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-rw-r--r--lib/libcrypto/ec/ecp_methods.c1656
1 files changed, 1656 insertions, 0 deletions
diff --git a/lib/libcrypto/ec/ecp_methods.c b/lib/libcrypto/ec/ecp_methods.c
new file mode 100644
index 00000000000..3dc7091850a
--- /dev/null
+++ b/lib/libcrypto/ec/ecp_methods.c
@@ -0,0 +1,1656 @@
+/* $OpenBSD: ecp_methods.c,v 1.1 2024/11/12 10:25:16 tb Exp $ */
+/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
+ * for the OpenSSL project.
+ * Includes code written by Bodo Moeller for the OpenSSL project.
+*/
+/* ====================================================================
+ * Copyright (c) 1998-2002 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 this software developed by SUN MICROSYSTEMS, INC.,
+ * and contributed to the OpenSSL project.
+ */
+
+#include <stdlib.h>
+
+#include <openssl/bn.h>
+#include <openssl/ec.h>
+#include <openssl/err.h>
+#include <openssl/objects.h>
+
+#include "bn_local.h"
+#include "ec_local.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 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);
+}
+
+int
+ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+{
+ if (!bn_copy(&dest->field, &src->field))
+ return 0;
+ if (!bn_copy(&dest->a, &src->a))
+ return 0;
+ if (!bn_copy(&dest->b, &src->b))
+ return 0;
+
+ dest->a_is_minus3 = src->a_is_minus3;
+
+ return 1;
+}
+
+static int
+ec_decode_scalar(const EC_GROUP *group, BIGNUM *bn, const BIGNUM *x, BN_CTX *ctx)
+{
+ if (bn == NULL)
+ return 1;
+
+ if (group->meth->field_decode != NULL)
+ return group->meth->field_decode(group, bn, x, ctx);
+
+ return bn_copy(bn, x);
+}
+
+static int
+ec_encode_scalar(const EC_GROUP *group, BIGNUM *bn, const BIGNUM *x, BN_CTX *ctx)
+{
+ if (!BN_nnmod(bn, x, &group->field, ctx))
+ return 0;
+
+ if (group->meth->field_encode != NULL)
+ return group->meth->field_encode(group, bn, bn, ctx);
+
+ return 1;
+}
+
+static int
+ec_encode_z_coordinate(const EC_GROUP *group, BIGNUM *bn, int *is_one,
+ const BIGNUM *z, BN_CTX *ctx)
+{
+ if (!BN_nnmod(bn, z, &group->field, ctx))
+ return 0;
+
+ *is_one = BN_is_one(bn);
+ if (*is_one && group->meth->field_set_to_one != NULL)
+ return group->meth->field_set_to_one(group, bn, ctx);
+
+ if (group->meth->field_encode != NULL)
+ return group->meth->field_encode(group, bn, bn, ctx);
+
+ return 1;
+}
+
+int
+ec_GFp_simple_group_set_curve(EC_GROUP *group,
+ const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+{
+ BIGNUM *a_plus_3;
+ int ret = 0;
+
+ /* p must be a prime > 3 */
+ if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
+ ECerror(EC_R_INVALID_FIELD);
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+
+ if ((a_plus_3 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ if (!bn_copy(&group->field, p))
+ goto err;
+ BN_set_negative(&group->field, 0);
+
+ if (!ec_encode_scalar(group, &group->a, a, ctx))
+ goto err;
+ if (!ec_encode_scalar(group, &group->b, b, ctx))
+ goto err;
+
+ if (!BN_set_word(a_plus_3, 3))
+ goto err;
+ if (!BN_mod_add(a_plus_3, a_plus_3, a, &group->field, ctx))
+ goto err;
+
+ group->a_is_minus3 = BN_is_zero(a_plus_3);
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+
+ return ret;
+}
+
+int
+ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
+ BIGNUM *b, BN_CTX *ctx)
+{
+ if (p != NULL) {
+ if (!bn_copy(p, &group->field))
+ return 0;
+ }
+ if (!ec_decode_scalar(group, a, &group->a, ctx))
+ return 0;
+ if (!ec_decode_scalar(group, b, &group->b, ctx))
+ return 0;
+
+ return 1;
+}
+
+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)
+{
+ BIGNUM *p, *a, *b, *discriminant;
+ int ret = 0;
+
+ BN_CTX_start(ctx);
+
+ if ((p = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((a = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((b = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((discriminant = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ if (!EC_GROUP_get_curve(group, p, a, b, ctx))
+ goto err;
+
+ /*
+ * Check that the discriminant 4a^3 + 27b^2 is non-zero modulo p.
