-/* crypto/ec/ecp_smpl.c */
/*
- * 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 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
*
+ * Licensed under the Apache License 2.0 (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
*/
-/* ====================================================================
- * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
- * Portions of this software developed by SUN MICROSYSTEMS, INC.,
- * and contributed to the OpenSSL project.
+
+/*
+ * ECDSA low level APIs are deprecated for public use, but still ok for
+ * internal use.
*/
+#include "internal/deprecated.h"
#include <openssl/err.h>
#include <openssl/symhacks.h>
-#include "ec_lcl.h"
+#include "ec_local.h"
const EC_METHOD *EC_GFp_simple_method(void)
{
ec_GFp_simple_group_set_curve,
ec_GFp_simple_group_get_curve,
ec_GFp_simple_group_get_degree,
+ ec_group_simple_order_bits,
ec_GFp_simple_group_check_discriminant,
ec_GFp_simple_point_init,
ec_GFp_simple_point_finish,
ec_GFp_simple_field_mul,
ec_GFp_simple_field_sqr,
0 /* field_div */ ,
+ ec_GFp_simple_field_inv,
0 /* field_encode */ ,
0 /* field_decode */ ,
- 0 /* field_set_to_one */
+ 0, /* field_set_to_one */
+ ec_key_simple_priv2oct,
+ ec_key_simple_oct2priv,
+ 0, /* set private */
+ ec_key_simple_generate_key,
+ ec_key_simple_check_key,
+ ec_key_simple_generate_public_key,
+ 0, /* keycopy */
+ 0, /* keyfinish */
+ ecdh_simple_compute_key,
+ ecdsa_simple_sign_setup,
+ ecdsa_simple_sign_sig,
+ ecdsa_simple_verify_sig,
+ 0, /* field_inverse_mod_ord */
+ ec_GFp_simple_blind_coordinates,
+ ec_GFp_simple_ladder_pre,
+ ec_GFp_simple_ladder_step,
+ ec_GFp_simple_ladder_post
};
return &ret;
group->field = BN_new();
group->a = BN_new();
group->b = BN_new();
- if (!group->field || !group->a || !group->b) {
- if (!group->field)
- BN_free(group->field);
- if (!group->a)
- BN_free(group->a);
- if (!group->b)
- BN_free(group->b);
+ if (group->field == NULL || group->a == NULL || group->b == NULL) {
+ BN_free(group->field);
+ BN_free(group->a);
+ BN_free(group->b);
return 0;
}
group->a_is_minus3 = 0;
}
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
err:
BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
if (a != NULL || b != NULL) {
if (group->meth->field_decode) {
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
ret = 1;
err:
- if (new_ctx)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
BN_CTX *new_ctx = NULL;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL) {
ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
ERR_R_MALLOC_FAILURE);
ret = 1;
err:
- if (ctx != NULL)
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
point->Z = BN_new();
point->Z_is_one = 0;
- if (!point->X || !point->Y || !point->Z) {
- if (point->X)
- BN_free(point->X);
- if (point->Y)
- BN_free(point->Y);
- if (point->Z)
- BN_free(point->Z);
+ if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
+ BN_free(point->X);
+ BN_free(point->Y);
+ BN_free(point->Z);
return 0;
}
return 1;
if (!BN_copy(dest->Z, src->Z))
return 0;
dest->Z_is_one = src->Z_is_one;
+ dest->curve_name = src->curve_name;
return 1;
}
int ret = 0;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
ret = 1;
err:
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
if (group->meth->field_decode != 0) {
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
ret = 1;
err:
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
}
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
}
}
} else {
- if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
+ if (!group->meth->field_inv(group, Z_1, Z_, ctx)) {
ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
ERR_R_BN_LIB);
goto err;
err:
BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
p = group->field;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
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);
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
p = group->field;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
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
- */
+ /*-
+ * 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;
err:
BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
p = group->field;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return -1;
}
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'.
- */
+ /*-
+ * 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))
err:
BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_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
- */
+ /*-
+ * 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 *);
field_sqr = group->meth->field_sqr;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return -1;
}
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).
- */
+ /*-
+ * 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))
end:
BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
return 1;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
if (ctx == NULL)
return 0;
}
if (y == NULL)
goto err;
- if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
+ if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
goto err;
- if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
+ if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
goto err;
if (!point->Z_is_one) {
ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
err:
BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
return ret;
}
return 1;
if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
+ ctx = new_ctx = BN_CTX_new_ex(group->libctx);
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)
+ if (tmp_Z == NULL)
goto err;
- prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
+ prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
if (prod_Z == NULL)
goto err;
for (i = 0; i < num; i++) {
* points[i]->Z by its inverse.
