/* 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 * [email protected]. * * 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 * ([email protected]). This product includes software written by Tim * Hudson ([email protected]). * */ /* ==================================================================== * 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 <assert.h> #include <openssl/bn.h> #include <openssl/ec.h> #include <openssl/ex_data.h> #include "../bn/internal.h" #if defined(__cplusplus) extern "C" { #endif // EC internals. // 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_BYTES … #define EC_MAX_WORDS … #define EC_MAX_COMPRESSED … #define EC_MAX_UNCOMPRESSED … static_assert; // Scalars. // 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. EC_SCALAR; // 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_scalar_to_bytes serializes |in| as a big-endian bytestring to |out| and // sets |*out_len| to the number of bytes written. The number of bytes written // is |BN_num_bytes(&group->order)|, which is at most |EC_MAX_BYTES|. OPENSSL_EXPORT void ec_scalar_to_bytes(const EC_GROUP *group, uint8_t *out, size_t *out_len, const EC_SCALAR *in); // ec_scalar_from_bytes deserializes |in| and stores the resulting scalar over // group |group| to |out|. It returns one on success and zero if |in| is // invalid. OPENSSL_EXPORT int ec_scalar_from_bytes(const EC_GROUP *group, EC_SCALAR *out, const uint8_t *in, size_t len); // ec_scalar_reduce sets |out| to |words|, reduced modulo the group order. // |words| must be less than order^2. |num| must be at most twice the width of // group order. This function treats |words| as secret. void ec_scalar_reduce(const EC_GROUP *group, EC_SCALAR *out, const BN_ULONG *words, size_t num); // 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_scalar_equal_vartime returns one if |a| and |b| are equal and zero // otherwise. Both values are treated as public. int ec_scalar_equal_vartime(const EC_GROUP *group, const EC_SCALAR *a, const EC_SCALAR *b); // ec_scalar_is_zero returns one if |a| is zero and zero otherwise. int ec_scalar_is_zero(const EC_GROUP *group, const EC_SCALAR *a); // ec_scalar_add sets |r| to |a| + |b|. void ec_scalar_add(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a, const EC_SCALAR *b); // ec_scalar_sub sets |r| to |a| - |b|. void ec_scalar_sub(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a, const EC_SCALAR *b); // ec_scalar_neg sets |r| to -|a|. void ec_scalar_neg(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a); // ec_scalar_to_montgomery sets |r| to |a| in Montgomery form. void ec_scalar_to_montgomery(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a); // ec_scalar_to_montgomery sets |r| to |a| converted from Montgomery form. void ec_scalar_from_montgomery(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a); // ec_scalar_mul_montgomery sets |r| to |a| * |b| where inputs and outputs are // in Montgomery form. void ec_scalar_mul_montgomery(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a, const EC_SCALAR *b); // ec_scalar_inv0_montgomery sets |r| to |a|^-1 where inputs and outputs are in // Montgomery form. If |a| is zero, |r| is set to zero. void ec_scalar_inv0_montgomery(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a); // ec_scalar_to_montgomery_inv_vartime sets |r| to |a|^-1 R. That is, it takes // in |a| not in Montgomery form and computes the inverse in Montgomery form. It // returns one on success and zero if |a| has no inverse. This function assumes // |a| is public and may leak information about it via timing. // // Note this is not the same operation as |ec_scalar_inv0_montgomery|. int ec_scalar_to_montgomery_inv_vartime(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a); // ec_scalar_select, in constant time, sets |out| to |a| if |mask| is all ones // and |b| if |mask| is all zeros. void ec_scalar_select(const EC_GROUP *group, EC_SCALAR *out, BN_ULONG mask, const EC_SCALAR *a, const EC_SCALAR *b); // Field elements. // An EC_FELEM represents a field element. Only the first |field->width| words // are used. An |EC_FELEM| is specific to an |EC_GROUP| and must not be mixed // between groups. Additionally, the representation (whether or not elements are // represented in Montgomery-form) may vary between |EC_METHOD|s. EC_FELEM; // ec_felem_one returns one in |group|'s field. const EC_FELEM *ec_felem_one(const EC_GROUP *group); // ec_bignum_to_felem converts |in| to an |EC_FELEM|. It returns one on success // and zero if |in| is out of range. int ec_bignum_to_felem(const EC_GROUP *group, EC_FELEM *out, const BIGNUM *in); // ec_felem_to_bignum converts |in| to a |BIGNUM|. It returns one on success and // zero on allocation failure. int ec_felem_to_bignum(const EC_GROUP *group, BIGNUM *out, const EC_FELEM *in); // ec_felem_to_bytes serializes |in| as a big-endian bytestring to |out| and // sets |*out_len| to the number of bytes written. The number of bytes written // is |BN_num_bytes(&group->order)|, which is at most |EC_MAX_BYTES|. void ec_felem_to_bytes(const EC_GROUP *group, uint8_t *out, size_t *out_len, const EC_FELEM *in); // ec_felem_from_bytes deserializes |in| and stores the resulting field element // to |out|. It returns one on success and zero if |in| is invalid. int ec_felem_from_bytes(const EC_GROUP *group, EC_FELEM *out, const uint8_t *in, size_t len); // ec_felem_neg sets |out| to -|a|. void ec_felem_neg(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a); // ec_felem_add sets |out| to |a| + |b|. void ec_felem_add(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, const EC_FELEM *b); // ec_felem_add sets |out| to |a| - |b|. void ec_felem_sub(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, const EC_FELEM *b); // ec_felem_non_zero_mask returns all ones if |a| is non-zero and all zeros // otherwise. BN_ULONG ec_felem_non_zero_mask(const EC_GROUP *group, const EC_FELEM *a); // ec_felem_select, in constant time, sets |out| to |a| if |mask| is all ones // and |b| if |mask| is all zeros. void ec_felem_select(const EC_GROUP *group, EC_FELEM *out, BN_ULONG mask, const EC_FELEM *a, const EC_FELEM *b); // ec_felem_equal returns one if |a| and |b| are equal and zero otherwise. int ec_felem_equal(const EC_GROUP *group, const EC_FELEM *a, const EC_FELEM *b); // Points. // // Points may represented in affine coordinates as |EC_AFFINE| or Jacobian // coordinates as |EC_JACOBIAN|. Affine coordinates directly represent a // point on the curve, but point addition over affine coordinates requires // costly field inversions, so arithmetic is done in Jacobian coordinates. // Converting from affine to Jacobian is cheap, while converting from Jacobian // to affine costs a field inversion. (Jacobian coordinates amortize the field // inversions needed in a sequence of point operations.) // An EC_JACOBIAN represents an elliptic curve point in Jacobian coordinates. // Unlike |EC_POINT|, it is a plain struct which can be stack-allocated and // needs no cleanup. It is specific to an |EC_GROUP| and must not be mixed // between groups. EC_JACOBIAN; // An EC_AFFINE represents an elliptic curve point in affine coordinates. // coordinates. Note the point at infinity cannot be represented in affine // coordinates. EC_AFFINE; // ec_affine_to_jacobian converts |p| to Jacobian form and writes the result to // |*out|. This operation is very cheap and only costs a few copies. void ec_affine_to_jacobian(const EC_GROUP *group, EC_JACOBIAN *out, const EC_AFFINE *p); // ec_jacobian_to_affine converts |p| to affine form and writes the result to // |*out|. It returns one on success and zero if |p| was the point at infinity. // This operation performs a field inversion and should only be done once per // point. // // If only extracting the x-coordinate, use |ec_get_x_coordinate_*| which is // slightly faster. OPENSSL_EXPORT int ec_jacobian_to_affine(const EC_GROUP *group, EC_AFFINE *out, const EC_JACOBIAN *p); // ec_jacobian_to_affine_batch converts |num| points in |in| from Jacobian // coordinates to affine coordinates and writes the results to |out|. It returns // one on success and zero if any of