+ */
+
+ if (BN_is_zero(a) && BN_is_zero(b))
+ goto err;
+ if (BN_is_zero(a) || BN_is_zero(b))
+ goto done;
+
+ /* Compute the discriminant: first 4a^3, then 27b^2, then their sum. */
+ if (!BN_mod_sqr(discriminant, a, p, ctx))
+ goto err;
+ if (!BN_mod_mul(discriminant, discriminant, a, p, ctx))
+ goto err;
+ if (!BN_lshift(discriminant, discriminant, 2))
+ goto err;
+
+ if (!BN_mod_sqr(b, b, p, ctx))
+ goto err;
+ if (!BN_mul_word(b, 27))
+ goto err;
+
+ if (!BN_mod_add(discriminant, discriminant, b, p, ctx))
+ goto err;
+
+ if (BN_is_zero(discriminant))
+ goto err;
+
+ done:
+ ret = 1;
+
+ err:
+ BN_CTX_end(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);
+ 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(const EC_GROUP *group,
+ EC_POINT *point, const BIGNUM *x, const BIGNUM *y, const BIGNUM *z,
+ BN_CTX *ctx)
+{
+ int ret = 0;
+
+ /*
+ * Setting individual coordinates allows the creation of bad points.
+ * EC_POINT_set_Jprojective_coordinates() checks at the API boundary.
+ */
+
+ if (x != NULL) {
+ if (!ec_encode_scalar(group, &point->X, x, ctx))
+ goto err;
+ }
+ if (y != NULL) {
+ if (!ec_encode_scalar(group, &point->Y, y, ctx))
+ goto err;
+ }
+ if (z != NULL) {
+ if (!ec_encode_z_coordinate(group, &point->Z, &point->Z_is_one,
+ z, ctx))
+ goto err;
+ }
+
+ ret = 1;
+
+ err:
+ return ret;
+}
+
+int
+ec_GFp_simple_get_Jprojective_coordinates(const EC_GROUP *group,
+ const EC_POINT *point, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
+{
+ int ret = 0;
+
+ if (!ec_decode_scalar(group, x, &point->X, ctx))
+ goto err;
+ if (!ec_decode_scalar(group, y, &point->Y, ctx))
+ goto err;
+ if (!ec_decode_scalar(group, z, &point->Z, ctx))
+ goto err;
+
+ ret = 1;
+
+ err:
+ 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 */
+ ECerror(ERR_R_PASSED_NULL_PARAMETER);
+ return 0;
+ }
+ return EC_POINT_set_Jprojective_coordinates(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)
+{
+ BIGNUM *z, *Z, *Z_1, *Z_2, *Z_3;
+ int ret = 0;
+
+ BN_CTX_start(ctx);
+
+ if ((z = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((Z = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((Z_1 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((Z_2 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((Z_3 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ /* Convert from projective coordinates (X, Y, Z) into (X/Z^2, Y/Z^3). */
+
+ if (!ec_decode_scalar(group, z, &point->Z, ctx))
+ goto err;
+
+ if (BN_is_one(z)) {
+ if (!ec_decode_scalar(group, x, &point->X, ctx))
+ goto err;
+ if (!ec_decode_scalar(group, y, &point->Y, ctx))
+ goto err;
+ goto done;
+ }
+
+ if (BN_mod_inverse_ct(Z_1, z, &group->field, ctx) == NULL) {
+ ECerror(ERR_R_BN_LIB);
+ goto err;
+ }
+ if (group->meth->field_encode == NULL) {
+ /* 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 == NULL) {
+ /* 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;
+ }
+
+ done:
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+
+ return ret;
+}
+
+int
+ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group,
+ EC_POINT *point, const BIGNUM *in_x, int y_bit, BN_CTX *ctx)
+{
+ const BIGNUM *p = &group->field, *a = &group->a, *b = &group->b;
+ BIGNUM *w, *x, *y;
+ int ret = 0;
+
+ y_bit = (y_bit != 0);
+
+ BN_CTX_start(ctx);
+
+ if ((w = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((x = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((y = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ /*
+ * Weierstrass equation: y^2 = x^3 + ax + b, so y is one of the
+ * square roots of x^3 + ax + b. The y-bit indicates which one.