*/
- if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
+ if (!group->meth->field_inv(group, tmp, prod_Z[num - 1], ctx)) {
ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
goto err;
}
err:
BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
+ BN_CTX_free(new_ctx);
if (prod_Z != NULL) {
for (i = 0; i < num; i++) {
if (prod_Z[i] == NULL)
{
return BN_mod_sqr(r, a, group->field, ctx);
}
+
+/*-
+ * Computes the multiplicative inverse of a in GF(p), storing the result in r.
+ * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
+ * Since we don't have a Mont structure here, SCA hardening is with blinding.
+ * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.)
+ */
+int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
+ BN_CTX *ctx)
+{
+ BIGNUM *e = NULL;
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL
+ && (ctx = new_ctx = BN_CTX_secure_new_ex(group->libctx)) == NULL)
+ return 0;
+
+ BN_CTX_start(ctx);
+ if ((e = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ do {
+ if (!BN_priv_rand_range_ex(e, group->field, ctx))
+ goto err;
+ } while (BN_is_zero(e));
+
+ /* r := a * e */
+ if (!group->meth->field_mul(group, r, a, e, ctx))
+ goto err;
+ /* r := 1/(a * e) */
+ if (!BN_mod_inverse(r, r, group->field, ctx)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
+ goto err;
+ }
+ /* r := e/(a * e) = 1/a */
+ if (!group->meth->field_mul(group, r, r, e, ctx))
+ goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+/*-
+ * Apply randomization of EC point projective coordinates:
+ *
+ * (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z)
+ * lambda = [1,group->field)
+ *
+ */
+int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
+ BN_CTX *ctx)
+{
+ int ret = 0;
+ BIGNUM *lambda = NULL;
+ BIGNUM *temp = NULL;
+
+ BN_CTX_start(ctx);
+ lambda = BN_CTX_get(ctx);
+ temp = BN_CTX_get(ctx);
+ if (temp == NULL) {
+ ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE);
+ goto end;
+ }
+
+ /*-
+ * Make sure lambda is not zero.
+ * If the RNG fails, we cannot blind but nevertheless want
+ * code to continue smoothly and not clobber the error stack.
+ */
+ do {
+ ERR_set_mark();
+ ret = BN_priv_rand_range_ex(lambda, group->field, ctx);
+ ERR_pop_to_mark();
+ if (ret == 0) {
+ ret = 1;
+ goto end;
+ }
+ } while (BN_is_zero(lambda));
+
+ /* if field_encode defined convert between representations */
+ if ((group->meth->field_encode != NULL
+ && !group->meth->field_encode(group, lambda, lambda, ctx))
+ || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx)
+ || !group->meth->field_sqr(group, temp, lambda, ctx)
+ || !group->meth->field_mul(group, p->X, p->X, temp, ctx)
+ || !group->meth->field_mul(group, temp, temp, lambda, ctx)
+ || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
+ goto end;
+
+ p->Z_is_one = 0;
+ ret = 1;
+
+ end:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*-
+ * Input:
+ * - p: affine coordinates
+ *
+ * Output:
+ * - s := p, r := 2p: blinded projective (homogeneous) coordinates
+ *
+ * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
+ * multiplication resistant against side channel attacks" appendix, described at
+ * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
+ * simplified for Z1=1.
+ *
+ * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z)
+ * for any non-zero \lambda that holds for projective (homogeneous) coords.
