/*
 * RELIC is an Efficient LIbrary for Cryptography
 * Copyright (c) 2009 RELIC Authors
 *
 * This file is part of RELIC. RELIC is legal property of its developers,
 * whose names are not listed here. Please refer to the COPYRIGHT file
 * for contact information.
 *
 * RELIC is free software; you can redistribute it and/or modify it under the
 * terms of the version 2.1 (or later) of the GNU Lesser General Public License
 * as published by the Free Software Foundation; or version 2.0 of the Apache
 * License as published by the Apache Software Foundation. See the LICENSE files
 * for more details.
 *
 * RELIC is distributed in the hope that it will be useful, but WITHOUT ANY
 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
 * A PARTICULAR PURPOSE. See the LICENSE files for more details.
 *
 * You should have received a copy of the GNU Lesser General Public or the
 * Apache License along with RELIC. If not, see <https://www.gnu.org/licenses/>
 * or <https://www.apache.org/licenses/>.
 */

/**
 * @defgroup eb Elliptic curves over binary fields
 */

/**
 * @file
 *
 * Interface of the module for arithmetic on binary elliptic curves.
 *
 * @ingroup eb
 */

#ifndef RLC_EB_H
#define RLC_EB_H

#include "relic_fb.h"
#include "relic_bn.h"
#include "relic_conf.h"
#include "relic_types.h"
#include "relic_label.h"

/*============================================================================*/
/* Constant definitions                                                       */
/*============================================================================*/

/**
 * Binary elliptic curve identifiers.
 */
enum {
	/** NIST B-163 binary curve. */
	NIST_B163 = 1,
	/** NIST K-163 Koblitz curve. */
	NIST_K163,
	/** NIST B-133 binary curve. */
	NIST_B233,
	/** NIST K-233 Koblitz curve. */
	NIST_K233,
	/** Curve over 2^{251} used in eBATs. */
	EBACS_B251,
	/** Curve over 2^{257} good for halving. */
	HALVE_B257,
	/** SECG K-239 binary curve. */
	SECG_K239,
	/** NIST B-283 binary curve. */
	NIST_B283,
	/** NIST K-283 Koblitz curve. */
	NIST_K283,
	/** NIST B-409 binary curve. */
	NIST_B409,
	/** NIST K-409 Koblitz curve. */
	NIST_K409,
	/** NIST B-571 binary curve. */
	NIST_B571,
	/** NIST K-571 Koblitz curve. */
	NIST_K571,
};

/**
 * Size of a precomputation table using the binary method.
 */
#define RLC_EB_TABLE_BASIC		(RLC_FB_BITS)

/**
 * Size of a precomputation table using the single-table comb method.
 */
#define RLC_EB_TABLE_COMBS      (1 << EB_DEPTH)

/**
 * Size of a precomputation table using the double-table comb method.
 */
#define RLC_EB_TABLE_COMBD		(1 << (EB_DEPTH + 1))

/**
 * Size of a precomputation table using the w-(T)NAF method.
 */
#define RLC_EB_TABLE_LWNAF		(1 << (EB_DEPTH - 2))

/**
 * Size of a precomputation table using the chosen algorithm.
 */
#if EB_FIX == BASIC
#define RLC_EB_TABLE			RLC_EB_TABLE_BASIC
#elif EB_FIX == COMBS
#define RLC_EB_TABLE			RLC_EB_TABLE_COMBS
#elif EB_FIX == COMBD
#define RLC_EB_TABLE			RLC_EB_TABLE_COMBD
#elif EB_FIX == LWNAF
#define RLC_EB_TABLE			RLC_EB_TABLE_LWNAF
#endif

/**
 * Maximum size of a precomputation table.
 */
#ifdef STRIP
#define RLC_EB_TABLE_MAX 		RLC_EB_TABLE
#else
#define RLC_EB_TABLE_MAX 		RLC_MAX(RLC_EB_TABLE_BASIC, RLC_EB_TABLE_COMBD)
#endif

