libecc::point< Polynomial, a, b > Class Template Reference

Point (x,y) on elliptic curve x³ + ax² + b = y² + xy. More...

#include <point.h>

List of all members.

Public Types
typedef Polynomial	polynomial_type
	The type of the field over which the elliptic curve is defined.
Public Member Functions
	point (void)
	Construct the point at infinity (zero).
	point (std::string x, std::string y)
	Construct a point (x, y) from the strings x and y.
	point (polynomial_type const &x, polynomial_type const &y)
	Construct a point (x, y) from the polynomials x and y.
point &	operator= (point const &p1)
	Copy constructor.
point &	operator+= (point const &p1)
	Add point p1 to this point.
void	MULTIPLY_and_assign (point const &pnt, mpz_class const &scalar)
	Multiply the point pnt with scalar and assign the result to this object.
mpz_class	order (order_algorithm algorithm=order_default) const
	Calculate the order of this point.
bool	operator== (point const &p1) const
	Compare for equality.
bool	operator!= (point const &p1) const
	Compare for inequality.
bool	check (void) const
	Check if the current point is a solution of the elliptic curve.
polynomial_type const &	get_x (void) const
	Retrieve the value of the x coordinate.
polynomial_type const &	get_y (void) const
	Retrieve the value of the y coordinate.
bool	is_zero (void) const
	Return if this is the point at infinity or not.
void	print_on (std::ostream &os) const
	Print the coordinates of this point to an ostream.
void	randomize (rds &random_source)
	Generate a random point on the curve.

---

Detailed Description

template<typename Polynomial, Polynomial const & a, Polynomial const & b>
class libecc::point< Polynomial, a, b >

Point (x,y) on elliptic curve x³ + ax² + b = y² + xy.

This class represents a point (x,y) on the elliptic curve x³ + ax² + b = y² + xy where x, y, a and b are of the type Polynomial, elements of F_2^m.

See also:

Theory: points on an Elliptic Curve

---

Member Typedef Documentation

template<typename Polynomial, Polynomial const & a, Polynomial const & b>

typedef Polynomial libecc::point< Polynomial, a, b >::polynomial_type

The type of the field over which the elliptic curve is defined.

---

Constructor & Destructor Documentation

template<typename Polynomial, Polynomial const & a, Polynomial const & b>

libecc::point< Polynomial, a, b >::point

(

void

)

[inline]

Construct the point at infinity (zero).

template<typename Polynomial, Polynomial const & a, Polynomial const & b>

libecc::point< Polynomial, a, b >::point	(	std::string	x,
		std::string	y
	)			[inline]

Construct a point (x, y) from the strings x and y.

The strings are passed directly to two variables of type polynomial_type.

template<typename Polynomial, Polynomial const & a, Polynomial const & b>

libecc::point< Polynomial, a, b >::point	(	polynomial_type const &	x,
		polynomial_type const &	y
	)			[inline]

Construct a point (x, y) from the polynomials x and y.

---

Member Function Documentation

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

bool libecc::point< Polynomial, a, b >::check

(

void

)

const

Check if the current point is a solution of the elliptic curve.

Returns:

true when the x and y coordinate are a solution of the elliptic curve, or when this is the point at infinity.

template<typename Polynomial, Polynomial const & a, Polynomial const & b>

polynomial_type const& libecc::point< Polynomial, a, b >::get_x

(

void

)

const [inline]

Retrieve the value of the x coordinate.

This value is only valid when is_zero returns false.

template<typename Polynomial, Polynomial const & a, Polynomial const & b>

polynomial_type const& libecc::point< Polynomial, a, b >::get_y

(

void

)

const [inline]

Retrieve the value of the y coordinate.

This value is only valid when is_zero returns false.

template<typename Polynomial, Polynomial const & a, Polynomial const & b>

bool libecc::point< Polynomial, a, b >::is_zero

(

void

)

const [inline]

Return if this is the point at infinity or not.

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

void libecc::point< Polynomial, a, b >::MULTIPLY_and_assign	(	point< Polynomial, a, b > const &	pnt,
		mpz_class const &	scalar
	)

Multiply the point pnt with scalar and assign the result to this object.

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

bool libecc::point< Polynomial, a, b >::operator!=

(

point< Polynomial, a, b > const &

p1

)

const [inline]

Compare for inequality.

Returns:

false if both points are zero, or if they have the same x and y coordinate. Otherwise true is returned.

Referenced by libecc::point< Polynomial, a, b >::operator==().

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

point< Polynomial, a, b > & libecc::point< Polynomial, a, b >::operator+=

(

point< Polynomial, a, b > const &

p1

)

Add point p1 to this point.

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

point< Polynomial, a, b > & libecc::point< Polynomial, a, b >::operator=

(

point< Polynomial, a, b > const &

p1

)

Copy constructor.

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

bool libecc::point< Polynomial, a, b >::operator==

(

point< Polynomial, a, b > const &

p1

)

const [inline]

Compare for equality.

Returns:

true if both points are zero, or if they have the same x and y coordinate. Otherwise false is returned;

References libecc::point< Polynomial, a, b >::operator!=().

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

mpz_class libecc::point< Polynomial, a, b >::order

(

order_algorithm

algorithm = order_default

)

const

Calculate the order of this point.

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

void libecc::point< Polynomial, a, b >::print_on

(

std::ostream &

os

)

const

Print the coordinates of this point to an ostream.

template<typename Polynomial , Polynomial const & a, Polynomial const & b>

void libecc::point< Polynomial, a, b >::randomize

(

rds &

random_source

)

Generate a random point on the curve.