| /* 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> |
| |
| #if defined(__cplusplus) |
| extern "C" { |
| #endif |
| |
| |
| /* Use default functions for poin2oct, oct2point and compressed coordinates */ |
| #define EC_FLAGS_DEFAULT_OCT 0x1 |
| |
| typedef struct ec_method_st EC_METHOD; |
| |
| struct ec_method_st { |
| /* Various method flags */ |
| int flags; |
| |
| /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */ |
| int (*group_init)(EC_GROUP *); |
| void (*group_finish)(EC_GROUP *); |
| void (*group_clear_finish)(EC_GROUP *); |
| int (*group_copy)(EC_GROUP *, const EC_GROUP *); |
| |
| /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */ |
| /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ |
| int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *); |
| int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, |
| BN_CTX *); |
| |
| /* used by EC_GROUP_get_degree: */ |
| int (*group_get_degree)(const EC_GROUP *); |
| |
| /* used by EC_GROUP_check: */ |
| int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *); |
| |
| /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */ |
| int (*point_init)(EC_POINT *); |
| void (*point_finish)(EC_POINT *); |
| void (*point_clear_finish)(EC_POINT *); |
| int (*point_copy)(EC_POINT *, const EC_POINT *); |
| |
| /* used by EC_POINT_set_to_infinity, |
| * EC_POINT_set_Jprojective_coordinates_GFp, |
| * EC_POINT_get_Jprojective_coordinates_GFp, |
| * EC_POINT_set_affine_coordinates_GFp, ..._GF2m, |
| * EC_POINT_get_affine_coordinates_GFp, ..._GF2m, |
| * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m: |
| */ |
| int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *); |
| int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, const BIGNUM *y, |
| const BIGNUM *z, BN_CTX *); |
| int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, |
| const EC_POINT *, BIGNUM *x, |
| BIGNUM *y, BIGNUM *z, BN_CTX *); |
| int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, const BIGNUM *y, |
| BN_CTX *); |
| int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *, |
| BIGNUM *x, BIGNUM *y, BN_CTX *); |
| int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, int y_bit, BN_CTX *); |
| |
| /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ |
| size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, |
| point_conversion_form_t form, unsigned char *buf, |
| size_t len, BN_CTX *); |
| int (*oct2point)(const EC_GROUP *, EC_POINT *, const unsigned char *buf, |
| size_t len, BN_CTX *); |
| |
| /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ |
| int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, |
| const EC_POINT *b, BN_CTX *); |
| int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); |
| int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *); |
| |
| /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */ |
| int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *); |
| int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *); |
| int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, |
| BN_CTX *); |
| |
| /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ |
| int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *); |
| int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT * [], |
| BN_CTX *); |
| |
| /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, |
| * EC_POINT_have_precompute_mult |
| * (default implementations are used if the 'mul' pointer is 0): */ |
| int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *); |
| int (*precompute_mult)(EC_GROUP *group, BN_CTX *); |
| int (*have_precompute_mult)(const EC_GROUP *group); |
| |
| |
| /* internal functions */ |
| |
| /* 'field_mul', 'field_sqr', and 'field_div' 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_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, |
| const BIGNUM *b, 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 */ |
| int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *); |
| } /* EC_METHOD */; |
| |
| const EC_METHOD* EC_GFp_mont_method(void); |
| |
| struct ec_pre_comp_st; |
| void ec_pre_comp_free(struct ec_pre_comp_st *pre_comp); |
| void *ec_pre_comp_dup(struct ec_pre_comp_st *pre_comp); |
| |
| struct ec_group_st { |
| const EC_METHOD *meth; |
| |
| EC_POINT *generator; /* optional */ |
| BIGNUM order, cofactor; |
| |
| int curve_name; /* optional NID for named curve */ |
| |
| struct ec_pre_comp_st *pre_comp; |
| |
| /* The following members are handled by the method functions, |
| * even if they appear generic */ |
| |
| BIGNUM field; /* Field specification. |
