Elliptic Curve over GF(2^n) More...

#include <ec2n.h>

Inheritance diagram for EC2N:

Public Types
typedef GF2NP	Field

typedef Field::Element	FieldElement

typedef EC2NPoint	Point

Public Types inherited from AbstractGroup< EC2NPoint >
typedef EC2NPoint	Element

Public Member Functions
	EC2N ()
	Construct an EC2N. More...

	EC2N (const Field &field, const Field::Element &a, const Field::Element &b)
	Construct an EC2N. More...

	EC2N (BufferedTransformation &bt)
	Construct an EC2N from BER encoded parameters. More...

void	DEREncode (BufferedTransformation &bt) const
	Encode the fields fieldID and curve of the sequence ECParameters. More...

bool	Equal (const Point &P, const Point &Q) const
	Compare two elements for equality. More...

const Point &	Identity () const
	Provides the Identity element. More...

const Point &	Inverse (const Point &P) const
	Inverts the element in the group. More...

bool	InversionIsFast () const
	Determine if inversion is fast. More...

const Point &	Add (const Point &P, const Point &Q) const
	Adds elements in the group. More...

const Point &	Double (const Point &P) const
	Doubles an element in the group. More...

Point	Multiply (const Integer &k, const Point &P) const

Point	CascadeMultiply (const Integer &k1, const Point &P, const Integer &k2, const Point &Q) const

bool	ValidateParameters (RandomNumberGenerator &rng, unsigned int level=3) const

bool	VerifyPoint (const Point &P) const
	Verifies points on elliptic curve. More...

unsigned int	EncodedPointSize (bool compressed=false) const
	Determines encoded point size. More...

bool	DecodePoint (Point &P, BufferedTransformation &bt, size_t len) const
	Decodes an elliptic curve point. More...

bool	DecodePoint (Point &P, const byte *encodedPoint, size_t len) const
	Decodes an elliptic curve point. More...

void	EncodePoint (byte *encodedPoint, const Point &P, bool compressed) const
	Encodes an elliptic curve point. More...

void	EncodePoint (BufferedTransformation &bt, const Point &P, bool compressed) const
	Encodes an elliptic curve point. More...

Point	BERDecodePoint (BufferedTransformation &bt) const
	BER Decodes an elliptic curve point. More...

void	DEREncodePoint (BufferedTransformation &bt, const Point &P, bool compressed) const
	DER Encodes an elliptic curve point. More...

Integer	FieldSize () const

const Field &	GetField () const

const FieldElement &	GetA () const

const FieldElement &	GetB () const

bool	operator== (const EC2N &rhs) const

Public Member Functions inherited from AbstractGroup< EC2NPoint >
virtual bool	Equal (const Element &a, const Element &b) const=0
	Compare two elements for equality. More...

virtual const Element &	Identity () const=0
	Provides the Identity element. More...

virtual const Element &	Add (const Element &a, const Element &b) const=0
	Adds elements in the group. More...

virtual const Element &	Inverse (const Element &a) const=0
	Inverts the element in the group. More...

virtual bool	InversionIsFast () const
	Determine if inversion is fast. More...

virtual const Element &	Double (const Element &a) const
	Doubles an element in the group. More...

virtual const Element &	Subtract (const Element &a, const Element &b) const
	Subtracts elements in the group. More...

virtual Element &	Accumulate (Element &a, const Element &b) const
	TODO. More...

virtual Element &	Reduce (Element &a, const Element &b) const
	Reduces an element in the congruence class. More...

virtual Element	ScalarMultiply (const Element &a, const Integer &e) const
	Performs a scalar multiplication. More...

virtual Element	CascadeScalarMultiply (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
	TODO. More...

virtual void	SimultaneousMultiply (Element results, const Element &base, const Integer exponents, unsigned int exponentsCount) const
	Multiplies a base to multiple exponents in a group. More...

virtual bool	DecodePoint (EC2NPoint &P, BufferedTransformation &bt, size_t len) const=0
	Decodes an elliptic curve point. More...

virtual bool	DecodePoint (EC2NPoint &P, const byte *encodedPoint, size_t len) const=0
	Decodes an elliptic curve point. More...

virtual bool	VerifyPoint (const EC2NPoint &P) const=0
	Verifies points on elliptic curve. More...

virtual unsigned int	EncodedPointSize (bool compressed=false) const=0
	Determines encoded point size. More...

virtual void	EncodePoint (byte *encodedPoint, const EC2NPoint &P, bool compressed) const=0
	Encodes an elliptic curve point. More...

virtual void	EncodePoint (BufferedTransformation &bt, const EC2NPoint &P, bool compressed) const=0
	Encodes an elliptic curve point. More...

virtual EC2NPoint	BERDecodePoint (BufferedTransformation &bt) const=0
	BER Decodes an elliptic curve point. More...

virtual void	DEREncodePoint (BufferedTransformation &bt, const EC2NPoint &P, bool compressed) const=0
	DER Encodes an elliptic curve point. More...