+ */
+int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
+ EC_POINT *r, EC_POINT *s,
+ EC_POINT *p, BN_CTX *ctx)
+{
+ BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL;
+
+ t1 = s->Z;
+ t2 = r->Z;
+ t3 = s->X;
+ t4 = r->X;
+ t5 = s->Y;
+
+ if (!p->Z_is_one /* r := 2p */
+ || !group->meth->field_sqr(group, t3, p->X, ctx)
+ || !BN_mod_sub_quick(t4, t3, group->a, group->field)
+ || !group->meth->field_sqr(group, t4, t4, ctx)
+ || !group->meth->field_mul(group, t5, p->X, group->b, ctx)
+ || !BN_mod_lshift_quick(t5, t5, 3, group->field)
+ /* r->X coord output */
+ || !BN_mod_sub_quick(r->X, t4, t5, group->field)
+ || !BN_mod_add_quick(t1, t3, group->a, group->field)
+ || !group->meth->field_mul(group, t2, p->X, t1, ctx)
+ || !BN_mod_add_quick(t2, group->b, t2, group->field)
+ /* r->Z coord output */
+ || !BN_mod_lshift_quick(r->Z, t2, 2, group->field))
+ return 0;
+
+ /* make sure lambda (r->Y here for storage) is not zero */
+ do {
+ if (!BN_priv_rand_range_ex(r->Y, group->field, ctx))
+ return 0;
+ } while (BN_is_zero(r->Y));
+
+ /* make sure lambda (s->Z here for storage) is not zero */
+ do {
+ if (!BN_priv_rand_range_ex(s->Z, group->field, ctx))
+ return 0;
+ } while (BN_is_zero(s->Z));
+
+ /* if field_encode defined convert between representations */
+ if (group->meth->field_encode != NULL
+ && (!group->meth->field_encode(group, r->Y, r->Y, ctx)
+ || !group->meth->field_encode(group, s->Z, s->Z, ctx)))
+ return 0;
+
+ /* blind r and s independently */
+ if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
+ || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)
+ || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */
+ return 0;
+
+ r->Z_is_one = 0;
+ s->Z_is_one = 0;
+
+ return 1;
+}
+
+/*-
+ * Input:
+ * - s, r: projective (homogeneous) coordinates
+ * - p: affine coordinates
+ *
+ * Output:
+ * - s := r + s, r := 2r: projective (homogeneous) coordinates
+ *
+ * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
+ * "A fast parallel elliptic curve multiplication resistant against side channel
+ * attacks", as described at
+ * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4
+ */
+int ec_GFp_simple_ladder_step(const EC_GROUP *group,
+ EC_POINT *r, EC_POINT *s,
+ EC_POINT *p, BN_CTX *ctx)
+{
+ int ret = 0;
+ BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
+
+ BN_CTX_start(ctx);
+ t0 = BN_CTX_get(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ t3 = BN_CTX_get(ctx);
+ t4 = BN_CTX_get(ctx);
+ t5 = BN_CTX_get(ctx);
+ t6 = BN_CTX_get(ctx);
+
+ if (t6 == NULL
+ || !group->meth->field_mul(group, t6, r->X, s->X, ctx)
+ || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
+ || !group->meth->field_mul(group, t4, r->X, s->Z, ctx)
+ || !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
+ || !group->meth->field_mul(group, t5, group->a, t0, ctx)
+ || !BN_mod_add_quick(t5, t6, t5, group->field)
+ || !BN_mod_add_quick(t6, t3, t4, group->field)
+ || !group->meth->field_mul(group, t5, t6, t5, ctx)
+ || !group->meth->field_sqr(group, t0, t0, ctx)
+ || !BN_mod_lshift_quick(t2, group->b, 2, group->field)
+ || !group->meth->field_mul(group, t0, t2, t0, ctx)
+ || !BN_mod_lshift1_quick(t5, t5, group->field)
+ || !BN_mod_sub_quick(t3, t4, t3, group->field)
+ /* s->Z coord output */
+ || !group->meth->field_sqr(group, s->Z, t3, ctx)
+ || !group->meth->field_mul(group, t4, s->Z, p->X, ctx)
+ || !BN_mod_add_quick(t0, t0, t5, group->field)
+ /* s->X coord output */
+ || !BN_mod_sub_quick(s->X, t0, t4, group->field)
+ || !group->meth->field_sqr(group, t4, r->X, ctx)
+ || !group->meth->field_sqr(group, t5, r->Z, ctx)
+ || !group->meth->field_mul(group, t6, t5, group->a, ctx)
+ || !BN_mod_add_quick(t1, r->X, r->Z, group->field)
+ || !group->meth->field_sqr(group, t1, t1, ctx)
+ || !BN_mod_sub_quick(t1, t1, t4, group->field)
+ || !BN_mod_sub_quick(t1, t1, t5, group->field)
+ || !BN_mod_sub_quick(t3, t4, t6, group->field)
+ || !group->meth->field_sqr(group, t3, t3, ctx)
+ || !group->meth->field_mul(group, t0, t5, t1, ctx)
+ || !group->meth->field_mul(group, t0, t2, t0, ctx)
+ /* r->X coord output */
+ || !BN_mod_sub_quick(r->X, t3, t0, group->field)
+ || !BN_mod_add_quick(t3, t4, t6, group->field)
+ || !group->meth->field_sqr(group, t4, t5, ctx)
+ || !group->meth->field_mul(group, t4, t4, t2, ctx)
+ || !group->meth->field_mul(group, t1, t1, t3, ctx)
+ || !BN_mod_lshift1_quick(t1, t1, group->field)
+ /* r->Z coord output */
+ || !BN_mod_add_quick(r->Z, t4, t1, group->field))
+ goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*-
+ * Input:
+ * - s, r: projective (homogeneous) coordinates
+ * - p: affine coordinates
+ *
+ * Output:
+ * - r := (x,y): affine coordinates
+ *
+ * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
+ * Elliptic Curves and Side-Channel Attacks", modified to work in mixed
+ * projective coords, i.e. p is affine and (r,s) in projective (homogeneous)
+ * coords, and return r in affine coordinates.
