/*
- * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 2002-2018 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
*
- * Licensed under the OpenSSL license (the "License"). You may not use
+ * 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
#ifndef OPENSSL_NO_EC2M
-const EC_METHOD *EC_GF2m_simple_method(void)
-{
- static const EC_METHOD ret = {
- EC_FLAGS_DEFAULT_OCT,
- NID_X9_62_characteristic_two_field,
- ec_GF2m_simple_group_init,
- ec_GF2m_simple_group_finish,
- ec_GF2m_simple_group_clear_finish,
- ec_GF2m_simple_group_copy,
- ec_GF2m_simple_group_set_curve,
- ec_GF2m_simple_group_get_curve,
- ec_GF2m_simple_group_get_degree,
- ec_group_simple_order_bits,
- ec_GF2m_simple_group_check_discriminant,
- ec_GF2m_simple_point_init,
- ec_GF2m_simple_point_finish,
- ec_GF2m_simple_point_clear_finish,
- ec_GF2m_simple_point_copy,
- ec_GF2m_simple_point_set_to_infinity,
- 0 /* set_Jprojective_coordinates_GFp */ ,
- 0 /* get_Jprojective_coordinates_GFp */ ,
- ec_GF2m_simple_point_set_affine_coordinates,
- ec_GF2m_simple_point_get_affine_coordinates,
- 0, 0, 0,
- ec_GF2m_simple_add,
- ec_GF2m_simple_dbl,
- ec_GF2m_simple_invert,
- ec_GF2m_simple_is_at_infinity,
- ec_GF2m_simple_is_on_curve,
- ec_GF2m_simple_cmp,
- ec_GF2m_simple_make_affine,
- ec_GF2m_simple_points_make_affine,
-
- /*
- * the following three method functions are defined in ec2_mult.c
- */
- ec_GF2m_simple_mul,
- ec_GF2m_precompute_mult,
- ec_GF2m_have_precompute_mult,
-
- ec_GF2m_simple_field_mul,
- ec_GF2m_simple_field_sqr,
- ec_GF2m_simple_field_div,
- 0 /* field_encode */ ,
- 0 /* field_decode */ ,
- 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
- };
-
- return &ret;
-}
-
/*
* Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
* are handled by EC_GROUP_new.
ret = 1;
err:
- if (ctx != NULL)
- BN_CTX_end(ctx);
+ BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
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;
}
if (!BN_copy(y0, a->Y))
goto err;
} else {
- if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx))
+ if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx))
goto err;
}
if (b->Z_is_one) {
if (!BN_copy(y1, b->Y))
goto err;
} else {
- if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx))
+ if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx))
goto err;
}
if (!BN_GF2m_add(y2, y2, y1))
goto err;
- if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx))
+ if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx))
goto err;
ret = 1;
if (!BN_GF2m_add(lh, lh, y2))
goto err;
ret = BN_is_zero(lh);
+
err:
- if (ctx)
- BN_CTX_end(ctx);
+ BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
if (bY == NULL)
goto err;
- if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx))
+ if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx))
goto err;
- if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx))
+ if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx))
goto err;
ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
err:
- if (ctx)
- BN_CTX_end(ctx);
+ BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
if (y == NULL)
goto err;
- if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx))
+ if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
goto err;
if (!BN_copy(point->X, x))
goto err;
ret = 1;
err:
- if (ctx)
- BN_CTX_end(ctx);
+ BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
return BN_GF2m_mod_div(r, a, b, group->field, ctx);
}
+/*-
+ * Lopez-Dahab ladder, pre step.
+ * See e.g. "Guide to ECC" Alg 3.40.
+ * Modified to blind s and r independently.
+ * s:= p, r := 2p
+ */
+static
+int ec_GF2m_simple_ladder_pre(const EC_GROUP *group,
+ EC_POINT *r, EC_POINT *s,
+ EC_POINT *p, BN_CTX *ctx)
+{
+ /* if p is not affine, something is wrong */
+ if (p->Z_is_one == 0)
+ return 0;
+
+ /* s blinding: make sure lambda (s->Z here) is not zero */
+ do {
+ if (!BN_priv_rand(s->Z, BN_num_bits(group->field) - 1,
+ BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY)) {
+ ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB);
+ 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, s->Z, s->Z, ctx))
+ || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx))
+ return 0;
+
+ /* r blinding: make sure lambda (r->Y here for storage) is not zero */
+ do {
+ if (!BN_priv_rand(r->Y, BN_num_bits(group->field) - 1,
+ BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY)) {
+ ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB);
+ return 0;
+ }
+ } while (BN_is_zero(r->Y));
+
+ if ((group->meth->field_encode != NULL
+ && !group->meth->field_encode(group, r->Y, r->Y, ctx))
+ || !group->meth->field_sqr(group, r->Z, p->X, ctx)
+ || !group->meth->field_sqr(group, r->X, r->Z, ctx)
+ || !BN_GF2m_add(r->X, r->X, group->b)
+ || !group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
+ || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx))
+ return 0;
+
+ s->Z_is_one = 0;
+ r->Z_is_one = 0;
+
+ return 1;
+}
+
+/*-
+ * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords.
+ * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3
+ * s := r + s, r := 2r
+ */
+static
+int ec_GF2m_simple_ladder_step(const EC_GROUP *group,
+ EC_POINT *r, EC_POINT *s,
+ EC_POINT *p, BN_CTX *ctx)
+{
+ if (!group->meth->field_mul(group, r->Y, r->Z, s->X, ctx)
+ || !group->meth->field_mul(group, s->X, r->X, s->Z, ctx)
+ || !group->meth->field_sqr(group, s->Y, r->Z, ctx)
+ || !group->meth->field_sqr(group, r->Z, r->X, ctx)
+ || !BN_GF2m_add(s->Z, r->Y, s->X)
+ || !group->meth->field_sqr(group, s->Z, s->Z, ctx)
+ || !group->meth->field_mul(group, s->X, r->Y, s->X, ctx)
+ || !group->meth->field_mul(group, r->Y, s->Z, p->X, ctx)
+ || !BN_GF2m_add(s->X, s->X, r->Y)
+ || !group->meth->field_sqr(group, r->Y, r->Z, ctx)
+ || !group->meth->field_mul(group, r->Z, r->Z, s->Y, ctx)
+ || !group->meth->field_sqr(group, s->Y, s->Y, ctx)
+ || !group->meth->field_mul(group, s->Y, s->Y, group->b, ctx)
+ || !BN_GF2m_add(r->X, r->Y, s->Y))
+ return 0;
+
+ return 1;
+}
+
+/*-
+ * Recover affine (x,y) result from Lopez-Dahab r and s, affine p.
+ * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m)
+ * without Precomputation" (Lopez and Dahab, CHES 1999),
+ * Appendix Alg Mxy.
+ */
+static
+int ec_GF2m_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 = 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)) {
+ ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_EC_LIB);
+ return 0;
+ }
+ return 1;
+ }
+
+ BN_CTX_start(ctx);
+ t0 = BN_CTX_get(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ if (t2 == NULL) {
+ ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+
+ if (!group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
+ || !group->meth->field_mul(group, t1, p->X, r->Z, ctx)
+ || !BN_GF2m_add(t1, r->X, t1)
+ || !group->meth->field_mul(group, t2, p->X, s->Z, ctx)
+ || !group->meth->field_mul(group, r->Z, r->X, t2, ctx)
+ || !BN_GF2m_add(t2, t2, s->X)
+ || !group->meth->field_mul(group, t1, t1, t2, ctx)
+ || !group->meth->field_sqr(group, t2, p->X, ctx)
+ || !BN_GF2m_add(t2, p->Y, t2)
+ || !group->meth->field_mul(group, t2, t2, t0, ctx)
+ || !BN_GF2m_add(t1, t2, t1)
+ || !group->meth->field_mul(group, t2, p->X, t0, ctx)
+ || !group->meth->field_inv(group, t2, t2, ctx)
+ || !group->meth->field_mul(group, t1, t1, t2, ctx)
+ || !group->meth->field_mul(group, r->X, r->Z, t2, ctx)
+ || !BN_GF2m_add(t2, p->X, r->X)
+ || !group->meth->field_mul(group, t2, t2, t1, ctx)
+ || !BN_GF2m_add(r->Y, p->Y, t2)
+ || !BN_one(r->Z))
+ goto err;
+
+ r->Z_is_one = 1;
+
+ /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
+ BN_set_negative(r->X, 0);
+ BN_set_negative(r->Y, 0);
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+static
+int ec_GF2m_simple_points_mul(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *scalar, size_t num,
+ const EC_POINT *points[],
+ const BIGNUM *scalars[],
+ BN_CTX *ctx)
+{
+ int ret = 0;
+ EC_POINT *t = NULL;
+
+ /*-
+ * We limit use of the ladder only to the following cases:
+ * - r := scalar * G
+ * Fixed point mul: scalar != NULL && num == 0;
+ * - r := scalars[0] * points[0]
+ * Variable point mul: scalar == NULL && num == 1;
+ * - r := scalar * G + scalars[0] * points[0]
+ * used, e.g., in ECDSA verification: scalar != NULL && num == 1
+ *
+ * In any other case (num > 1) we use the default wNAF implementation.