the input points were infinity. // // This function is not implemented for all curves. Add implementations as // needed. int ec_jacobian_to_affine_batch(const EC_GROUP *group, EC_AFFINE *out, const EC_JACOBIAN *in, size_t num); // ec_point_set_affine_coordinates sets |out|'s to a point with affine // coordinates |x| and |y|. It returns one if the point is on the curve and // zero otherwise. If the point is not on the curve, the value of |out| is // undefined. int ec_point_set_affine_coordinates(const EC_GROUP *group, EC_AFFINE *out, const EC_FELEM *x, const EC_FELEM *y); // ec_point_mul_no_self_test does the same as |EC_POINT_mul|, but doesn't try to // run the self-test first. This is for use in the self tests themselves, to // prevent an infinite loop. int ec_point_mul_no_self_test(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx); // ec_point_mul_scalar sets |r| to |p| * |scalar|. Both inputs are considered // secret. int ec_point_mul_scalar(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *p, const EC_SCALAR *scalar); // ec_point_mul_scalar_base sets |r| to generator * |scalar|. |scalar| is // treated as secret. int ec_point_mul_scalar_base(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *scalar); // ec_point_mul_scalar_batch sets |r| to |p0| * |scalar0| + |p1| * |scalar1| + // |p2| * |scalar2|. |p2| may be NULL to skip that term. // // The inputs are treated as secret, however, this function leaks information // about whether intermediate computations add a point to itself. Callers must // ensure that discrete logs between |p0|, |p1|, and |p2| are uniformly // distributed and independent of the scalars, which should be uniformly // selected and not under the attackers control. This ensures the doubling case // will occur with negligible probability. // // This function is not implemented for all curves. Add implementations as // needed. // // TODO(davidben): This function does not use base point tables. For now, it is // only used with the generic |EC_GFp_mont_method| implementation which has // none. If generalizing to tuned curves, this may be useful. However, we still // must double up to the least efficient input, so precomputed tables can only // save table setup and allow a wider window size. int ec_point_mul_scalar_batch(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *p0, const EC_SCALAR *scalar0, const EC_JACOBIAN *p1, const EC_SCALAR *scalar1, const EC_JACOBIAN *p2, const EC_SCALAR *scalar2); #define EC_MONT_PRECOMP_COMB_SIZE … // An |EC_PRECOMP| stores precomputed information about a point, to optimize // repeated multiplications involving it. It is a union so different // |EC_METHOD|s can store different information in it. EC_PRECOMP; // ec_init_precomp precomputes multiples of |p| and writes the result to |out|. // It returns one on success and zero on error. The resulting table may be used // with |ec_point_mul_scalar_precomp|. This function will fail if |p| is the // point at infinity. // // This function is not implemented for all curves. Add implementations as // needed. int ec_init_precomp(const EC_GROUP *group, EC_PRECOMP *out, const EC_JACOBIAN *p); // ec_point_mul_scalar_precomp sets |r| to |p0| * |scalar0| + |p1| * |scalar1| + // |p2| * |scalar2|. |p1| or |p2| may be NULL to skip the corresponding term. // The points are represented as |EC_PRECOMP| and must be initialized with // |ec_init_precomp|. This function runs faster than |ec_point_mul_scalar_batch| // but requires setup work per input point, so it is only appropriate for points // which are used frequently. // // The inputs are treated as secret, however, this function leaks information // about whether intermediate computations add a point to itself. Callers must // ensure that discrete logs between |p0|, |p1|, and |p2| are uniformly // distributed and independent of the scalars, which should be uniformly // selected and not under the attackers control. This ensures the doubling case // will occur with negligible probability. // // This function is not implemented for all curves. Add implementations