+ */
+
+ /* XXX - should we not insist on 0 <= x < p instead? */
+ if (!BN_nnmod(x, in_x, p, ctx))
+ goto err;
+
+ if (group->meth->field_encode != NULL) {
+ if (!group->meth->field_encode(group, x, x, ctx))
+ goto err;
+ }
+
+ /* y = x^3 */
+ if (!group->meth->field_sqr(group, y, x, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, y, y, x, ctx))
+ goto err;
+
+ /* y += ax */
+ if (group->a_is_minus3) {
+ if (!BN_mod_lshift1_quick(w, x, p))
+ goto err;
+ if (!BN_mod_add_quick(w, w, x, p))
+ goto err;
+ if (!BN_mod_sub_quick(y, y, w, p))
+ goto err;
+ } else {
+ if (!group->meth->field_mul(group, w, a, x, ctx))
+ goto err;
+ if (!BN_mod_add_quick(y, y, w, p))
+ goto err;
+ }
+
+ /* y += b */
+ if (!BN_mod_add_quick(y, y, b, p))
+ goto err;
+
+ if (group->meth->field_decode != NULL) {
+ if (!group->meth->field_decode(group, x, x, ctx))
+ goto err;
+ if (!group->meth->field_decode(group, y, y, ctx))
+ goto err;
+ }
+
+ if (!BN_mod_sqrt(y, y, p, ctx)) {
+ ECerror(EC_R_INVALID_COMPRESSED_POINT);
+ goto err;
+ }
+
+ if (y_bit == BN_is_odd(y))
+ goto done;
+
+ if (BN_is_zero(y)) {
+ ECerror(EC_R_INVALID_COMPRESSION_BIT);
+ goto err;
+ }
+ if (!BN_usub(y, &group->field, y))
+ goto err;
+
+ if (y_bit != BN_is_odd(y)) {
+ /* Can only happen if p is even and should not be reachable. */
+ ECerror(ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ done:
+ if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
+ goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(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 *);
+ BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
+ const BIGNUM *p;
+ 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;
+
+ BN_CTX_start(ctx);
+
+ if ((n0 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((n1 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((n2 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((n3 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((n4 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((n5 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((n6 = BN_CTX_get(ctx)) == 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:
+ BN_CTX_end(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;
+ BIGNUM *n0, *n1, *n2, *n3;
+ int ret = 0;
+
+ if (EC_POINT_is_at_infinity(group, a))
+ return EC_POINT_set_to_infinity(group, r);
+
+ field_mul = group->meth->field_mul;
+ field_sqr = group->meth->field_sqr;
+ p = &group->field;
+
+ BN_CTX_start(ctx);
+
+ if ((n0 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((n1 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((n2 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((n3 = BN_CTX_get(ctx)) == 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);
+
+ 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;
+ 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;
+
+ BN_CTX_start(ctx);
+
+ if ((rh = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((tmp = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((Z4 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((Z6 = BN_CTX_get(ctx)) == 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);
+
+ 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 *);
+ 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);
+
+ 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;
+
+ BN_CTX_start(ctx);
+
+ if ((tmp1 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((tmp2 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((Za23 = BN_CTX_get(ctx)) == NULL)
+ goto end;
+ if ((Zb23 = BN_CTX_get(ctx)) == 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);
+
+ return ret;
+}
+
+int
+ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+{
+ BIGNUM *x, *y;
+ int ret = 0;
+
+ if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
+ return 1;
+
+ BN_CTX_start(ctx);
+
+ if ((x = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((y = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
+ goto err;
+ if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
+ goto err;
+ if (!point->Z_is_one) {
+ ECerror(ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+
+ return ret;
+}
+
+int
+ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
+{
+ BIGNUM *tmp0, *tmp1;
+ size_t pow2 = 0;
+ BIGNUM **heap = NULL;
+ size_t i;
+ int ret = 0;
+
+ if (num == 0)
+ return 1;
+
+ BN_CTX_start(ctx);
+
+ if ((tmp0 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((tmp1 = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ /*
+ * Before converting the individual points, compute inverses of all Z
+ * values. Modular inversion is rather slow, but luckily we can do
+ * with a single explicit inversion, plus about 3 multiplications per
+ * input value.
