/*

 * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.

 * Copyright 2015-2016 Cryptography Research, Inc.

 *

 * 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

 *

 * Originally written by Mike Hamburg

 */

#ifndef HEADER_POINT_448_H

# define HEADER_POINT_448_H

# include "curve448utils.h"

# include "field.h"

/* Comb config: number of combs, n, t, s. */

#define COMBS_N 5

#define COMBS_T 5

#define COMBS_S 18

/* Projective Niels coordinates */

typedef struct {

    gf a, b, c;

} niels_s, niels_t[1];

typedef struct {

    niels_t n;

    gf z;

} pniels_t[1];

/* Precomputed base */

struct curve448_precomputed_s {

    niels_t table[COMBS_N << (COMBS_T - 1)];

};

# define C448_SCALAR_LIMBS ((446-1)/C448_WORD_BITS+1)

/* The number of bits in a scalar */

# define C448_SCALAR_BITS 446

/* Number of bytes in a serialized scalar. */

# define C448_SCALAR_BYTES 56

/* X448 encoding ratio. */

# define X448_ENCODE_RATIO 2

/* Number of bytes in an x448 public key */

# define X448_PUBLIC_BYTES 56

/* Number of bytes in an x448 private key */

# define X448_PRIVATE_BYTES 56

/* Twisted Edwards extended homogeneous coordinates */

typedef struct curve448_point_s {

    gf x, y, z, t;

} curve448_point_t[1];

/* Precomputed table based on a point.  Can be trivial implementation. */

struct curve448_precomputed_s;

/* Precomputed table based on a point.  Can be trivial implementation. */

typedef struct curve448_precomputed_s curve448_precomputed_s;

/* Scalar is stored packed, because we don't need the speed. */

typedef struct curve448_scalar_s {

    c448_word_t limb[C448_SCALAR_LIMBS];

} curve448_scalar_t[1];

/* A scalar equal to 1. */

extern const curve448_scalar_t curve448_scalar_one;

/* A scalar equal to 0. */

extern const curve448_scalar_t curve448_scalar_zero;

/* The identity point on the curve. */

extern const curve448_point_t curve448_point_identity;

/* Precomputed table for the base point on the curve. */

extern const struct curve448_precomputed_s *curve448_precomputed_base;

extern const niels_t *curve448_wnaf_base;

/*

 * Read a scalar from wire format or from bytes.

 *

 * ser (in): Serialized form of a scalar.

 * out (out): Deserialized form.

 *

 * Returns:

 * C448_SUCCESS: The scalar was correctly encoded.

 * C448_FAILURE: The scalar was greater than the modulus, and has been reduced

 * modulo that modulus.

 */

c448_error_t curve448_scalar_decode(curve448_scalar_t out,

                                    const unsigned char ser[C448_SCALAR_BYTES]);

/*

 * Read a scalar from wire format or from bytes.  Reduces mod scalar prime.

 *

 * ser (in): Serialized form of a scalar.

 * ser_len (in): Length of serialized form.

 * out (out): Deserialized form.

 */

void curve448_scalar_decode_long(curve448_scalar_t out,

                                 const unsigned char *ser, size_t ser_len);

/*

 * Serialize a scalar to wire format.

 *

 * ser (out): Serialized form of a scalar.

 * s (in): Deserialized scalar.

 */

void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],

                            const curve448_scalar_t s);

/*

 * Add two scalars. |a|, |b| and |out| may alias each other.

 * 

 * a (in): One scalar.

 * b (in): Another scalar.

 * out (out): a+b.

 */

void curve448_scalar_add(curve448_scalar_t out,

                         const curve448_scalar_t a, const curve448_scalar_t b);

/*

 * Subtract two scalars.  |a|, |b| and |out| may alias each other.

 * a (in): One scalar.

 * b (in): Another scalar.

 * out (out): a-b.

 */

void curve448_scalar_sub(curve448_scalar_t out,

                         const curve448_scalar_t a, const curve448_scalar_t b);

/*

 * Multiply two scalars. |a|, |b| and |out| may alias each other.

 * 

 * a (in): One scalar.

 * b (in): Another scalar.

 * out (out): a*b.

 */

void curve448_scalar_mul(curve448_scalar_t out,

                         const curve448_scalar_t a, const curve448_scalar_t b);

/*

* Halve a scalar.  |a| and |out| may alias each other.

* 

* a (in): A scalar.

* out (out): a/2.

*/

void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);

/*

 * Copy a scalar.  The scalars may alias each other, in which case this

 * function does nothing.

 * 

 * a (in): A scalar.

 * out (out): Will become a copy of a.

