320 lines
13 KiB
C
320 lines
13 KiB
C
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/* Originally written by Bodo Moeller for the OpenSSL project.
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* ====================================================================
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* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* openssl-core@openssl.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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*
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* This product includes cryptographic software written by Eric Young
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com).
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*
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*/
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/* ====================================================================
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* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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*
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* Portions of the attached software ("Contribution") are developed by
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* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
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*
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* The Contribution is licensed pursuant to the OpenSSL open source
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* license provided above.
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*
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* The elliptic curve binary polynomial software is originally written by
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* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
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* Laboratories. */
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#ifndef OPENSSL_HEADER_EC_INTERNAL_H
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#define OPENSSL_HEADER_EC_INTERNAL_H
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#include <openssl/base.h>
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#include <openssl/bn.h>
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#include <openssl/ex_data.h>
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#include <openssl/thread.h>
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#include <openssl/type_check.h>
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#include "../bn/internal.h"
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#if defined(__cplusplus)
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extern "C" {
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#endif
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// Cap the size of all field elements and scalars, including custom curves, to
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// 66 bytes, large enough to fit secp521r1 and brainpoolP512r1, which appear to
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// be the largest fields anyone plausibly uses.
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#define EC_MAX_SCALAR_BYTES 66
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#define EC_MAX_SCALAR_WORDS ((66 + BN_BYTES - 1) / BN_BYTES)
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OPENSSL_COMPILE_ASSERT(EC_MAX_SCALAR_WORDS <= BN_SMALL_MAX_WORDS,
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bn_small_functions_applicable);
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// An EC_SCALAR is an integer fully reduced modulo the order. Only the first
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// |order->top| words are used. An |EC_SCALAR| is specific to an |EC_GROUP| and
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// must not be mixed between groups.
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typedef union {
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// bytes is the representation of the scalar in little-endian order.
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uint8_t bytes[EC_MAX_SCALAR_BYTES];
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BN_ULONG words[EC_MAX_SCALAR_WORDS];
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} EC_SCALAR;
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struct ec_method_st {
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int (*group_init)(EC_GROUP *);
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void (*group_finish)(EC_GROUP *);
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int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
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const BIGNUM *b, BN_CTX *);
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int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
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BIGNUM *x, BIGNUM *y, BN_CTX *);
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// Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar|
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// are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null.
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// Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar|
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// and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is
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// non-null.
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int (*mul)(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
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const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
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// mul_public performs the same computation as mul. It further assumes that
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// the inputs are public so there is no concern about leaking their values
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// through timing.
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int (*mul_public)(const EC_GROUP *group, EC_POINT *r,
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const EC_SCALAR *g_scalar, const EC_POINT *p,
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const EC_SCALAR *p_scalar, BN_CTX *ctx);
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// 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the
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// same implementations of point operations can be used with different
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// optimized implementations of expensive field operations:
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int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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const BIGNUM *b, BN_CTX *);
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int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
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int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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BN_CTX *); // e.g. to Montgomery
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int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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BN_CTX *); // e.g. from Montgomery
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} /* EC_METHOD */;
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const EC_METHOD *EC_GFp_mont_method(void);
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struct ec_group_st {
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const EC_METHOD *meth;
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// Unlike all other |EC_POINT|s, |generator| does not own |generator->group|
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// to avoid a reference cycle.
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EC_POINT *generator;
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BIGNUM order;
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int curve_name; // optional NID for named curve
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BN_MONT_CTX *order_mont; // data for ECDSA inverse
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// The following members are handled by the method functions,
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// even if they appear generic
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BIGNUM field; // For curves over GF(p), this is the modulus.
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BIGNUM a, b; // Curve coefficients.
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int a_is_minus3; // enable optimized point arithmetics for special case
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CRYPTO_refcount_t references;
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BN_MONT_CTX *mont; // Montgomery structure.
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BIGNUM one; // The value one.
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} /* EC_GROUP */;
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struct ec_point_st {
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// group is an owning reference to |group|, unless this is
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// |group->generator|.
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EC_GROUP *group;
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BIGNUM X;
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BIGNUM Y;
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BIGNUM Z; // Jacobian projective coordinates:
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// (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0
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} /* EC_POINT */;
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EC_GROUP *ec_group_new(const EC_METHOD *meth);
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// ec_bignum_to_scalar converts |in| to an |EC_SCALAR| and writes it to
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// |*out|. It returns one on success and zero if |in| is out of range.
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int ec_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
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const BIGNUM *in);
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// ec_bignum_to_scalar_unchecked behaves like |ec_bignum_to_scalar| but does not
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// check |in| is fully reduced.