+ */
+
+ pow2 = 1;
+ while (num > pow2)
+ pow2 <<= 1;
+ /*
+ * Now pow2 is the smallest power of 2 satifsying pow2 >= num. We
+ * need twice that.
+ */
+ pow2 <<= 1;
+
+ heap = reallocarray(NULL, pow2, sizeof heap[0]);
+ if (heap == NULL)
+ goto err;
+
+ /*
+ * The array is used as a binary tree, exactly as in heapsort:
+ *
+ * heap[1] heap[2] heap[3] heap[4] heap[5]
+ * heap[6] heap[7] heap[8]heap[9] heap[10]heap[11]
+ * heap[12]heap[13] heap[14] heap[15]
+ *
+ * We put the Z's in the last line; then we set each other node to the
+ * product of its two child-nodes (where empty or 0 entries are
+ * treated as ones); then we invert heap[1]; then we invert each
+ * other node by replacing it by the product of its parent (after
+ * inversion) and its sibling (before inversion).
+ */
+ heap[0] = NULL;
+ for (i = pow2 / 2 - 1; i > 0; i--)
+ heap[i] = NULL;
+ for (i = 0; i < num; i++)
+ heap[pow2 / 2 + i] = &points[i]->Z;
+ for (i = pow2 / 2 + num; i < pow2; i++)
+ heap[i] = NULL;
+
+ /* set each node to the product of its children */
+ for (i = pow2 / 2 - 1; i > 0; i--) {
+ heap[i] = BN_new();
+ if (heap[i] == NULL)
+ goto err;
+
+ if (heap[2 * i] != NULL) {
+ if ((heap[2 * i + 1] == NULL) || BN_is_zero(heap[2 * i + 1])) {
+ if (!bn_copy(heap[i], heap[2 * i]))
+ goto err;
+ } else {
+ if (BN_is_zero(heap[2 * i])) {
+ if (!bn_copy(heap[i], heap[2 * i + 1]))
+ goto err;
+ } else {
+ if (!group->meth->field_mul(group, heap[i],
+ heap[2 * i], heap[2 * i + 1], ctx))
+ goto err;
+ }
+ }
+ }
+ }
+
+ /* invert heap[1] */
+ if (!BN_is_zero(heap[1])) {
+ if (BN_mod_inverse_ct(heap[1], heap[1], &group->field, ctx) == NULL) {
+ ECerror(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 have need to multiply by the Montgomery
+ * factor twice
+ */
+ if (!group->meth->field_encode(group, heap[1], heap[1], ctx))
+ goto err;
+ if (!group->meth->field_encode(group, heap[1], heap[1], ctx))
+ goto err;
+ }
+ /* set other heap[i]'s to their inverses */
+ for (i = 2; i < pow2 / 2 + num; i += 2) {
+ /* i is even */
+ if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) {
+ if (!group->meth->field_mul(group, tmp0, heap[i / 2], heap[i + 1], ctx))
+ goto err;
+ if (!group->meth->field_mul(group, tmp1, heap[i / 2], heap[i], ctx))
+ goto err;
+ if (!bn_copy(heap[i], tmp0))
+ goto err;
+ if (!bn_copy(heap[i + 1], tmp1))
+ goto err;
+ } else {
+ if (!bn_copy(heap[i], heap[i / 2]))
+ goto err;
+ }
+ }
+
+ /*
+ * we have replaced all non-zero Z's by their inverses, now fix up
+ * all the 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, tmp1, &p->Z, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx))
+ goto err;
+
+ if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, 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 (heap != NULL) {
+ /*
+ * heap[pow2/2] .. heap[pow2-1] have not been allocated
+ * locally!