| * For curves over GF(p), this is the modulus; |
| * for curves over GF(2^m), this is the |
| * irreducible polynomial defining the field. */ |
| |
| int poly[6]; /* Field specification for curves over GF(2^m). |
| * The irreducible f(t) is then of the form: |
| * t^poly[0] + t^poly[1] + ... + t^poly[k] |
| * where m = poly[0] > poly[1] > ... > poly[k] = 0. |
| * The array is terminated with poly[k+1]=-1. |
| * All elliptic curve irreducibles have at most 5 |
| * non-zero terms. */ |
| |
| BIGNUM a, b; /* Curve coefficients. |
| * (Here the assumption is that BIGNUMs can be used |
| * or abused for all kinds of fields, not just GF(p).) |
| * For characteristic > 3, the curve is defined |
| * by a Weierstrass equation of the form |
| * y^2 = x^3 + a*x + b. |
| * For characteristic 2, the curve is defined by |
| * an equation of the form |
| * y^2 + x*y = x^3 + a*x^2 + b. */ |
| |
| int a_is_minus3; /* enable optimized point arithmetics for special case */ |
| |
| void *field_data1; /* method-specific (e.g., Montgomery structure) */ |
| void *field_data2; /* method-specific */ |
| int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, |
| BN_CTX *); /* method-specific */ |
| } /* EC_GROUP */; |
| |
| struct ec_point_st { |
| const EC_METHOD *meth; |
| |
| /* All members except 'meth' are handled by the method functions, |
| * even if they appear generic */ |
| |
| BIGNUM X; |
| BIGNUM Y; |
| BIGNUM Z; /* Jacobian projective coordinates: |
| * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ |
| int Z_is_one; /* enable optimized point arithmetics for special case */ |
| } /* EC_POINT */; |
| |
| EC_GROUP *ec_group_new(const EC_METHOD *meth); |
| |
| int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *); |
| int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); |
| int ec_wNAF_have_precompute_mult(const EC_GROUP *group); |
| |
| /* method functions in simple.c */ |
| int ec_GFp_simple_group_init(EC_GROUP *); |
| void ec_GFp_simple_group_finish(EC_GROUP *); |
| void ec_GFp_simple_group_clear_finish(EC_GROUP *); |
| int ec_GFp_simple_group_copy(EC_GROUP *, const 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 *); |
| int ec_GFp_simple_group_get_degree(const EC_GROUP *); |
| int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); |
| int ec_GFp_simple_point_init(EC_POINT *); |
| void ec_GFp_simple_point_finish(EC_POINT *); |
| void ec_GFp_simple_point_clear_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_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, |
| const BIGNUM *y, |
| const BIGNUM *z, BN_CTX *); |
| int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, |
| const EC_POINT *, BIGNUM *x, |
| BIGNUM *y, BIGNUM *z, |
| BN_CTX *); |
| 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_point_get_affine_coordinates(const EC_GROUP *, |
| const EC_POINT *, BIGNUM *x, |
| BIGNUM *y, BN_CTX *); |
| int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, int y_bit, |
| 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 *); |
| void ec_GFp_mont_group_clear_finish(EC_GROUP *); |
| int ec_GFp_mont_group_copy(EC_GROUP *, const 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 *); |
| int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); |
| |
| int ec_point_set_Jprojective_coordinates_GFp(const EC_GROUP *group, |
| EC_POINT *point, const BIGNUM *x, |
| const BIGNUM *y, const BIGNUM *z, |
| BN_CTX *ctx); |
| |
| struct ec_key_st { |
| int version; |
| |
| EC_GROUP *group; |
| |
| EC_POINT *pub_key; |
| BIGNUM *priv_key; |
| |
| unsigned int enc_flag; |
| point_conversion_form_t conv_form; |
| |
| int references; |
| int flags; |
| |
| ECDSA_METHOD *ecdsa_meth; |
| |
| CRYPTO_EX_DATA ex_data; |
| } /* EC_KEY */; |
| |
| /* curve_data contains data about a built-in elliptic curve. */ |
| struct curve_data { |
| /* 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; |
| /* cofactor is the cofactor of the group (i.e. the number of elements in the |
| * group divided by the size of the main subgroup. */ |
| uint8_t cofactor; /* promoted to BN_ULONG */ |
| /* data 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 data[]; |
| }; |
| |
| struct built_in_curve { |
| int nid; |
| const struct curve_data *data; |
| const EC_METHOD *(*method)(void); |
| }; |
| |
| /* OPENSSL_built_in_curves is terminated with an entry where |nid| is |
| * |NID_undef|. */ |
| extern const struct built_in_curve OPENSSL_built_in_curves[]; |
| |
| #if defined(__cplusplus) |
| } /* extern C */ |
| #endif |
| |
| #endif /* OPENSSL_HEADER_EC_INTERNAL_H */ |