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int ec_bignum_to_scalar_unchecked(const EC_GROUP *group, EC_SCALAR *out,
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const BIGNUM *in);
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// ec_random_nonzero_scalar sets |out| to a uniformly selected random value from
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// 1 to |group->order| - 1. It returns one on success and zero on error.
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int ec_random_nonzero_scalar(const EC_GROUP *group, EC_SCALAR *out,
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const uint8_t additional_data[32]);
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// ec_point_mul_scalar sets |r| to generator * |g_scalar| + |p| *
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// |p_scalar|. Unlike other functions which take |EC_SCALAR|, |g_scalar| and
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// |p_scalar| need not be fully reduced. They need only contain as many bits as
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// the order.
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int ec_point_mul_scalar(const EC_GROUP *group, EC_POINT *r,
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const EC_SCALAR *g_scalar, const EC_POINT *p,
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const EC_SCALAR *p_scalar, BN_CTX *ctx);
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// ec_point_mul_scalar_public performs the same computation as
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// ec_point_mul_scalar. It further assumes that the inputs are public so
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// there is no concern about leaking their values through timing.
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int ec_point_mul_scalar_public(const EC_GROUP *group, EC_POINT *r,
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const EC_SCALAR *g_scalar, const EC_POINT *p,
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const EC_SCALAR *p_scalar, BN_CTX *ctx);
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int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
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const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
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// method functions in simple.c
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int ec_GFp_simple_group_init(EC_GROUP *);
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void ec_GFp_simple_group_finish(EC_GROUP *);
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int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
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const BIGNUM *b, BN_CTX *);
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int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
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BIGNUM *b, BN_CTX *);
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unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *);
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int ec_GFp_simple_point_init(EC_POINT *);
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void ec_GFp_simple_point_finish(EC_POINT *);
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int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
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int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
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int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
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const BIGNUM *x, const BIGNUM *y,
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BN_CTX *);
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int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
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const EC_POINT *b, BN_CTX *);
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int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
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BN_CTX *);
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int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
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int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
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int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
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int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
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BN_CTX *);
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int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
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int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
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EC_POINT * [], BN_CTX *);
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int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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const BIGNUM *b, BN_CTX *);
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int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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BN_CTX *);
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// method functions in montgomery.c
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int ec_GFp_mont_group_init(EC_GROUP *);
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int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
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const BIGNUM *b, BN_CTX *);
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void ec_GFp_mont_group_finish(EC_GROUP *);
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int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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const BIGNUM *b, BN_CTX *);
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int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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BN_CTX *);
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int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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BN_CTX *);
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int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
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BN_CTX *);
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void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in);
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const EC_METHOD *EC_GFp_nistp224_method(void);
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const EC_METHOD *EC_GFp_nistp256_method(void);
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// EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with
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// x86-64 optimized P256. See http://eprint.iacr.org/2013/816.
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const EC_METHOD *EC_GFp_nistz256_method(void);
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struct ec_key_st {
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EC_GROUP *group;
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EC_POINT *pub_key;
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BIGNUM *priv_key;
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// fixed_k may contain a specific value of 'k', to be used in ECDSA signing.
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// This is only for the FIPS power-on tests.
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BIGNUM *fixed_k;
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unsigned int enc_flag;
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point_conversion_form_t conv_form;
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CRYPTO_refcount_t references;
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ECDSA_METHOD *ecdsa_meth;
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CRYPTO_EX_DATA ex_data;
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} /* EC_KEY */;
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struct built_in_curve {
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int nid;
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const uint8_t *oid;
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uint8_t oid_len;
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// comment is a human-readable string describing the curve.
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const char *comment;
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// param_len is the number of bytes needed to store a field element.
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uint8_t param_len;
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// params points to an array of 6*|param_len| bytes which hold the field
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// elements of the following (in big-endian order): prime, a, b, generator x,
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// generator y, order.
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const uint8_t *params;
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const EC_METHOD *method;
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};
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#define OPENSSL_NUM_BUILT_IN_CURVES 4
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struct built_in_curves {
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struct built_in_curve curves[OPENSSL_NUM_BUILT_IN_CURVES];
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};
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// OPENSSL_built_in_curves returns a pointer to static information about
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// standard curves. The array is terminated with an entry where |nid| is
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// |NID_undef|.
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const struct built_in_curves *OPENSSL_built_in_curves(void);
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#if defined(__cplusplus)
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} // extern C
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#endif
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#endif // OPENSSL_HEADER_EC_INTERNAL_H
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