+ */
+ for (i = pow2 / 2 - 1; i > 0; i--) {
+ BN_free(heap[i]);
+ }
+ free(heap);
+ }
+ 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);
+}
+
+/*
+ * Apply randomization of EC point projective coordinates:
+ *
+ * (X, Y, Z) = (lambda^2 * X, lambda^3 * Y, lambda * Z)
+ *
+ * where lambda is in the interval [1, group->field).
+ */
+int
+ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx)
+{
+ BIGNUM *lambda = NULL;
+ BIGNUM *tmp = NULL;
+ int ret = 0;
+
+ BN_CTX_start(ctx);
+ if ((lambda = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((tmp = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ /* Generate lambda in [1, group->field). */
+ if (!bn_rand_interval(lambda, 1, &group->field))
+ goto err;
+
+ if (group->meth->field_encode != NULL &&
+ !group->meth->field_encode(group, lambda, lambda, ctx))
+ goto err;
+
+ /* Z = lambda * Z */
+ if (!group->meth->field_mul(group, &p->Z, lambda, &p->Z, ctx))
+ goto err;
+
+ /* tmp = lambda^2 */
+ if (!group->meth->field_sqr(group, tmp, lambda, ctx))
+ goto err;
+
+ /* X = lambda^2 * X */
+ if (!group->meth->field_mul(group, &p->X, tmp, &p->X, ctx))
+ goto err;
+
+ /* tmp = lambda^3 */
+ if (!group->meth->field_mul(group, tmp, tmp, lambda, ctx))
+ goto err;
+
+ /* Y = lambda^3 * Y */
+ if (!group->meth->field_mul(group, &p->Y, tmp, &p->Y, ctx))
+ goto err;
+
+ /* Disable optimized arithmetics after replacing Z by lambda * Z. */
+ p->Z_is_one = 0;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+#define EC_POINT_BN_set_flags(P, flags) do { \
+ BN_set_flags(&(P)->X, (flags)); \
+ BN_set_flags(&(P)->Y, (flags)); \
+ BN_set_flags(&(P)->Z, (flags)); \
+} while(0)
+
+#define EC_POINT_CSWAP(c, a, b, w, t) do { \
+ if (!BN_swap_ct(c, &(a)->X, &(b)->X, w) || \
+ !BN_swap_ct(c, &(a)->Y, &(b)->Y, w) || \
+ !BN_swap_ct(c, &(a)->Z, &(b)->Z, w)) \
+ goto err; \
+ t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
+ (a)->Z_is_one ^= (t); \
+ (b)->Z_is_one ^= (t); \
+} while(0)
+
+/*
+ * This function computes (in constant time) a point multiplication over the
+ * EC group.
+ *
+ * At a high level, it is Montgomery ladder with conditional swaps.
+ *
+ * It performs either a fixed point multiplication
+ * (scalar * generator)
+ * when point is NULL, or a variable point multiplication
+ * (scalar * point)
+ * when point is not NULL.
+ *
+ * scalar should be in the range [0,n) otherwise all constant time bets are off.
+ *
+ * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
+ * which of course are not constant time themselves.
+ *
+ * The product is stored in r.
+ *
+ * Returns 1 on success, 0 otherwise.
+ */
+static int
+ec_GFp_simple_mul_ct(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ const EC_POINT *point, BN_CTX *ctx)
+{
+ int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
+ EC_POINT *s = NULL;
+ BIGNUM *k = NULL;
+ BIGNUM *lambda = NULL;
+ BIGNUM *cardinality = NULL;
+ int ret = 0;
+
+ BN_CTX_start(ctx);
+
+ if ((s = EC_POINT_new(group)) == NULL)
+ goto err;
+
+ if (point == NULL) {
+ if (!EC_POINT_copy(s, group->generator))
+ goto err;
+ } else {
+ if (!EC_POINT_copy(s, point))
+ goto err;
+ }
+
+ EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
+
+ if ((cardinality = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((lambda = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((k = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if (!BN_mul(cardinality, &group->order, &group->cofactor, ctx))
+ goto err;
+
+ /*
+ * Group cardinalities are often on a word boundary.