/*============================================================================*/
/* Type definitions                                                           */
/*============================================================================*/

/**
 * Represents an elliptic curve point over a binary field.
 */
typedef struct {
	/** The first coordinate. */
	fb_st x;
	/** The second coordinate. */
	fb_st y;
	/** The third coordinate (projective representation). */
	fb_st z;
	/** Flag to indicate the coordinate system of this point. */
	int coord;
} eb_st;

/**
 * Pointer to an elliptic curve point.
 */
#if ALLOC == AUTO
typedef eb_st eb_t[1];
#else
typedef eb_st *eb_t;
#endif

/*============================================================================*/
/* Macro definitions                                                          */
/*============================================================================*/

/**
 * Initializes a point on a binary elliptic curve with a null value.
 *
 * @param[out] A			- the point to initialize.
 */
#if ALLOC == AUTO
#define eb_null(A)			/* empty */
#else
#define eb_null(A)			A = NULL;
#endif

/**
 * Calls a function to allocate a point on a binary elliptic curve.
 *
 * @param[out] A			- the new point.
 * @throw ERR_NO_MEMORY		- if there is no available memory.
 */
#if ALLOC == DYNAMIC
#define eb_new(A)															\
	A = (eb_t)calloc(1, sizeof(eb_st));										\
	if (A == NULL) {														\
		RLC_THROW(ERR_NO_MEMORY);											\
	}																		\

#elif ALLOC == AUTO
#define eb_new(A)			/* empty */

#endif

/**
 * Calls a function to clean and free a point on a binary elliptic curve.
 *
 * @param[out] A			- the point to clean and free.
 */
#if ALLOC == DYNAMIC
#define eb_free(A)															\
	if (A != NULL) {														\
		free(A);															\
		A = NULL;															\
	}																		\

#elif ALLOC == AUTO
#define eb_free(A)			/* empty */

#endif

/**
 * Negates a binary elliptic curve point. Computes R = -P.
 *
 * @param[out] R			- the result.
 * @param[in] P				- the point to negate.
 */
#if EB_ADD == BASIC
#define eb_neg(R, P)		eb_neg_basic(R, P)
#elif EB_ADD == PROJC
#define eb_neg(R, P)		eb_neg_projc(R, P)
#endif

/**
 * Adds two binary elliptic curve points. Computes R = P + Q.
 *
 * @param[out] R			- the result.
 * @param[in] P				- the first point to add.
 * @param[in] Q				- the second point to add.
 */
#if EB_ADD == BASIC
#define eb_add(R, P, Q)		eb_add_basic(R, P, Q);
#elif EB_ADD == PROJC
#define eb_add(R, P, Q)		eb_add_projc(R, P, Q);
#endif

/**
 * Subtracts a binary elliptic curve point from another. Computes R = P - Q.
 *
 * @param[out] R			- the result.
 * @param[in] P				- the first point.
 * @param[in] Q				- the second point.
 */
#if EB_ADD == BASIC
#define eb_sub(R, P, Q)		eb_sub_basic(R, P, Q)
#elif EB_ADD == PROJC
#define eb_sub(R, P, Q)		eb_sub_projc(R, P, Q)
#endif

/**
 * Doubles a binary elliptic curve point. Computes R = 2P.
 *
 * @param[out] R			- the result.
 * @param[in] P				- the point to double.
 */
#if EB_ADD == BASIC
#define eb_dbl(R, P)		eb_dbl_basic(R, P);
#elif EB_ADD == PROJC
#define eb_dbl(R, P)		eb_dbl_projc(R, P);
#endif


/**
 * Multiplies a binary elliptic curve point by an integer. Computes R = [k]P.
 *
 * @param[out] R			- the result.
 * @param[in] P				- the point to multiply.
 * @param[in] K				- the integer.
 */
#if EB_MUL == BASIC
#define eb_mul(R, P, K)		eb_mul_basic(R, P, K)
#elif EB_MUL == LODAH
#define eb_mul(R, P, K)		eb_mul_lodah(R, P, K)
#elif EB_MUL == HALVE
#define eb_mul(R, P, K)		eb_mul_halve(R, P, K)
#elif EB_MUL == LWNAF
#define eb_mul(R, P, K)		eb_mul_lwnaf(R, P, K)
#elif EB_MUL == RWNAF
#define eb_mul(R, P, K)		eb_mul_rwnaf(R, P, K)
#endif