as // needed. // // TODO(davidben): This function does not use base point tables. For now, it is // only used with the generic |EC_GFp_mont_method| implementation which has // none. If generalizing to tuned curves, we should add a parameter for the base // point and arrange for the generic implementation to have base point tables // available. int ec_point_mul_scalar_precomp(const EC_GROUP *group, EC_JACOBIAN *r, const EC_PRECOMP *p0, const EC_SCALAR *scalar0, const EC_PRECOMP *p1, const EC_SCALAR *scalar1, const EC_PRECOMP *p2, const EC_SCALAR *scalar2); // ec_point_mul_scalar_public sets |r| to // generator * |g_scalar| + |p| * |p_scalar|. It 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_JACOBIAN *r, const EC_SCALAR *g_scalar, const EC_JACOBIAN *p, const EC_SCALAR *p_scalar); // ec_point_mul_scalar_public_batch sets |r| to the sum of generator * // |g_scalar| and |points[i]| * |scalars[i]| where |points| and |scalars| have // |num| elements. It assumes that the inputs are public so there is no concern // about leaking their values through timing. |g_scalar| may be NULL to skip // that term. // // This function is not implemented for all curves. Add implementations as // needed. int ec_point_mul_scalar_public_batch(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *g_scalar, const EC_JACOBIAN *points, const EC_SCALAR *scalars, size_t num); // ec_point_select, in constant time, sets |out| to |a| if |mask| is all ones // and |b| if |mask| is all zeros. void ec_point_select(const EC_GROUP *group, EC_JACOBIAN *out, BN_ULONG mask, const EC_JACOBIAN *a, const EC_JACOBIAN *b); // ec_affine_select behaves like |ec_point_select| but acts on affine points. void ec_affine_select(const EC_GROUP *group, EC_AFFINE *out, BN_ULONG mask, const EC_AFFINE *a, const EC_AFFINE *b); // ec_precomp_select behaves like |ec_point_select| but acts on |EC_PRECOMP|. void ec_precomp_select(const EC_GROUP *group, EC_PRECOMP *out, BN_ULONG mask, const EC_PRECOMP *a, const EC_PRECOMP *b); // ec_cmp_x_coordinate compares the x (affine) coordinate of |p|, mod the group // order, with |r|. It returns one if the values match and zero if |p| is the // point at infinity of the values do not match. |p| is treated as public. int ec_cmp_x_coordinate(const EC_GROUP *group, const EC_JACOBIAN *p, const EC_SCALAR *r); // ec_get_x_coordinate_as_scalar sets |*out| to |p|'s x-coordinate, modulo // |group->order|. It returns one on success and zero if |p| is the point at // infinity. int ec_get_x_coordinate_as_scalar(const EC_GROUP *group, EC_SCALAR *out, const EC_JACOBIAN *p); // ec_get_x_coordinate_as_bytes writes |p|'s affine x-coordinate to |out|, which // must have at must |max_out| bytes. It sets |*out_len| to the number of bytes // written. The value is written big-endian and zero-padded to the size of the // field. This function returns one on success and zero on failure. int ec_get_x_coordinate_as_bytes(const EC_GROUP *group, uint8_t *out, size_t *out_len, size_t max_out, const EC_JACOBIAN *p); // ec_point_byte_len returns the number of bytes in the byte representation of // a non-infinity point in |group|, encoded according to |form|, or zero if // |form| is invalid. size_t ec_point_byte_len(const EC_GROUP *group, point_conversion_form_t form); // ec_point_to_bytes encodes |point| according to |form| and writes the result // |buf|. It returns the size of the output on success or zero on error. At most // |max_out| bytes will be written. The buffer should be at least // |ec_point_byte_len| long to guarantee success. size_t ec_point_to_bytes(const EC_GROUP *group, const EC_AFFINE *point, point_conversion_form_t form, uint8_t *buf, size_t max_out); // ec_point_from_uncompressed parses |in| as a point in uncompressed form and // sets the result to |out|. It returns one on success and zero if the input was // invalid. int ec_point_from_uncompressed(const EC_GROUP *group, EC_AFFINE *out, const uint8_t *in, size_t len); // ec_set_to_safe_point sets |out| to an arbitrary point on |group|, either the // generator or the point at