+ * So when we pad the scalar, some timing diff might
+ * pop if it needs to be expanded due to carries.
+ * So expand ahead of time.
+ */
+ cardinality_bits = BN_num_bits(cardinality);
+ group_top = cardinality->top;
+ if (!bn_wexpand(k, group_top + 2) ||
+ !bn_wexpand(lambda, group_top + 2))
+ goto err;
+
+ if (!bn_copy(k, scalar))
+ goto err;
+
+ BN_set_flags(k, BN_FLG_CONSTTIME);
+
+ if (BN_num_bits(k) > cardinality_bits || BN_is_negative(k)) {
+ /*
+ * This is an unusual input, and we don't guarantee
+ * constant-timeness
+ */
+ if (!BN_nnmod(k, k, cardinality, ctx))
+ goto err;
+ }
+
+ if (!BN_add(lambda, k, cardinality))
+ goto err;
+ BN_set_flags(lambda, BN_FLG_CONSTTIME);
+ if (!BN_add(k, lambda, cardinality))
+ goto err;
+ /*
+ * lambda := scalar + cardinality
+ * k := scalar + 2*cardinality
+ */
+ kbit = BN_is_bit_set(lambda, cardinality_bits);
+ if (!BN_swap_ct(kbit, k, lambda, group_top + 2))
+ goto err;
+
+ group_top = group->field.top;
+ if (!bn_wexpand(&s->X, group_top) ||
+ !bn_wexpand(&s->Y, group_top) ||
+ !bn_wexpand(&s->Z, group_top) ||
+ !bn_wexpand(&r->X, group_top) ||
+ !bn_wexpand(&r->Y, group_top) ||
+ !bn_wexpand(&r->Z, group_top))
+ goto err;
+
+ /*
+ * Apply coordinate blinding for EC_POINT if the underlying EC_METHOD
+ * implements it.
+ */
+ if (!ec_point_blind_coordinates(group, s, ctx))
+ goto err;
+
+ /* top bit is a 1, in a fixed pos */
+ if (!EC_POINT_copy(r, s))
+ goto err;
+
+ EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
+
+ if (!EC_POINT_dbl(group, s, s, ctx))
+ goto err;
+
+ pbit = 0;
+
+ /*
+ * The ladder step, with branches, is
+ *
+ * k[i] == 0: S = add(R, S), R = dbl(R)
+ * k[i] == 1: R = add(S, R), S = dbl(S)
+ *
+ * Swapping R, S conditionally on k[i] leaves you with state
+ *
+ * k[i] == 0: T, U = R, S
+ * k[i] == 1: T, U = S, R
+ *
+ * Then perform the ECC ops.
+ *
+ * U = add(T, U)
+ * T = dbl(T)
+ *
+ * Which leaves you with state
+ *
+ * k[i] == 0: U = add(R, S), T = dbl(R)
+ * k[i] == 1: U = add(S, R), T = dbl(S)
+ *
+ * Swapping T, U conditionally on k[i] leaves you with state
+ *
+ * k[i] == 0: R, S = T, U
+ * k[i] == 1: R, S = U, T
+ *
+ * Which leaves you with state
+ *
+ * k[i] == 0: S = add(R, S), R = dbl(R)
+ * k[i] == 1: R = add(S, R), S = dbl(S)
+ *
+ * So we get the same logic, but instead of a branch it's a
+ * conditional swap, followed by ECC ops, then another conditional swap.
+ *
+ * Optimization: The end of iteration i and start of i-1 looks like
+ *
+ * ...
+ * CSWAP(k[i], R, S)
+ * ECC
+ * CSWAP(k[i], R, S)
+ * (next iteration)
+ * CSWAP(k[i-1], R, S)
+ * ECC
+ * CSWAP(k[i-1], R, S)
+ * ...
+ *
+ * So instead of two contiguous swaps, you can merge the condition
+ * bits and do a single swap.
+ *
+ * k[i] k[i-1] Outcome
+ * 0 0 No Swap
+ * 0 1 Swap
+ * 1 0 Swap
+ * 1 1 No Swap
+ *
+ * This is XOR. pbit tracks the previous bit of k.