/**
 * Builds a precomputation table for multiplying a fixed binary elliptic point
 * point.
 *
 * @param[out] T			- the precomputation table.
 * @param[in] P				- the point to multiply.
 */
#if EB_FIX == BASIC
#define eb_mul_pre(T, P)	eb_mul_pre_basic(T, P)
#elif EB_FIX == COMBS
#define eb_mul_pre(T, P)	eb_mul_pre_combs(T, P)
#elif EB_FIX == COMBD
#define eb_mul_pre(T, P)	eb_mul_pre_combd(T, P)
#elif EB_FIX == LWNAF
#define eb_mul_pre(T, P)	eb_mul_pre_lwnaf(T, P)
#endif

/**
 * Multiplies a fixed binary elliptic point using a precomputation table.
 * Computes R = [k]P.
 *
 * @param[out] R			- the result.
 * @param[in] T				- the precomputation table.
 * @param[in] K				- the integer.
 */
#if EB_FIX == BASIC
#define eb_mul_fix(R, T, K)	eb_mul_fix_basic(R, T, K)
#elif EB_FIX == COMBS
#define eb_mul_fix(R, T, K)	eb_mul_fix_combs(R, T, K)
#elif EB_FIX == COMBD
#define eb_mul_fix(R, T, K)	eb_mul_fix_combd(R, T, K)
#elif EB_FIX == LWNAF
#define eb_mul_fix(R, T, K)	eb_mul_fix_lwnaf(R, T, K)
#endif

/**
 * Multiplies and adds two binary elliptic curve points simultaneously. Computes
 * R = [k]P + [m]Q.
 *
 * @param[out] R			- the result.
 * @param[in] P				- the first point to multiply.
 * @param[in] K				- the first integer.
 * @param[in] Q				- the second point to multiply.
 * @param[in] M				- the second integer,
 */
#if EB_SIM == BASIC
#define eb_mul_sim(R, P, K, Q, M)	eb_mul_sim_basic(R, P, K, Q, M)
#elif EB_SIM == TRICK
#define eb_mul_sim(R, P, K, Q, M)	eb_mul_sim_trick(R, P, K, Q, M)
#elif EB_SIM == INTER
#define eb_mul_sim(R, P, K, Q, M)	eb_mul_sim_inter(R, P, K, Q, M)
#elif EB_SIM == JOINT
#define eb_mul_sim(R, P, K, Q, M)	eb_mul_sim_joint(R, P, K, Q, M)
#endif

/*============================================================================*/
/* Function prototypes                                                        */
/*============================================================================*/

/**
 * Initializes the binary elliptic curve arithmetic module.
 */
void eb_curve_init(void);

/**
 * Finalizes the binary elliptic curve arithmetic module.
 */
void eb_curve_clean(void);

/**
 * Returns the a-coefficient of the currently configured binary elliptic
 * curve.
 *
 * @return the a-coefficient of the elliptic curve.
 */
dig_t *eb_curve_get_a(void);

/**
 * Returns the b-coefficient of the currently configured binary elliptic
 * curve.
 *
 * @return the b-coefficient of the elliptic curve.
 */
dig_t *eb_curve_get_b(void);

/**
 * Returns a optimization identifier based on the a-coefficient of the curve.
 *
 * @return the optimization identifier.
 */
int eb_curve_opt_a(void);

/**
 * Returns a optimization identifier based on the b-coefficient of the curve.
 *
 * @return the optimization identifier.
 */
int eb_curve_opt_b(void);

