/*

 * Copyright 2001-2019 The OpenSSL Project Authors. All Rights Reserved.

 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved

 *

 * Licensed under the OpenSSL license (the "License").  You may not use

 * this file except in compliance with the License.  You can obtain a copy

 * in the file LICENSE in the source distribution or at

 * https://www.openssl.org/source/license.html

 */

#include <stdlib.h>

#include <openssl/obj_mac.h>

#include <openssl/ec.h>

#include <openssl/bn.h>

#include "internal/refcount.h"

#include "crypto/ec.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

/* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */

#define EC_FLAGS_CUSTOM_CURVE   0x2

/* Curve does not support signing operations */

#define EC_FLAGS_NO_SIGN        0x4

/*

 * 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, EC_GROUP_get_curve: */

    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 *);

    int (*group_order_bits) (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,

     * EC_POINT_get_affine_coordinates,

     * EC_POINT_set_compressed_coordinates:

     */

    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):

     */

    /*-

     * mul() calculates the value

     *

     *   r := generator * scalar

     *        + points[0] * scalars[0]

     *        + ...

     *        + points[num-1] * scalars[num-1].

     *

     * For a fixed point multiplication (scalar != NULL, num == 0)

     * or a variable point multiplication (scalar == NULL, num == 1),

     * mul() must use a constant time algorithm: in both cases callers

     * should provide an input scalar (either scalar or scalars[0])

     * in the range [0, ec_group_order); for robustness, implementers

     * should handle the case when the scalar has not been reduced, but

     * may treat it as an unusual input, without any constant-timeness

     * guarantee.

     */

    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 *);

    /*-

     * 'field_inv' computes the multiplicative inverse of a in the field,

     * storing the result in r.

     *

     * If 'a' is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error.

     */

    int (*field_inv) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 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 *);

    /* private key operations */

    size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len);

    int (*oct2priv)(EC_KEY *eckey, const unsigned char *buf, size_t len);

    int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key);

    int (*keygen)(EC_KEY *eckey);

    int (*keycheck)(const EC_KEY *eckey);

    int (*keygenpub)(EC_KEY *eckey);

    int (*keycopy)(EC_KEY *dst, const EC_KEY *src);

    void (*keyfinish)(EC_KEY *eckey);

    /* custom ECDH operation */

    int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen,

                            const EC_POINT *pub_key, const EC_KEY *ecdh);

    /* custom ECDSA */

    int (*ecdsa_sign_setup)(EC_KEY *eckey, BN_CTX *ctx, BIGNUM **kinvp,

                            BIGNUM **rp);

    ECDSA_SIG *(*ecdsa_sign_sig)(const unsigned char *dgst, int dgstlen,

                                 const BIGNUM *kinv, const BIGNUM *r,

                                 EC_KEY *eckey);

    int (*ecdsa_verify_sig)(const unsigned char *dgst, int dgstlen,

                            const ECDSA_SIG *sig, EC_KEY *eckey);

    /* Inverse modulo order */

    int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r,

                                 const BIGNUM *x, BN_CTX *);

    int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);

    int (*ladder_pre)(const EC_GROUP *group,

                      EC_POINT *r, EC_POINT *s,

                      EC_POINT *p, BN_CTX *ctx);

    int (*ladder_step)(const EC_GROUP *group,

                       EC_POINT *r, EC_POINT *s,

                       EC_POINT *p, BN_CTX *ctx);

    int (*ladder_post)(const EC_GROUP *group,

                       EC_POINT *r, EC_POINT *s,

                       EC_POINT *p, BN_CTX *ctx);

};

/*

 * Types and functions to manipulate pre-computed values.

 */

typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;

typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;

typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;

typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;

typedef struct ec_pre_comp_st EC_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 */

    int asn1_flag;              /* flag to control the asn1 encoding */

    int decoded_from_explicit_params; /* set if decoded from explicit

                                       * curve parameters encoding */

    point_conversion_form_t asn1_form;

    unsigned char *seed;        /* optional seed for parameters (appears in

                                 * ASN1) */

    size_t seed_len;

    /*

     * 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 *);

    /* data for ECDSA inverse */

    BN_MONT_CTX *mont_data;

    /*

     * Precomputed values for speed. The PCT_xxx names match the

     * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP

     * macros, below.