+ *
+ * We also let the default implementation handle degenerate cases like group
+ * order or cofactor set to 0.
+ */
+ if (num > 1 || BN_is_zero(group->order) || BN_is_zero(group->cofactor))
+ return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
+
+ if (scalar != NULL && num == 0)
+ /* Fixed point multiplication */
+ return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
+
+ if (scalar == NULL && num == 1)
+ /* Variable point multiplication */
+ return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);
+
+ /*-
+ * Double point multiplication:
+ * r := scalar * G + scalars[0] * points[0]
+ */
+
+ if ((t = EC_POINT_new(group)) == NULL) {
+ ECerr(EC_F_EC_GF2M_SIMPLE_POINTS_MUL, ERR_R_MALLOC_FAILURE);
+ return 0;
+ }
+
+ if (!ec_scalar_mul_ladder(group, t, scalar, NULL, ctx)
+ || !ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx)
+ || !EC_POINT_add(group, r, t, r, ctx))
+ goto err;
+
+ ret = 1;
+
+ err:
+ EC_POINT_free(t);
+ return ret;
+}
+
+/*-
+ * Computes the multiplicative inverse of a in GF(2^m), storing the result in r.
+ * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
+ * SCA hardening is with blinding: BN_GF2m_mod_inv does that.
+ */
+static int ec_GF2m_simple_field_inv(const EC_GROUP *group, BIGNUM *r,
+ const BIGNUM *a, BN_CTX *ctx)
+{
+ int ret;
+
+ if (!(ret = BN_GF2m_mod_inv(r, a, group->field, ctx)))
+ ECerr(EC_F_EC_GF2M_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
+ return ret;
+}
+
+const EC_METHOD *EC_GF2m_simple_method(void)
+{
+ static const EC_METHOD ret = {
+ EC_FLAGS_DEFAULT_OCT,
+ NID_X9_62_characteristic_two_field,
+ ec_GF2m_simple_group_init,
+ ec_GF2m_simple_group_finish,
+ ec_GF2m_simple_group_clear_finish,
+ ec_GF2m_simple_group_copy,
+ ec_GF2m_simple_group_set_curve,
+ ec_GF2m_simple_group_get_curve,
+ ec_GF2m_simple_group_get_degree,
+ ec_group_simple_order_bits,
+ ec_GF2m_simple_group_check_discriminant,
+ ec_GF2m_simple_point_init,
+ ec_GF2m_simple_point_finish,
+ ec_GF2m_simple_point_clear_finish,
+ ec_GF2m_simple_point_copy,
+ ec_GF2m_simple_point_set_to_infinity,
+ 0, /* set_Jprojective_coordinates_GFp */
+ 0, /* get_Jprojective_coordinates_GFp */
+ ec_GF2m_simple_point_set_affine_coordinates,
+ ec_GF2m_simple_point_get_affine_coordinates,
+ 0, /* point_set_compressed_coordinates */
+ 0, /* point2oct */
+ 0, /* oct2point */
+ ec_GF2m_simple_add,
+ ec_GF2m_simple_dbl,
+ ec_GF2m_simple_invert,
+ ec_GF2m_simple_is_at_infinity,
+ ec_GF2m_simple_is_on_curve,
+ ec_GF2m_simple_cmp,
+ ec_GF2m_simple_make_affine,
+ ec_GF2m_simple_points_make_affine,
+ ec_GF2m_simple_points_mul,
+ 0, /* precompute_mult */
+ 0, /* have_precompute_mult */
+ ec_GF2m_simple_field_mul,
+ ec_GF2m_simple_field_sqr,
+ ec_GF2m_simple_field_div,
+ ec_GF2m_simple_field_inv,
+ 0, /* field_encode */
+ 0, /* field_decode */
+ 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,
+ 0, /* field_inverse_mod_ord */
+ 0, /* blind_coordinates */
+ ec_GF2m_simple_ladder_pre,
+ ec_GF2m_simple_ladder_step,
+ ec_GF2m_simple_ladder_post
+ };
+
+ return &ret;
+}
+
#endif
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