/* 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. */
#ifndef OPENSSL_HEADER_EC_INTERNAL_H
#define OPENSSL_HEADER_EC_INTERNAL_H
#include <openssl/base.h>
#include <openssl/bn.h>
#include <openssl/ex_data.h>
#include <openssl/thread.h>
#include <openssl/type_check.h>
#include "../bn/internal.h"
#if defined(__cplusplus)
extern "C" {
#endif
// Cap the size of all field elements and scalars, including custom curves, to
// 66 bytes, large enough to fit secp521r1 and brainpoolP512r1, which appear to
// be the largest fields anyone plausibly uses.
#define EC_MAX_SCALAR_BYTES 66
#define EC_MAX_SCALAR_WORDS ((66 + BN_BYTES - 1) / BN_BYTES)
OPENSSL_COMPILE_ASSERT(EC_MAX_SCALAR_WORDS <= BN_SMALL_MAX_WORDS,
bn_small_functions_applicable);
// An EC_SCALAR is an integer fully reduced modulo the order. Only the first
// |order->top| words are used. An |EC_SCALAR| is specific to an |EC_GROUP| and
// must not be mixed between groups.
typedef union {
// bytes is the representation of the scalar in little-endian order.
uint8_t bytes[EC_MAX_SCALAR_BYTES];
BN_ULONG words[EC_MAX_SCALAR_WORDS];
} EC_SCALAR;
struct ec_method_st {
int (*group_init)(EC_GROUP *);
void (*group_finish)(EC_GROUP *);
int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
const BIGNUM *b, BN_CTX *);
int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
// Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar|
// are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null.
// Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar|
// and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is
// non-null.
int (*mul)(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
// mul_public performs the same computation as mul. It further assumes that
// the inputs are public so there is no concern about leaking their values
// through timing.
int (*mul_public)(const EC_GROUP *group, EC_POINT *r,
const EC_SCALAR *g_scalar, const EC_POINT *p,
const EC_SCALAR *p_scalar, BN_CTX *ctx);
// 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the
// same implementations of point operations can be used with different
// optimized implementations of expensive field operations:
int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
const BIGNUM *b, BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
BN_CTX *); // e.g. to Montgomery
int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
BN_CTX *); // e.g. from Montgomery
} /* EC_METHOD */;
const EC_METHOD *EC_GFp_mont_method(void);
struct ec_group_st {
const EC_METHOD *meth;
// Unlike all other |EC_POINT|s, |generator| does not own |generator->group|
// to avoid a reference cycle.
EC_POINT *generator;
BIGNUM order;
int curve_name; // optional NID for named curve
BN_MONT_CTX *order_mont; // data for ECDSA inverse
// The following members are handled by the method functions,
// even if they appear generic
BIGNUM field; // For curves over GF(p), this is the modulus.
BIGNUM a, b; // Curve coefficients.
int a_is_minus3; // enable optimized point arithmetics for special case
CRYPTO_refcount_t references;
BN_MONT_CTX *mont; // Montgomery structure.
BIGNUM one; // The value one.
} /* EC_GROUP */;
struct ec_point_st {
// group is an owning reference to |group|, unless this is
// |group->generator|.
EC_GROUP *group;
BIGNUM X;
BIGNUM Y;
BIGNUM Z; // Jacobian projective coordinates:
// (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0
} /* EC_POINT */;
EC_GROUP *ec_group_new(const EC_METHOD *meth);
// ec_bignum_to_scalar converts |in| to an |EC_SCALAR| and writes it to
// |*out|. It returns one on success and zero if |in| is out of range.
int ec_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
const BIGNUM *in);
// ec_bignum_to_scalar_unchecked behaves like |ec_bignum_to_scalar| but does not
// check |in| is fully reduced.
int ec_bignum_to_scalar_unchecked(const EC_GROUP *group, EC_SCALAR *out,
const BIGNUM *in);
// ec_random_nonzero_scalar sets |out| to a uniformly selected random value from
// 1 to |group->order| - 1. It returns one on success and zero on error.