+ *
+ * X4 = two*Y1*X2*Z3*Z2;
+ * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2);
+ * Z4 = two*Y1*Z3*SQR(Z2);
+ *
+ * Z4 != 0 because:
+ * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch);
+ * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch);
+ * - Y1==0 implies p has order 2, so either r or s are infinity and handled by
+ * one of the BN_is_zero(...) branches.
+ */
+int ec_GFp_simple_ladder_post(const EC_GROUP *group,
+ EC_POINT *r, EC_POINT *s,
+ EC_POINT *p, BN_CTX *ctx)
+{
+ int ret = 0;
+ BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
+
+ if (BN_is_zero(r->Z))
+ return EC_POINT_set_to_infinity(group, r);
+
+ if (BN_is_zero(s->Z)) {
+ if (!EC_POINT_copy(r, p)
+ || !EC_POINT_invert(group, r, ctx))
+ return 0;
+ return 1;
+ }
+
+ BN_CTX_start(ctx);
+ t0 = BN_CTX_get(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ t3 = BN_CTX_get(ctx);
+ t4 = BN_CTX_get(ctx);
+ t5 = BN_CTX_get(ctx);
+ t6 = BN_CTX_get(ctx);
+
+ if (t6 == NULL
+ || !BN_mod_lshift1_quick(t4, p->Y, group->field)
+ || !group->meth->field_mul(group, t6, r->X, t4, ctx)
+ || !group->meth->field_mul(group, t6, s->Z, t6, ctx)
+ || !group->meth->field_mul(group, t5, r->Z, t6, ctx)
+ || !BN_mod_lshift1_quick(t1, group->b, group->field)
+ || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
+ || !group->meth->field_sqr(group, t3, r->Z, ctx)
+ || !group->meth->field_mul(group, t2, t3, t1, ctx)
+ || !group->meth->field_mul(group, t6, r->Z, group->a, ctx)
+ || !group->meth->field_mul(group, t1, p->X, r->X, ctx)
+ || !BN_mod_add_quick(t1, t1, t6, group->field)
+ || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
+ || !group->meth->field_mul(group, t0, p->X, r->Z, ctx)
+ || !BN_mod_add_quick(t6, r->X, t0, group->field)
+ || !group->meth->field_mul(group, t6, t6, t1, ctx)
+ || !BN_mod_add_quick(t6, t6, t2, group->field)
+ || !BN_mod_sub_quick(t0, t0, r->X, group->field)
+ || !group->meth->field_sqr(group, t0, t0, ctx)
+ || !group->meth->field_mul(group, t0, t0, s->X, ctx)
+ || !BN_mod_sub_quick(t0, t6, t0, group->field)
+ || !group->meth->field_mul(group, t1, s->Z, t4, ctx)
+ || !group->meth->field_mul(group, t1, t3, t1, ctx)
+ || (group->meth->field_decode != NULL
+ && !group->meth->field_decode(group, t1, t1, ctx))
+ || !group->meth->field_inv(group, t1, t1, ctx)
+ || (group->meth->field_encode != NULL
+ && !group->meth->field_encode(group, t1, t1, ctx))
+ || !group->meth->field_mul(group, r->X, t5, t1, ctx)
+ || !group->meth->field_mul(group, r->Y, t0, t1, ctx))
+ goto err;
+
+ if (group->meth->field_set_to_one != NULL) {
+ if (!group->meth->field_set_to_one(group, r->Z, ctx))
+ goto err;
+ } else {
+ if (!BN_one(r->Z))
+ goto err;
+ }
+
+ r->Z_is_one = 1;
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
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