| /* 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/ec.h> |
| #include <openssl/ex_data.h> |
| #include <openssl/type_check.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 66 |
| #define EC_MAX_WORDS ((EC_MAX_BYTES + BN_BYTES - 1) / BN_BYTES) |
| |
| OPENSSL_STATIC_ASSERT(EC_MAX_WORDS <= BN_SMALL_MAX_WORDS, |
| "bn_*_small functions not usable"); |
| |
| |
| // 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. |
| typedef union { |
| // bytes is the representation of the scalar in little-endian order. |
| uint8_t bytes[EC_MAX_BYTES]; |
| BN_ULONG words[EC_MAX_WORDS]; |
| } 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. |
| 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_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. |
| typedef union { |
| // bytes is the representation of the field element in little-endian order. |
| uint8_t bytes[EC_MAX_BYTES]; |
| BN_ULONG words[EC_MAX_WORDS]; |
| } EC_FELEM; |
| |
| // 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. |
| |
| // An EC_RAW_POINT represents an elliptic curve point. 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. |
| typedef struct { |
| EC_FELEM X, Y, Z; |
| // X, Y, and Z are Jacobian projective coordinates. They represent |
| // (X/Z^2, Y/Z^3) if Z != 0 and the point at infinity otherwise. |
| } EC_RAW_POINT; |
| |
| // 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_RAW_POINT *out, |
| const EC_FELEM *x, const EC_FELEM *y); |
| |
| // ec_point_mul_scalar sets |r| to |p| * |scalar|. Both inputs are considered |
| // secret. |
| int ec_point_mul_scalar(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_RAW_POINT *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_RAW_POINT *r, |
| const EC_SCALAR *scalar); |
| |
| // 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_RAW_POINT *r, |
| const EC_SCALAR *g_scalar, |
| const EC_RAW_POINT *p, |
| const EC_SCALAR *p_scalar); |
| |
| // 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_RAW_POINT *out, BN_ULONG mask, |
| const EC_RAW_POINT *a, const EC_RAW_POINT *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. |
| int ec_cmp_x_coordinate(const EC_GROUP *group, const EC_RAW_POINT *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_RAW_POINT *p); |
| |
| // ec_point_get_affine_coordinate_bytes writes |p|'s affine coordinates to |
| // |out_x| and |out_y|, each of which must have at must |max_out| bytes. It sets |
| // |*out_len| to the number of bytes written in each buffer. Coordinates are |
| // written big-endian and zero-padded to the size of the field. |
| // |
| // Either of |out_x| or |out_y| may be NULL to omit that coordinate. This |
| // function returns one on success and zero on failure. |
| int ec_point_get_affine_coordinate_bytes(const EC_GROUP *group, uint8_t *out_x, |
| uint8_t *out_y, size_t *out_len, |
| size_t max_out, const EC_RAW_POINT *p); |
| |
| // ec_point_to_bytes behaves like |EC_POINT_point2oct| but takes an |
| // |EC_RAW_POINT|. |
| OPENSSL_EXPORT size_t ec_point_to_bytes(const EC_GROUP *group, |
| const EC_RAW_POINT *point, |
| point_conversion_form_t form, |
| uint8_t *buf, size_t len); |
| |
| // 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_RAW_POINT *out, |
| const uint8_t *in, size_t len); |
| |
| |
| // Implementation details. |
| |
| 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 *); |
| |
| // point_get_affine_coordinates sets |*x| and |*y| to the affine coordinates |
| // of |p|. Either |x| or |y| may be NULL to omit it. It returns one on success |
| // and zero if |p| is the point at infinity. |
| // |
| // Note: unlike |EC_FELEM|s used as intermediate values internal to the |
| // |EC_METHOD|, |*x| and |*y| are not encoded in Montgomery form. |
| int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_RAW_POINT *p, |
| EC_FELEM *x, EC_FELEM *y); |
| |
| // add sets |r| to |a| + |b|. |
| void (*add)(const EC_GROUP *group, EC_RAW_POINT *r, const EC_RAW_POINT *a, |
| const EC_RAW_POINT *b); |
| // dbl sets |r| to |a| + |a|. |
| void (*dbl)(const EC_GROUP *group, EC_RAW_POINT *r, const EC_RAW_POINT *a); |
| |
| // mul sets |r| to |scalar|*|p|. |
| void (*mul)(const EC_GROUP *group, EC_RAW_POINT *r, const EC_RAW_POINT *p, |
| const EC_SCALAR *scalar); |
| // mul_base sets |r| to |scalar|*generator. |
| void (*mul_base)(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_SCALAR *scalar); |
| // mul_public sets |r| to |g_scalar|*generator + |p_scalar|*|p|. It assumes |
| // that the inputs are public so there is no concern about leaking their |
| // values through timing. |
| void (*mul_public)(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, |
| const EC_SCALAR *p_scalar); |
| |
| // felem_mul and felem_sqr implement multiplication and squaring, |
| // respectively, so that the generic |EC_POINT_add| and |EC_POINT_dbl| |
| // implementations can work both with |EC_GFp_mont_method| and the tuned |