+ */
+
+ for (i = cardinality_bits - 1; i >= 0; i--) {
+ kbit = BN_is_bit_set(k, i) ^ pbit;
+ EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
+ if (!EC_POINT_add(group, s, r, s, ctx))
+ goto err;
+ if (!EC_POINT_dbl(group, r, r, ctx))
+ goto err;
+ /*
+ * pbit logic merges this cswap with that of the
+ * next iteration
+ */
+ pbit ^= kbit;
+ }
+ /* one final cswap to move the right value into r */
+ EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
+
+ ret = 1;
+
+ err:
+ EC_POINT_free(s);
+ BN_CTX_end(ctx);
+
+ return ret;
+}
+
+#undef EC_POINT_BN_set_flags
+#undef EC_POINT_CSWAP
+
+int
+ec_GFp_simple_mul_generator_ct(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *scalar, BN_CTX *ctx)
+{
+ return ec_GFp_simple_mul_ct(group, r, scalar, NULL, ctx);
+}
+
+int
+ec_GFp_simple_mul_single_ct(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx)
+{
+ return ec_GFp_simple_mul_ct(group, r, scalar, point, ctx);
+}
+
+int
+ec_GFp_simple_mul_double_nonct(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *g_scalar, const BIGNUM *p_scalar, const EC_POINT *point,
+ BN_CTX *ctx)
+{
+ return ec_wNAF_mul(group, r, g_scalar, 1, &point, &p_scalar, ctx);
+}
+
+static const EC_METHOD ec_GFp_simple_method = {
+ .field_type = NID_X9_62_prime_field,
+ .group_init = ec_GFp_simple_group_init,
+ .group_finish = ec_GFp_simple_group_finish,
+ .group_copy = ec_GFp_simple_group_copy,
+ .group_set_curve = ec_GFp_simple_group_set_curve,
+ .group_get_curve = ec_GFp_simple_group_get_curve,
+ .group_get_degree = ec_GFp_simple_group_get_degree,
+ .group_order_bits = ec_group_simple_order_bits,
+ .group_check_discriminant = ec_GFp_simple_group_check_discriminant,
+ .point_init = ec_GFp_simple_point_init,
+ .point_finish = ec_GFp_simple_point_finish,
+ .point_copy = ec_GFp_simple_point_copy,
+ .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity,
+ .point_set_Jprojective_coordinates =
+ ec_GFp_simple_set_Jprojective_coordinates,
+ .point_get_Jprojective_coordinates =
+ ec_GFp_simple_get_Jprojective_coordinates,
+ .point_set_affine_coordinates =
+ ec_GFp_simple_point_set_affine_coordinates,
+ .point_get_affine_coordinates =
+ ec_GFp_simple_point_get_affine_coordinates,
+ .point_set_compressed_coordinates =
+ ec_GFp_simple_set_compressed_coordinates,
+ .add = ec_GFp_simple_add,
+ .dbl = ec_GFp_simple_dbl,
+ .invert = ec_GFp_simple_invert,
+ .is_at_infinity = ec_GFp_simple_is_at_infinity,
+ .is_on_curve = ec_GFp_simple_is_on_curve,
+ .point_cmp = ec_GFp_simple_cmp,
+ .make_affine = ec_GFp_simple_make_affine,
+ .points_make_affine = ec_GFp_simple_points_make_affine,
+ .mul_generator_ct = ec_GFp_simple_mul_generator_ct,
+ .mul_single_ct = ec_GFp_simple_mul_single_ct,
+ .mul_double_nonct = ec_GFp_simple_mul_double_nonct,
+ .field_mul = ec_GFp_simple_field_mul,
+ .field_sqr = ec_GFp_simple_field_sqr,
+ .blind_coordinates = ec_GFp_simple_blind_coordinates,
+};
+
+const EC_METHOD *
+EC_GFp_simple_method(void)
+{
+ return &ec_GFp_simple_method;
+}
+LCRYPTO_ALIAS(EC_GFp_simple_method);
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-25 12:43:34 +0000