 */

static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,

                                             const curve448_scalar_t a)

{

    *out = *a;

}

Unexecuted instantiation: curve448.c:curve448_scalar_copy

Unexecuted instantiation: curve448_tables.c:curve448_scalar_copy

Unexecuted instantiation: eddsa.c:curve448_scalar_copy

Unexecuted instantiation: scalar.c:curve448_scalar_copy

/*

 * Copy a point.  The input and output may alias, in which case this function

 * does nothing.

 *

 * a (out): A copy of the point.

 * b (in): Any point.

 */

static ossl_inline void curve448_point_copy(curve448_point_t a,

                                            const curve448_point_t b)

{

    *a = *b;

}

Unexecuted instantiation: curve448.c:curve448_point_copy

Unexecuted instantiation: curve448_tables.c:curve448_point_copy

Unexecuted instantiation: eddsa.c:curve448_point_copy

Unexecuted instantiation: scalar.c:curve448_point_copy

/*

 * Test whether two points are equal.  If yes, return C448_TRUE, else return

 * C448_FALSE.

 *

 * a (in): A point.

 * b (in): Another point.

 * 

 * Returns:

 * C448_TRUE: The points are equal.

 * C448_FALSE: The points are not equal.

 */

__owur c448_bool_t curve448_point_eq(const curve448_point_t a,

                                     const curve448_point_t b);

/*

 * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially

 * faster.

 *

 * two_a (out): The sum a+a.

 * a (in): A point.

 */

void curve448_point_double(curve448_point_t two_a, const curve448_point_t a);

/*

 * RFC 7748 Diffie-Hellman scalarmul.  This function uses a different

 * (non-Decaf) encoding.

 *

 * out (out): The scaled point base*scalar

 * base (in): The point to be scaled.

 * scalar (in): The scalar to multiply by.

 *

 * Returns:

 * C448_SUCCESS: The scalarmul succeeded.

 * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a

 * small subgroup.

 */

__owur c448_error_t x448_int(uint8_t out[X448_PUBLIC_BYTES],

                             const uint8_t base[X448_PUBLIC_BYTES],

                             const uint8_t scalar[X448_PRIVATE_BYTES]);

/*

 * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748.

 *

 * This function is mainly used internally, but is exported in case

 * it will be useful.

 *

 * The ratio is necessary because the internal representation doesn't

 * track the cofactor information, so on output we must clear the cofactor.

 * This would multiply by the cofactor, but in fact internally points are always

 * even, so it multiplies by half the cofactor instead.

 *

 * As it happens, this aligns with the base point definitions; that is,

 * if you pass the Decaf/Ristretto base point to this function, the result

 * will be X448_ENCODE_RATIO times the X448

 * base point.

 *

 * out (out): The scaled and encoded point.

 * p (in): The point to be scaled and encoded.

 */

void curve448_point_mul_by_ratio_and_encode_like_x448(

                                        uint8_t out[X448_PUBLIC_BYTES],

                                        const curve448_point_t p);

/*

 * RFC 7748 Diffie-Hellman base point scalarmul.  This function uses a different

 * (non-Decaf) encoding.

 * 

 * out (out): The scaled point base*scalar

 * scalar (in): The scalar to multiply by.

 */

void x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES],

                            const uint8_t scalar[X448_PRIVATE_BYTES]);

/*

 * Multiply a precomputed base point by a scalar: out = scalar*base.

 *

 * scaled (out): The scaled point base*scalar

 * base (in): The point to be scaled.

 * scalar (in): The scalar to multiply by.

 */

void curve448_precomputed_scalarmul(curve448_point_t scaled,

                                    const curve448_precomputed_s * base,

                                    const curve448_scalar_t scalar);

/*

 * Multiply two base points by two scalars:

 * combo = scalar1*curve448_point_base + scalar2*base2.

 *

 * Otherwise equivalent to curve448_point_double_scalarmul, but may be

 * faster at the expense of being variable time.

 *

 * combo (out): The linear combination scalar1*base + scalar2*base2.

 * scalar1 (in): A first scalar to multiply by.

 * base2 (in): A second point to be scaled.

 * scalar2 (in) A second scalar to multiply by.

 *

 * Warning: This function takes variable time, and may leak the scalars used. 

 * It is designed for signature verification.

 */

void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,

                                               const curve448_scalar_t scalar1,

                                               const curve448_point_t base2,

                                               const curve448_scalar_t scalar2);

/*

 * Test that a point is valid, for debugging purposes.

 *

 * to_test (in): The point to test.

 *

 * Returns:

 * C448_TRUE The point is valid.

 * C448_FALSE The point is invalid.

 */

__owur c448_bool_t curve448_point_valid(const curve448_point_t to_test);

/* Overwrite scalar with zeros. */

void curve448_scalar_destroy(curve448_scalar_t scalar);

/* Overwrite point with zeros. */

void curve448_point_destroy(curve448_point_t point);

#endif                          /* HEADER_POINT_448_H */