| // operations. |
| // |
| // TODO(davidben): This constrains |EC_FELEM|'s internal representation, adds |
| // many indirect calls in the middle of the generic code, and a bunch of |
| // conversions. If p224-64.c were easily convertable to Montgomery form, we |
| // could say |EC_FELEM| is always in Montgomery form. If we routed the rest of |
| // simple.c to |EC_METHOD|, we could give |EC_POINT| an |EC_METHOD|-specific |
| // representation and say |EC_FELEM| is purely a |EC_GFp_mont_method| type. |
| void (*felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a, |
| const EC_FELEM *b); |
| void (*felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a); |
| |
| void (*felem_to_bytes)(const EC_GROUP *group, uint8_t *out, size_t *out_len, |
| const EC_FELEM *in); |
| int (*felem_from_bytes)(const EC_GROUP *group, EC_FELEM *out, |
| const uint8_t *in, size_t len); |
| |
| // felem_reduce sets |out| to |words|, reduced modulo the field size, p. |
| // |words| must be less than p^2. |num| must be at most twice the width of p. |
| // This function treats |words| as secret. |
| // |
| // This function is only used in hash-to-curve and may be omitted in curves |
| // that do not support it. |
| void (*felem_reduce)(const EC_GROUP *group, EC_FELEM *out, |
| const BN_ULONG *words, size_t num); |
| |
| // felem_exp sets |out| to |a|^|exp|. It treats |a| is secret but |exp| as |
| // public. |
| // |
| // This function is used in hash-to-curve and may be NULL in curves not used |
| // with hash-to-curve. |
| void (*felem_exp)(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, |
| const BN_ULONG *exp, size_t num_exp); |
| |
| // scalar_inv0_montgomery implements |ec_scalar_inv0_montgomery|. |
| void (*scalar_inv0_montgomery)(const EC_GROUP *group, EC_SCALAR *out, |
| const EC_SCALAR *in); |
| |
| // scalar_to_montgomery_inv_vartime implements |
| // |ec_scalar_to_montgomery_inv_vartime|. |
| int (*scalar_to_montgomery_inv_vartime)(const EC_GROUP *group, EC_SCALAR *out, |
| const EC_SCALAR *in); |
| |
| // 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. |
| int (*cmp_x_coordinate)(const EC_GROUP *group, const EC_RAW_POINT *p, |
| const EC_SCALAR *r); |
| } /* 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. |
| |
| EC_FELEM a, b; // Curve coefficients. |
| |
| // a_is_minus3 is one if |a| is -3 mod |field| and zero otherwise. Point |
| // arithmetic is optimized for -3. |
| int a_is_minus3; |
| |
| // field_greater_than_order is one if |field| is greate than |order| and zero |
| // otherwise. |
| int field_greater_than_order; |
| |
| // field_minus_order, if |field_greater_than_order| is true, is |field| minus |
| // |order| represented as an |EC_FELEM|. Otherwise, it is zero. |
| // |
| // Note: unlike |EC_FELEM|s used as intermediate values internal to the |
| // |EC_METHOD|, this value is not encoded in Montgomery form. |
| EC_FELEM field_minus_order; |
| |
| CRYPTO_refcount_t references; |
| |
| BN_MONT_CTX *mont; // Montgomery structure. |
| |
| EC_FELEM 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; |
| // raw is the group-specific point data. Functions that take |EC_POINT| |
| // typically check consistency with |EC_GROUP| while functions that take |
| // |EC_RAW_POINT| do not. Thus accesses to this field should be externally |
| // checked for consistency. |
| EC_RAW_POINT raw; |
| } /* EC_POINT */; |
| |
| EC_GROUP *ec_group_new(const EC_METHOD *meth); |
| |
| void ec_GFp_mont_mul(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_RAW_POINT *p, const EC_SCALAR *scalar); |
| void ec_GFp_mont_mul_base(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_SCALAR *scalar); |
| |
| // 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); |
| |
| void ec_GFp_mont_mul_public(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, |
| const EC_SCALAR *p_scalar); |
| |
| // 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); |
| void ec_GFp_simple_point_init(EC_RAW_POINT *); |
| void ec_GFp_simple_point_copy(EC_RAW_POINT *, const EC_RAW_POINT *); |
| void ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_RAW_POINT *); |
| void ec_GFp_mont_add(const EC_GROUP *, EC_RAW_POINT *r, const EC_RAW_POINT *a, |
| const EC_RAW_POINT *b); |
| void ec_GFp_mont_dbl(const EC_GROUP *, EC_RAW_POINT *r, const EC_RAW_POINT *a); |
| void ec_GFp_simple_invert(const EC_GROUP *, EC_RAW_POINT *); |
| int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_RAW_POINT *); |
| int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_RAW_POINT *); |
| int ec_GFp_simple_points_equal(const EC_GROUP *, const EC_RAW_POINT *a, |
| const EC_RAW_POINT *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_RAW_POINT *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 |
| 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 *); |
| 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(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 |