/**
 * Tests if the configured binary elliptic curve is a Koblitz curve.
 *
 * @return 1 if the binary elliptic curve is a Koblitz curve, 0 otherwise.
 */
int eb_curve_is_kbltz(void);

/**
 * Returns the generator of the group of points in the binary elliptic curve.
 *
 * @param[out] g			- the returned generator.
 */
void eb_curve_get_gen(eb_t g);

/**
 * Returns the precomputation table for the generator.
 *
 * @return the table.
 */
const eb_t *eb_curve_get_tab(void);

/**
 * Returns the order of the group of points in the binary elliptic curve.
 *
 * @param[out] n			- the returned order.
 */
void eb_curve_get_ord(bn_t n);

/**
 * Returns the cofactor of the binary elliptic curve.
 *
 * @param[out] n			- the returned cofactor.
 */
void eb_curve_get_cof(bn_t h);

/**
 * Configures an ordinary binary elliptic curve by its coefficients and
 * generator.
 *
 * @param[in] a				- the a-coefficient of the curve.
 * @param[in] b				- the b-coefficient of the curve.
 * @param[in] g				- the generator.
 * @param[in] n				- the order of the generator.
 * @param[in] h				- the cofactor of the group order.
 */
void eb_curve_set(const fb_t a, const fb_t b, const eb_t g, const bn_t n,
		const bn_t h);

/**
 * Configures a new binary elliptic curve by its parameter identifier.
 *
 * @param[in] param			- the parameters identifier.
 */
void eb_param_set(int param);

/**
 * Configures some set of curve parameters for the current security level.
 */
int eb_param_set_any(void);

/**
 * Configures a set of curve parameters without endormorphisms for the current
 * security level.
 *
 * @return RLC_OK if there is a curve at this security level, RLC_ERR otherwise.
 */
int eb_param_set_any_plain(void);

/**
 * Configures a set of Koblitz curve parameters for the current security level.
 *
 * @return RLC_OK if there is a curve at this security level, RLC_ERR otherwise.
 */
int eb_param_set_any_kbltz(void);

/**
 * Returns the parameter identifier of the currently configured binary elliptic
 * curve.
 *
 * @return the parameter identifier.
 */
int eb_param_get(void);

/**
 * Prints the current configured binary elliptic curve.
 */
void eb_param_print(void);

/**
 * Returns the current security level.
 */
int eb_param_level(void);

/**
 * Tests if a point on a binary elliptic curve is at the infinity.
 *
 * @param[in] p				- the point to test.
 * @return 1 if the point is at infinity, 0 otherise.
 */
int eb_is_infty(const eb_t p);

/**
 * Assigns a binary elliptic curve point to the point at infinity.
 *
 * @param[out] p			- the point to assign.
 */
void eb_set_infty(eb_t p);

/**
 * Copies the second argument to the first argument.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the binary elliptic curve point to copy.
 */
void eb_copy(eb_t r, const eb_t p);

/**
 * Compares two binary elliptic curve points.
 *
 * @param[in] p				- the first binary elliptic curve point.
 * @param[in] q				- the second binary elliptic curve point.
 * @return RLC_EQ if p == q and RLC_NE if p != q.
 */
int eb_cmp(const eb_t p, const eb_t q);

/**
 * Assigns a random value to a binary elliptic curve point.
 *
 * @param[out] p			- the binary elliptic curve point to assign.
 */
void eb_rand(eb_t p);

/**
 * Randomizes coordinates of a binary elliptic curve point.
 *
 * @param[out] r			- the blinded binary elliptic curve point.
 * @param[in] p				- the binary elliptic curve point to blind.
 */
void eb_blind(eb_t r, const eb_t p);

/**
 * Computes the right-hand side of the elliptic curve equation at a certain
 * elliptic curve point.
 *
 * @param[out] rhs			- the result.
 * @param[in] p				- the point.
 */
void eb_rhs(fb_t rhs, const eb_t p);

/** Tests if a point is in the curve.
 *
 * @param[in] p				- the point to test.
 */
int eb_on_curve(const eb_t p);

