;
+ }
+ // n1 = 3 * X_a^2 + a_curve * Z_a^4
+ }
+
+ // Z_r
+ if (BN_cmp(&a->Z, &group->one) == 0) {
+ 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_consttime(&r->Z, n0, p, ctx)) {
+ goto err;
+ }
+ // Z_r = 2 * Y_a * Z_a
+
+ // n2
+ if (!field_sqr(group, n3, &a->Y, ctx) ||
+ !field_mul(group, n2, &a->X, n3, ctx) ||
+ !bn_mod_lshift_consttime(n2, n2, 2, p, ctx)) {
+ goto err;
+ }
+ // n2 = 4 * X_a * Y_a^2
+
+ // X_r
+ if (!bn_mod_lshift1_consttime(n0, n2, p, ctx) ||
+ !field_sqr(group, &r->X, n1, ctx) ||
+ !bn_mod_sub_consttime(&r->X, &r->X, n0, p, ctx)) {
+ goto err;
+ }
+ // X_r = n1^2 - 2 * n2
+
+ // n3
+ if (!field_sqr(group, n0, n3, ctx) ||
+ !bn_mod_lshift_consttime(n3, n0, 3, p, ctx)) {
+ goto err;
+ }
+ // n3 = 8 * Y_a^4
+
+ // Y_r
+ if (!bn_mod_sub_consttime(n0, n2, &r->X, p, ctx) ||
+ !field_mul(group, n0, n1, n0, ctx) ||
+ !bn_mod_sub_consttime(&r->Y, n0, n3, p, ctx)) {
+ goto err;
+ }
+ // Y_r = n1 * (n2 - X_r) - n3
+
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ 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 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 = 0;
+
+ 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 0;
+ }
+ }
+
+ 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 (BN_cmp(&point->Z, &group->one) != 0) {
+ if (!field_sqr(group, tmp, &point->Z, ctx) ||
+ !field_sqr(group, Z4, tmp, ctx) ||
+ !field_mul(group, Z6, Z4, tmp, ctx)) {
+ goto err;
+ }
+
+ // rh := (rh + a*Z^4)*X
+ if (group->a_is_minus3) {
+ if (!bn_mod_lshift1_consttime(tmp, Z4, p, ctx) ||
+ !bn_mod_add_consttime(tmp, tmp, Z4, p, ctx) ||
+ !bn_mod_sub_consttime(rh, rh, tmp, p, ctx) ||
+ !field_mul(group, rh, rh, &point->X, ctx)) {
+ goto err;
+ }
+ } else {
+ if (!field_mul(group, tmp, Z4, &group->a, ctx) ||
+ !bn_mod_add_consttime(rh, rh, tmp, p, ctx) ||
+ !field_mul(group, rh, rh, &point->X, ctx)) {
+ goto err;
+ }
+ }
+
+ // rh := rh + b*Z^6
+ if (!field_mul(group, tmp, &group->b, Z6, ctx) ||
+ !bn_mod_add_consttime(rh, rh, tmp, p, ctx)) {
+ goto err;
+ }
+ } else {
+ // rh := (rh + a)*X
+ if (!bn_mod_add_consttime(rh, rh, &group->a, p, ctx) ||
+ !field_mul(group, rh, rh, &point->X, ctx)) {
+ goto err;
+ }
+ // rh := rh + b
+ if (!bn_mod_add_consttime(rh, rh, &group->b, p, ctx)) {
+ 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);
+ 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_GFp_simple_is_at_infinity(group, a)) {
+ return ec_GFp_simple_is_at_infinity(group, b) ? 0 : 1;
+ }
+
+ if (ec_GFp_simple_is_at_infinity(group, b)) {
+ return 1;
+ }
+
+ int a_Z_is_one = BN_cmp(&a->Z, &group->one) == 0;
+ int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0;
+
+ 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) ||
+ !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) ||
+ !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) ||
+ !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) ||
+ !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);
+ 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 (BN_cmp(&point->Z, &group->one) == 0 ||
+ 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) ||
+ !EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
+ goto err;
+ }
+ if (BN_cmp(&point->Z, &group->one) != 0) {
+ OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ 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;
+ 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;
+ }
+ OPENSSL_memset(prod_Z, 0, num * sizeof(prod_Z[0]));
+ for (size_t 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 (BN_copy(prod_Z[0], &group->one) == NULL) {
+ goto err;
+ }
+ }
+
+ for (size_t 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. We use |BN_mod_inverse_odd| instead of doing a constant-
+ // time inversion using Fermat's Little Theorem because this function is
+ // usually only used for converting multiples of a public key point to
+ // affine, and a public key point isn't secret. If we were to use Fermat's
+ // Little Theorem then the cost of the inversion would usually be so high
+ // that converting the multiples to affine would be counterproductive.
+ int no_inverse;
+ if (!BN_mod_inverse_odd(tmp, &no_inverse, prod_Z[num - 1], &group->field,
+ ctx)) {
+ OPENSSL_PUT_ERROR(EC, 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 (size_t 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 (size_t 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 (BN_copy(&p->Z, &group->one) == NULL) {
+ goto err;
+ }
+ }
+ }
+
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ if (prod_Z != NULL) {
+ for (size_t 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);
+}
git://repos.xcallymotion.com / motion2.git / blobdiff