infinity. This is used to guard against callers of // external APIs not checking the return value. void ec_set_to_safe_point(const EC_GROUP *group, EC_JACOBIAN *out); // ec_affine_jacobian_equal returns one if |a| and |b| represent the same point // and zero otherwise. It treats both inputs as secret. int ec_affine_jacobian_equal(const EC_GROUP *group, const EC_AFFINE *a, const EC_JACOBIAN *b); // Implementation details. struct ec_method_st { … } /* EC_METHOD */; const EC_METHOD *EC_GFp_mont_method(void); struct ec_point_st { … } /* EC_POINT */; struct ec_group_st { … } /* EC_GROUP */; EC_GROUP *ec_group_new(const EC_METHOD *meth, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); void ec_GFp_mont_mul(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *p, const EC_SCALAR *scalar); void ec_GFp_mont_mul_base(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *scalar); void ec_GFp_mont_mul_batch(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *p0, const EC_SCALAR *scalar0, const EC_JACOBIAN *p1, const EC_SCALAR *scalar1, const EC_JACOBIAN *p2, const EC_SCALAR *scalar2); int ec_GFp_mont_init_precomp(const EC_GROUP *group, EC_PRECOMP *out, const EC_JACOBIAN *p); void ec_GFp_mont_mul_precomp(const EC_GROUP *group, EC_JACOBIAN *r, const EC_PRECOMP *p0, const EC_SCALAR *scalar0, const EC_PRECOMP *p1, const EC_SCALAR *scalar1, const EC_PRECOMP *p2, const EC_SCALAR *scalar2); void ec_GFp_mont_felem_reduce(const EC_GROUP *group, EC_FELEM *out, const BN_ULONG *words, size_t num); void ec_GFp_mont_felem_exp(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, const BN_ULONG *exp, size_t num_exp); // ec_compute_wNAF writes the modified width-(w+1) Non-Adjacent Form (wNAF) of // |scalar| to |out|. |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. void ec_compute_wNAF(const EC_GROUP *group, int8_t *out, const EC_SCALAR *scalar, size_t bits, int w); int ec_GFp_mont_mul_public_batch(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *g_scalar, const EC_JACOBIAN *points, const EC_SCALAR *scalars, size_t num); // method functions in simple.c 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); void ec_GFp_simple_point_init(EC_JACOBIAN *); void ec_GFp_simple_point_copy(EC_JACOBIAN *, const EC_JACOBIAN *); void ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_JACOBIAN *); void ec_GFp_mont_add(const EC_GROUP *, EC_JACOBIAN *r, const EC_JACOBIAN *a, const EC_JACOBIAN *b); void ec_GFp_mont_dbl(const EC_GROUP *, EC_JACOBIAN *r, const EC_JACOBIAN *a); void ec_GFp_simple_invert(const EC_GROUP *, EC_JACOBIAN *); int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_JACOBIAN *); int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_JACOBIAN *); int ec_GFp_simple_points_equal(const EC_GROUP *, const EC_JACOBIAN *a, const EC_JACOBIAN *b); void ec_simple_scalar_inv0_montgomery(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a); int ec_simple_scalar_to_montgomery_inv_vartime(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a); int ec_GFp_simple_cmp_x_coordinate(const EC_GROUP *group, const EC_JACOBIAN *p, const EC_SCALAR *r); void ec_GFp_simple_felem_to_bytes(const EC_GROUP *group, uint8_t *out, size_t *out_len, const EC_FELEM *in); int ec_GFp_simple_felem_from_bytes(const EC_GROUP *group, EC_FELEM *out, const uint8_t *in, size_t len); // method functions in montgomery.c void ec_GFp_mont_felem_mul(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a, const EC_FELEM *b); void ec_GFp_mont_felem_sqr(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a); void ec_GFp_mont_felem_to_bytes(const EC_GROUP *group, uint8_t *out, size_t *out_len, const EC_FELEM *in); int ec_GFp_mont_felem_from_bytes(const EC_GROUP *group, EC_FELEM *out, const uint8_t *in, size_t len); void ec_GFp_nistp_recode_scalar_bits(crypto_word_t *sign, crypto_word_t *digit, crypto_word_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. EC_WRAPPED_SCALAR; struct ec_key_st { … } /* EC_KEY */; #if defined(__cplusplus) } // extern C #endif #endif // OPENSSL_HEADER_EC_INTERNAL_H
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