/* crypto/ec/ec_lcl.h */ /* * Originally written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== * Copyright (c) 1998-2010 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. * */ #include <stdlib.h> #include <openssl/obj_mac.h> #include <openssl/ec.h> #include <openssl/bn.h> #if defined(__SUNPRO_C) # if __SUNPRO_C >= 0x520 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE) # endif #endif /* Use default functions for poin2oct, oct2point and compressed coordinates */ #define EC_FLAGS_DEFAULT_OCT 0x1 /* * Structure details are not part of the exported interface, so all this may * change in future versions. */ struct ec_method_st { /* Various method flags */ int flags; /* used by EC_METHOD_get_field_type: */ int field_type; /* a NID */ /* * 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 *); /* e.g. to Montgomery */ int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */ int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *); } /* EC_METHOD */ ; typedef struct ec_extra_data_st { struct ec_extra_data_st *next; void *data; void *(*dup_func) (void *); void (*free_func) (void *); void (*clear_free_func) (void *); } EC_EXTRA_DATA; /* used in EC_GROUP */ struct ec_group_st { const EC_METHOD *meth; EC_POINT *generator; /* optional */ BIGNUM order, cofactor; int curve_name; /* optional NID for named curve */ int asn1_flag; /* flag to control the asn1 encoding */ /* * Kludge: upper bit of ans1_flag is used to denote structure * version. Is set, then last field is present. This is done * for interoperation with FIPS code. */ #define EC_GROUP_ASN1_FLAG_MASK 0x7fffffff #define EC_GROUP_VERSION(p) (p->asn1_flag&~EC_GROUP_ASN1_FLAG_MASK) point_conversion_form_t asn1_form; unsigned char *seed; /* optional seed for parameters (appears in * ASN1) */ size_t seed_len; EC_EXTRA_DATA *extra_data; /* linked list */ /* * The following members are handled by the method functions, even if * they appear generic */ /* * 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. */ BIGNUM field; /* * 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. */ int poly[6]; /* * 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. */ BIGNUM a, b; /* enable optimized point arithmetics for special case */ int a_is_minus3; /* method-specific (e.g., Montgomery structure) */ void *field_data1; /* method-specific */ void *field_data2; /* method-specific */ int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); BN_MONT_CTX *mont_data; /* data for ECDSA inverse */ } /* EC_GROUP */ ; 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; EC_EXTRA_DATA *method_data; } /* EC_KEY */ ; /* * Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs * only (with visibility limited to 'package' level for now). We use the * function pointers as index for retrieval; this obviates global * ex_data-style index tables. */ int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data, void *(*dup_func) (void *), void (*free_func) (void *), void (*clear_free_func) (void *)); void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, void *(*dup_func) (void *), void (*free_func) (void *), void (*clear_free_func) (void *)); void EC_EX_DATA_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *), void (*free_func) (void *), void (*clear_free_func) (void *)); void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *), void (*free_func) (void *), void (*clear_free_func) (void *)); void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **); void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **); 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 */ ; /* * method functions in ec_mult.c (ec_lib.c uses these as defaults if * group->method->mul is 0) */ 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 ecp_smpl.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 *); size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, unsigned char *buf, size_t len, BN_CTX *); int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, const unsigned char *buf, size_t len, 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 ecp_mont.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 *); /* method functions in ecp_nist.c */ int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* method functions in ec2_smpl.c */ int ec_GF2m_simple_group_init(EC_GROUP *); void ec_GF2m_simple_group_finish(EC_GROUP *); void ec_GF2m_simple_group_clear_finish(EC_GROUP *); int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); int ec_GF2m_simple_group_get_degree(const EC_GROUP *); int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); int ec_GF2m_simple_point_init(EC_POINT *); void ec_GF2m_simple_point_finish(EC_POINT *); void ec_GF2m_simple_point_clear_finish(EC_POINT *); int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, const BIGNUM *x, const BIGNUM *y, BN_CTX *); int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *, BIGNUM *x, BIGNUM *y, BN_CTX *); int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, const BIGNUM *x, int y_bit, BN_CTX *); size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, unsigned char *buf, size_t len, BN_CTX *); int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, const unsigned char *buf, size_t len, BN_CTX *); int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); /* method functions in ec2_mult.c */ int ec_GF2m_simple_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_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GF2m_have_precompute_mult(const EC_GROUP *group); #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 /* method functions in ecp_nistp224.c */ int ec_GFp_nistp224_group_init(EC_GROUP *group); int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); int ec_GFp_nistp224_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_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); /* method functions in ecp_nistp256.c */ int ec_GFp_nistp256_group_init(EC_GROUP *group); int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); int ec_GFp_nistp256_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_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); /* method functions in ecp_nistp521.c */ int ec_GFp_nistp521_group_init(EC_GROUP *group); int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); int ec_GFp_nistp521_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_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); /* utility functions in ecp_nistputil.c */ void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, size_t felem_size, void *tmp_felems, void (*felem_one) (void *out), int (*felem_is_zero) (const void *in), void (*felem_assign) (void *out, const void *in), void (*felem_square) (void *out, const void *in), void (*felem_mul) (void *out, const void *in1, const void *in2), void (*felem_inv) (void *out, const void *in), void (*felem_contract) (void *out, const void *in)); void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in); #endif int ec_precompute_mont_data(EC_GROUP *); #ifdef ECP_NISTZ256_ASM /** Returns GFp methods using montgomery multiplication, with x86-64 optimized * P256. See http://eprint.iacr.org/2013/816. * \return EC_METHOD object */ const EC_METHOD *EC_GFp_nistz256_method(void); #endif #ifdef OPENSSL_FIPS EC_GROUP *FIPS_ec_group_new_curve_gfp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); EC_GROUP *FIPS_ec_group_new_curve_gf2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); EC_GROUP *FIPS_ec_group_new_by_curve_name(int nid); #endif