--- /dev/null
+/* 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->width| 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.
+OPENSSL_EXPORT 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.
+OPENSSL_EXPORT 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);
+
+// ec_compute_wNAF writes the modified width-(w+1) Non-Adjacent Form (wNAF) of
+// |scalar| to |out| and returns one on success or zero on internal error. |out|
+// must have room for |bits| + 1 elements, each of which will be either zero or
+// odd with an absolute value less than 2^w satisfying
+// scalar = \sum_j out[j]*2^j
+// where at most one of any w+1 consecutive digits is non-zero
+// with the exception that the most significant digit may be only
+// w-1 zeros away from that next non-zero digit.
+int ec_compute_wNAF(const EC_GROUP *group, int8_t *out, const EC_SCALAR *scalar,
+ size_t bits, int w);
+
+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);
+
+// An EC_WRAPPED_SCALAR is an |EC_SCALAR| with a parallel |BIGNUM|
+// representation. It exists to support the |EC_KEY_get0_private_key| API.
+typedef struct {
+ BIGNUM bignum;
+ EC_SCALAR scalar;
+} EC_WRAPPED_SCALAR;
+
+struct ec_key_st {
+ EC_GROUP *group;
+
+ EC_POINT *pub_key;
+ EC_WRAPPED_SCALAR *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
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