/**
 * Builds a precomputation table for multiplying a random binary elliptic point.
 *
 * @param[out] t			- the precomputation table.
 * @param[in] p				- the point to multiply.
 * @param[in] w				- the window width.
 */
void eb_tab(eb_t *t, const eb_t p, int w);

/**
 * Prints a binary elliptic curve point.
 *
 * @param[in] p				- the binary elliptic curve point to print.
 */
void eb_print(const eb_t p);

/**
 * Returns the number of bytes necessary to store a binary elliptic curve point
 * with optional point compression.
 *
 * @param[in] a				- the binary field element.
 * @param[in] pack			- the flag to indicate compression.
 * @return the number of bytes.
 */
int eb_size_bin(const eb_t a, int pack);

/**
 * Reads a binary elliptic curve point from a byte vector in big-endian format.
 *
 * @param[out] a			- the result.
 * @param[in] bin			- the byte vector.
 * @param[in] len			- the buffer capacity.
 * @throw ERR_NO_VALID		- if the encoded point is invalid.
 * @throw ERR_NO_BUFFER		- if the buffer capacity is invalid.
 */
void eb_read_bin(eb_t a, const uint8_t *bin, int len);

/**
 * Writes a binary field element to a byte vector in big-endian format with
 * optional point compression.
 *
 * @param[out] bin			- the byte vector.
 * @param[in] len			- the buffer capacity.
 * @param[in] a				- the binary elliptic curve point to write.
 * @param[in] pack			- the flag to indicate point compression.
 * @throw ERR_NO_BUFFER		- if the buffer capacity is invalid.
 */
void eb_write_bin(uint8_t *bin, int len, const eb_t a, int pack);

/**
 * Negates a binary elliptic curve point represented by affine coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to negate.
 */
void eb_neg_basic(eb_t r, const eb_t p);

/**
 * Negates a binary elliptic curve point represented by projective coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to negate.
 */
void eb_neg_projc(eb_t r, const eb_t p);

/**
 * Adds two binary elliptic curve points represented in affine coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point to add.
 * @param[in] q				- the second point to add.
 */
void eb_add_basic(eb_t r, const eb_t p, const eb_t q);

/**
 * Adds two binary elliptic curve points represented in projective coordinates.
 * Computes R = P + Q.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point to add.
 * @param[in] q				- the second point to add.
 */
void eb_add_projc(eb_t r, const eb_t p, const eb_t q);

/**
 * Subtracts a binary elliptic curve point from another, both points represented
 * by affine coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point.
 * @param[in] q				- the second point.
 */
void eb_sub_basic(eb_t r, const eb_t p, const eb_t q);

/**
 * Subtracts a binary elliptic curve point from another, both points represented
 * by projective coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point.
 * @param[in] q				- the second point.
 */
void eb_sub_projc(eb_t r, const eb_t p, const eb_t q);

/**
 * Doubles a binary elliptic curve point represented in affine coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to double.
 */
void eb_dbl_basic(eb_t r, const eb_t p);

/**
 * Doubles a binary elliptic curve point represented in projective coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to double.
 */
void eb_dbl_projc(eb_t r, const eb_t p);

/**
 * Halves a point represented in affine coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to halve.
 */
void eb_hlv(eb_t r, const eb_t p);

/**
 * Computes the Frobenius map of a binary elliptic curve point on a Koblitz
 * curve. Computes R = \tau(P) = \tau(x, y) = (x^2, y^2).
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point.
 */
void eb_frb(eb_t r, const eb_t p);

/**
 * Multiplies a binary elliptic point by an integer using the binary method.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to multiply.
 * @param[in] k				- the integer.
 */
void eb_mul_basic(eb_t r, const eb_t p, const bn_t k);

/**
 * Multiplies a binary elliptic point by an integer using the constant-time
 * Lopez-Dahab point multiplication method.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to multiply.
 * @param[in] k				- the integer.
 */
void eb_mul_lodah(eb_t r, const eb_t p, const bn_t k);