int ec_random_nonzero_scalar(const EC_GROUP *group, EC_SCALAR *out,
const uint8_t additional_data[32]);
// ec_point_mul_scalar sets |r| to generator * |g_scalar| + |p| *
// |p_scalar|. Unlike other functions which take |EC_SCALAR|, |g_scalar| and
// |p_scalar| need not be fully reduced. They need only contain as many bits as
// the order.
int ec_point_mul_scalar(const EC_GROUP *group, EC_POINT *r,
const EC_SCALAR *g_scalar, const EC_POINT *p,
const EC_SCALAR *p_scalar, BN_CTX *ctx);
// ec_point_mul_scalar_public performs the same computation as
// ec_point_mul_scalar. It further assumes that the inputs are public so
// there is no concern about leaking their values through timing.
int ec_point_mul_scalar_public(const EC_GROUP *group, EC_POINT *r,
const EC_SCALAR *g_scalar, const EC_POINT *p,
const EC_SCALAR *p_scalar, BN_CTX *ctx);
int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
// method functions in simple.c
int ec_GFp_simple_group_init(EC_GROUP *);
void ec_GFp_simple_group_finish(EC_GROUP *);
int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
const BIGNUM *b, BN_CTX *);
int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
BIGNUM *b, BN_CTX *);
unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *);
int ec_GFp_simple_point_init(EC_POINT *);
void ec_GFp_simple_point_finish(EC_POINT *);
int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y,
BN_CTX *);
int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
const EC_POINT *b, BN_CTX *);
int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
BN_CTX *);
int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
BN_CTX *);
int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
EC_POINT * [], BN_CTX *);
int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
const BIGNUM *b, BN_CTX *);
int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
BN_CTX *);
// method functions in montgomery.c
int ec_GFp_mont_group_init(EC_GROUP *);
int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
const BIGNUM *b, BN_CTX *);
void ec_GFp_mont_group_finish(EC_GROUP *);
int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
const BIGNUM *b, BN_CTX *);
int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
BN_CTX *);
int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
BN_CTX *);
int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
BN_CTX *);
void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in);
const EC_METHOD *EC_GFp_nistp224_method(void);
const EC_METHOD *EC_GFp_nistp256_method(void);
// EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with
// x86-64 optimized P256. See http://eprint.iacr.org/2013/816.
const EC_METHOD *EC_GFp_nistz256_method(void);
struct ec_key_st {
EC_GROUP *group;
EC_POINT *pub_key;
BIGNUM *priv_key;
// fixed_k may contain a specific value of 'k', to be used in ECDSA signing.
// This is only for the FIPS power-on tests.
BIGNUM *fixed_k;
unsigned int enc_flag;
point_conversion_form_t conv_form;
CRYPTO_refcount_t references;
ECDSA_METHOD *ecdsa_meth;
CRYPTO_EX_DATA ex_data;
} /* EC_KEY */;
struct built_in_curve {
int nid;
const uint8_t *oid;
uint8_t oid_len;
// comment is a human-readable string describing the curve.
const char *comment;
// param_len is the number of bytes needed to store a field element.
uint8_t param_len;
// params points to an array of 6*|param_len| bytes which hold the field
// elements of the following (in big-endian order): prime, a, b, generator x,
// generator y, order.
const uint8_t *params;
const EC_METHOD *method;
};
#define OPENSSL_NUM_BUILT_IN_CURVES 4
struct built_in_curves {
struct built_in_curve curves[OPENSSL_NUM_BUILT_IN_CURVES];
};
// OPENSSL_built_in_curves returns a pointer to static information about
// standard curves. The array is terminated with an entry where |nid| is
// |NID_undef|.
const struct built_in_curves *OPENSSL_built_in_curves(void);
#if defined(__cplusplus)
} // extern C
#endif
#endif // OPENSSL_HEADER_EC_INTERNAL_H