     */

    enum {

        PCT_none,

        PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256,

        PCT_ec

    } pre_comp_type;

    union {

        NISTP224_PRE_COMP *nistp224;

        NISTP256_PRE_COMP *nistp256;

        NISTP521_PRE_COMP *nistp521;

        NISTZ256_PRE_COMP *nistz256;

        EC_PRE_COMP *ec;

    } pre_comp;

};

#define SETPRECOMP(g, type, pre) \

    g->pre_comp_type = PCT_##type, g->pre_comp.type = pre

#define HAVEPRECOMP(g, type) \

    g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL

struct ec_key_st {

    const EC_KEY_METHOD *meth;

    ENGINE *engine;

    int version;

    EC_GROUP *group;

    EC_POINT *pub_key;

    BIGNUM *priv_key;

    unsigned int enc_flag;

    point_conversion_form_t conv_form;

    CRYPTO_REF_COUNT references;

    int flags;

    CRYPTO_EX_DATA ex_data;

    CRYPTO_RWLOCK *lock;

};

struct ec_point_st {

    const EC_METHOD *meth;

    /* NID for the curve if known */

    int curve_name;

    /*

     * 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 */

};

static ossl_inline int ec_point_is_compat(const EC_POINT *point,

                                          const EC_GROUP *group)

{

    if (group->meth != point->meth

        || (group->curve_name != 0

            && point->curve_name != 0

            && group->curve_name != point->curve_name))

        return 0;

    return 1;

}

NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);

NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);

NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);

NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);

NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);

EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);

void EC_pre_comp_free(EC_GROUP *group);

void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);

void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);

void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);

void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);

void EC_ec_pre_comp_free(EC_PRE_COMP *);

/*

 * 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 *);

int ec_GFp_simple_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,

                            BN_CTX *);

int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,

                                    BN_CTX *ctx);

int ec_GFp_simple_ladder_pre(const EC_GROUP *group,

                             EC_POINT *r, EC_POINT *s,

                             EC_POINT *p, BN_CTX *ctx);

int ec_GFp_simple_ladder_step(const EC_GROUP *group,

                              EC_POINT *r, EC_POINT *s,

                              EC_POINT *p, BN_CTX *ctx);

int ec_GFp_simple_ladder_post(const EC_GROUP *group,

                              EC_POINT *r, EC_POINT *s,

                              EC_POINT *p, BN_CTX *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_inv(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 *);

#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_group_simple_order_bits(const EC_GROUP *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 S390X_EC_ASM

const EC_METHOD *EC_GFp_s390x_nistp256_method(void);

const EC_METHOD *EC_GFp_s390x_nistp384_method(void);

const EC_METHOD *EC_GFp_s390x_nistp521_method(void);

#endif

size_t ec_key_simple_priv2oct(const EC_KEY *eckey,

                              unsigned char *buf, size_t len);

int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len);

int ec_key_simple_generate_key(EC_KEY *eckey);

int ec_key_simple_generate_public_key(EC_KEY *eckey);

int ec_key_simple_check_key(const EC_KEY *eckey);

int ec_curve_nid_from_params(const EC_GROUP *group, BN_CTX *ctx);

/* EC_METHOD definitions */

struct ec_key_method_st {

    const char *name;

    int32_t flags;

    int (*init)(EC_KEY *key);

    void (*finish)(EC_KEY *key);

    int (*copy)(EC_KEY *dest, const EC_KEY *src);

    int (*set_group)(EC_KEY *key, const EC_GROUP *grp);

    int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);

    int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);

    int (*keygen)(EC_KEY *key);

    int (*compute_key)(unsigned char **pout, size_t *poutlen,

                       const EC_POINT *pub_key, const EC_KEY *ecdh);

    int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char

                *sig, unsigned int *siglen, const BIGNUM *kinv,

                const BIGNUM *r, EC_KEY *eckey);

    int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,

                      BIGNUM **rp);

    ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,

                           const BIGNUM *in_kinv, const BIGNUM *in_r,

                           EC_KEY *eckey);

    int (*verify)(int type, const unsigned char *dgst, int dgst_len,

                  const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);

    int (*verify_sig)(const unsigned char *dgst, int dgst_len,

                      const ECDSA_SIG *sig, EC_KEY *eckey);

};

#define EC_KEY_METHOD_DYNAMIC   1

int ossl_ec_key_gen(EC_KEY *eckey);

int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,

                          const EC_POINT *pub_key, const EC_KEY *ecdh);

int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,

                            const EC_POINT *pub_key, const EC_KEY *ecdh);

struct ECDSA_SIG_st {

    BIGNUM *r;

    BIGNUM *s;

};

int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,

                          BIGNUM **rp);

int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,

                    unsigned char *sig, unsigned int *siglen,

                    const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);

ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,

                               const BIGNUM *in_kinv, const BIGNUM *in_r,

                               EC_KEY *eckey);

int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,

                      const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);

int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,

                          const ECDSA_SIG *sig, EC_KEY *eckey);

int ecdsa_simple_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,

                            BIGNUM **rp);

ECDSA_SIG *ecdsa_simple_sign_sig(const unsigned char *dgst, int dgst_len,

                                 const BIGNUM *in_kinv, const BIGNUM *in_r,

                                 EC_KEY *eckey);

int ecdsa_simple_verify_sig(const unsigned char *dgst, int dgst_len,

                            const ECDSA_SIG *sig, EC_KEY *eckey);

int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,

                 const uint8_t public_key[32], const uint8_t private_key[32]);

int ED25519_verify(const uint8_t *message, size_t message_len,

                   const uint8_t signature[64], const uint8_t public_key[32]);

void ED25519_public_from_private(uint8_t out_public_key[32],

                                 const uint8_t private_key[32]);

int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],

           const uint8_t peer_public_value[32]);

void X25519_public_from_private(uint8_t out_public_value[32],

                                const uint8_t private_key[32]);

/*-

 * This functions computes a single point multiplication over the EC group,

 * using, at a high level, a Montgomery ladder with conditional swaps, with

 * various timing attack defenses.

 *

 * It performs either a fixed point multiplication

 *          (scalar * generator)

 * when point is NULL, or a variable point multiplication

 *          (scalar * point)

 * when point is not NULL.

 *

 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all

 * constant time bets are off (where n is the cardinality of the EC group).

 *

 * This function expects `group->order` and `group->cardinality` to be well

 * defined and non-zero: it fails with an error code otherwise.

 *

 * NB: This says nothing about the constant-timeness of the ladder step

 * implementation (i.e., the default implementation is based on EC_POINT_add and

 * EC_POINT_dbl, which of course are not constant time themselves) or the

 * underlying multiprecision arithmetic.

 *

 * The product is stored in `r`.

 *

 * This is an internal function: callers are in charge of ensuring that the

 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.

 *

 * Returns 1 on success, 0 otherwise.

 */

int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,

                         const BIGNUM *scalar, const EC_POINT *point,

                         BN_CTX *ctx);

int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);

static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group,

                                           EC_POINT *r, EC_POINT *s,

                                           EC_POINT *p, BN_CTX *ctx)

{

    if (group->meth->ladder_pre != NULL)

        return group->meth->ladder_pre(group, r, s, p, ctx);

    if (!EC_POINT_copy(s, p)

        || !EC_POINT_dbl(group, r, s, ctx))

        return 0;

    return 1;

}

static ossl_inline int ec_point_ladder_step(const EC_GROUP *group,

                                            EC_POINT *r, EC_POINT *s,

                                            EC_POINT *p, BN_CTX *ctx)

{

    if (group->meth->ladder_step != NULL)

        return group->meth->ladder_step(group, r, s, p, ctx);

    if (!EC_POINT_add(group, s, r, s, ctx)

        || !EC_POINT_dbl(group, r, r, ctx))

        return 0;

    return 1;

}

static ossl_inline int ec_point_ladder_post(const EC_GROUP *group,

                                            EC_POINT *r, EC_POINT *s,

                                            EC_POINT *p, BN_CTX *ctx)

{

    if (group->meth->ladder_post != NULL)

        return group->meth->ladder_post(group, r, s, p, ctx);

    return 1;

}