/**
 * Multiplies a binary elliptic point by an integer using the left-to-right
 * w-NAF method. If the binary curve is a Koblitz curve, w-TNAF is used.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to multiply.
 * @param[in] k				- the integer.
 */
void eb_mul_lwnaf(eb_t r, const eb_t p, const bn_t k);

/**
 * Multiplies a binary elliptic point by an integer using the right-to-left
 * w-NAF method. If the binary curve is a Koblitz curve, w-TNAF is used.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to multiply.
 * @param[in] k				- the integer.
 */
void eb_mul_rwnaf(eb_t r, const eb_t p, const bn_t k);

/**
 * Multiplies a binary elliptic point by an integer using the halving method.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to multiply.
 * @param[in] k				- the integer.
 */
void eb_mul_halve(eb_t r, const eb_t p, const bn_t k);

/**
 * Multiplies the generator of a binary elliptic curve by an integer.
 *
 * @param[out] r			- the result.
 * @param[in] k				- the integer.
 */
void eb_mul_gen(eb_t r, const bn_t k);

/**
 * Multiplies a binary elliptic point by a small positive integer.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to multiply.
 * @param[in] k				- the integer.
 */
void eb_mul_dig(eb_t r, const eb_t p, const dig_t k);

/**
 * Builds a precomputation table for multiplying a fixed binary elliptic point
 * using the binary method.
 *
 * @param[out] t			- the precomputation table.
 * @param[in] p				- the point to multiply.
 */
void eb_mul_pre_basic(eb_t *t, const eb_t p);

/**
 * Builds a precomputation table for multiplying a fixed binary elliptic point
 * using Yao's windowing method.
 *
 * @param[out] t			- the precomputation table.
 * @param[in] p				- the point to multiply.
 */
void eb_mul_pre_yaowi(eb_t *t, const eb_t p);

/**
 * Builds a precomputation table for multiplying a fixed binary elliptic point
 * using the NAF windowing method.
 *
 * @param[out] t			- the precomputation table.
 * @param[in] p				- the point to multiply.
 */
void eb_mul_pre_nafwi(eb_t *t, const eb_t p);

/**
 * Builds a precomputation table for multiplying a fixed binary elliptic point
 * using the single-table comb method.
 *
 * @param[out] t			- the precomputation table.
 * @param[in] p				- the point to multiply.
 */
void eb_mul_pre_combs(eb_t *t, const eb_t p);

/**
 * Builds a precomputation table for multiplying a fixed binary elliptic point
 * using the double-table comb method.
 *
 * @param[out] t			- the precomputation table.
 * @param[in] p				- the point to multiply.
 */
void eb_mul_pre_combd(eb_t *t, const eb_t p);

/**
 * Builds a precomputation table for multiplying a fixed binary elliptic point
 * using the w-(T)NAF method.
 *
 * @param[out] t			- the precomputation table.
 * @param[in] p				- the point to multiply.
 */
void eb_mul_pre_lwnaf(eb_t *t, const eb_t p);

/**
 * Multiplies a fixed binary elliptic point using a precomputation table and
 * the binary method.
 *
 * @param[out] r			- the result.
 * @param[in] t				- the precomputation table.
 * @param[in] k				- the integer.
 */
void eb_mul_fix_basic(eb_t r, const eb_t *t, const bn_t k);

/**
 * Multiplies a fixed binary elliptic point using a precomputation table and
 * Yao's windowing method
 *
 * @param[out] r			- the result.
 * @param[in] t				- the precomputation table.
 * @param[in] k				- the integer.
 */
void eb_mul_fix_yaowi(eb_t r, const eb_t *t, const bn_t k);

/**
 * Multiplies a fixed binary elliptic point using a precomputation table and
 * the w-(T)NAF method.
 *
 * @param[out] r			- the result.
 * @param[in] t				- the precomputation table.
 * @param[in] k				- the integer.
 */
void eb_mul_fix_nafwi(eb_t r, const eb_t *t, const bn_t k);

/**
 * Multiplies a fixed binary elliptic point using a precomputation table and
 * the single-table comb method.
 *
 * @param[out] r			- the result.
 * @param[in] t				- the precomputation table.
 * @param[in] k				- the integer.
 */
void eb_mul_fix_combs(eb_t r, const eb_t *t, const bn_t k);

/**
 * Multiplies a fixed binary elliptic point using a precomputation table and
 * the double-table comb method.
 *
 * @param[out] r			- the result.
 * @param[in] t				- the precomputation table.
 * @param[in] k				- the integer.
 */
void eb_mul_fix_combd(eb_t r, const eb_t *t, const bn_t k);

/**
 * Multiplies a fixed binary elliptic point using a precomputation table and
 * the w-(T)NAF method.
 *
 * @param[out] r			- the result.
 * @param[in] t				- the precomputation table.
 * @param[in] k				- the integer.
 */
void eb_mul_fix_lwnaf(eb_t r, const eb_t *t, const bn_t k);

/**
 * Multiplies and adds two binary elliptic curve points simultaneously using
 * scalar multiplication and point addition.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point to multiply.
 * @param[in] k				- the first integer.
 * @param[in] q				- the second point to multiply.
 * @param[in] m				- the second integer,
 */
void eb_mul_sim_basic(eb_t r, const eb_t p, const bn_t k, const eb_t q,
		const bn_t m);

/**
 * Multiplies and adds two binary elliptic curve points simultaneously using
 * shamir's trick.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point to multiply.
 * @param[in] k				- the first integer.
 * @param[in] q				- the second point to multiply.
 * @param[in] m				- the second integer,
 */
void eb_mul_sim_trick(eb_t r, const eb_t p, const bn_t k, const eb_t q,
		const bn_t m);

/**
 * Multiplies and adds two binary elliptic curve points simultaneously using
 * interleaving of NAFs.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point to multiply.
 * @param[in] k				- the first integer.
 * @param[in] q				- the second point to multiply.
 * @param[in] m				- the second integer,
 */
void eb_mul_sim_inter(eb_t r, const eb_t p, const bn_t k, const eb_t q,
		const bn_t m);

/**
 * Multiplies and adds two binary elliptic curve points simultaneously using
 * Solinas' Joint Sparse Form.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the first point to multiply.
 * @param[in] k				- the first integer.
 * @param[in] q				- the second point to multiply.
 * @param[in] m				- the second integer,
 */
void eb_mul_sim_joint(eb_t r, const eb_t p, const bn_t k, const eb_t q,
		const bn_t m);

/**
 * Multiplies and adds the generator and a binary elliptic curve point
 * simultaneously. Computes R = [k]G + [m]Q.
 *
 * @param[out] r			- the result.
 * @param[in] k				- the first integer.
 * @param[in] q				- the second point to multiply.
 * @param[in] m				- the second integer.
 */
void eb_mul_sim_gen(eb_t r, const bn_t k, const eb_t q, const bn_t m);

/**
 * Converts a point to affine coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to convert.
 */
void eb_norm(eb_t r, const eb_t p);

/**
 * Converts multiple points to affine coordinates.
 *
 * @param[out] r			- the result.
 * @param[in] t				- the points to convert.
 * @param[in] n				- the number of points.
 */
void eb_norm_sim(eb_t *r, const eb_t *t, int n);

/**
 * Maps a byte array to a point in a binary elliptic curve.
 *
 * @param[out] p			- the result.
 * @param[in] msg			- the byte array to map.
 * @param[in] len			- the array length in bytes.
 */
void eb_map(eb_t p, const uint8_t *msg, int len);

/**
 * Compresses a point.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to compress.
 */
void eb_pck(eb_t r, const eb_t p);

/**
 * Decompresses a point.
 *
 * @param[out] r			- the result.
 * @param[in] p				- the point to decompress.
 * @return if the decompression was successful
 */
int eb_upk(eb_t r, const eb_t p);

#endif /* !RLC_EB_H */