Detailed Description

Elliptic Curve over GF(2^n)

Definition at line 26 of file ec2n.h.

Member Typedef Documentation

◆ Field

typedef GF2NP EC2N::Field

Definition at line 29 of file ec2n.h.

◆ FieldElement

typedef Field::Element EC2N::FieldElement

Definition at line 30 of file ec2n.h.

◆ Point

typedef EC2NPoint EC2N::Point

Definition at line 31 of file ec2n.h.

Constructor & Destructor Documentation

◆ ~EC2N()

virtual EC2N::~EC2N ( )

inlinevirtual

Definition at line 33 of file ec2n.h.

◆ EC2N() [1/3]

EC2N::EC2N ( )

inline

Construct an EC2N.

Definition at line 36 of file ec2n.h.

◆ EC2N() [2/3]

EC2N::EC2N	(	const Field &	field,
		const Field::Element &	a,
		const Field::Element &	b
	)

inline

Construct an EC2N.

Parameters

field	Field, GF2NP derived class
a	Field::Element
b	Field::Element

Definition at line 42 of file ec2n.h.

◆ EC2N() [3/3]

EC2N::EC2N ( BufferedTransformation & bt )

Construct an EC2N from BER encoded parameters.

Parameters

bt	BufferedTransformation derived object

This constructor will decode and extract the fields fieldID and curve of the sequence ECParameters

Member Function Documentation

◆ DEREncode()

void EC2N::DEREncode ( BufferedTransformation & bt ) const

Encode the fields fieldID and curve of the sequence ECParameters.

Parameters

bt	BufferedTransformation derived object

◆ Equal()

bool EC2N::Equal	(	const Point &	a,
		const Point &	b
	)		const

virtual

Compare two elements for equality.

Parameters

a	first element
b	second element

Returns: true if the elements are equal, false otherwise

Equal() tests the elements for equality using a==b

Implements AbstractGroup< EC2NPoint >.

◆ Identity()

const Point & EC2N::Identity ( ) const

virtual

Provides the Identity element.

Returns: the Identity element

Implements AbstractGroup< EC2NPoint >.

◆ Inverse()

const Point & EC2N::Inverse ( const Point & a ) const

virtual

Inverts the element in the group.

Parameters

a	first element

Returns: the inverse of the element

Implements AbstractGroup< EC2NPoint >.

◆ InversionIsFast()

bool EC2N::InversionIsFast ( ) const

inlinevirtual

Determine if inversion is fast.

Returns: true if inversion is fast, false otherwise

Reimplemented from AbstractGroup< EC2NPoint >.

Definition at line 57 of file ec2n.h.

◆ Add()

const Point & EC2N::Add	(	const Point &	a,
		const Point &	b
	)		const

virtual

Adds elements in the group.

Parameters

a	first element
b	second element

Returns: the sum of a and b

Implements AbstractGroup< EC2NPoint >.

◆ Double()

const Point & EC2N::Double ( const Point & a ) const

virtual

Doubles an element in the group.

Parameters

a	the element

Returns: the element doubled

Reimplemented from AbstractGroup< EC2NPoint >.

◆ Multiply()

Point EC2N::Multiply	(	const Integer &	k,
		const Point &	P
	)		const

inline

Definition at line 61 of file ec2n.h.

◆ CascadeMultiply()

Point EC2N::CascadeMultiply	(	const Integer &	k1,
		const Point &	P,
		const Integer &	k2,
		const Point &	Q
	)		const

inline

Definition at line 63 of file ec2n.h.

◆ VerifyPoint()

bool EC2N::VerifyPoint ( const Point & P ) const

virtual

Verifies points on elliptic curve.

Parameters

P	point to verify

Returns: true if the point is valid, false otherwise

Implements EncodedPoint< EC2NPoint >.

◆ EncodedPointSize()

unsigned int EC2N::EncodedPointSize ( bool compressed = false ) const

inlinevirtual

Determines encoded point size.

Parameters

compressed flag indicating if the point is compressed

Returns: the minimum number of bytes required to encode the point

Implements EncodedPoint< EC2NPoint >.

Definition at line 69 of file ec2n.h.

◆ DecodePoint() [1/2]

bool EC2N::DecodePoint	(	Point &	P,
		BufferedTransformation &	bt,
		size_t	len
	)		const

virtual

Decodes an elliptic curve point.

Parameters

P	point which is decoded
bt	source BufferedTransformation
len	number of bytes to read from the BufferedTransformation

Returns: true if a point was decoded, false otherwise

Implements EncodedPoint< EC2NPoint >.

◆ DecodePoint() [2/2]

bool EC2N::DecodePoint	(	Point &	P,
		const byte *	encodedPoint,
		size_t	len
	)		const

virtual

Decodes an elliptic curve point.

Parameters

P	point which is decoded
encodedPoint	byte array with the encoded point
len	the size of the array

Returns: true if a point was decoded, false otherwise

Implements EncodedPoint< EC2NPoint >.

◆ EncodePoint() [1/2]

void EC2N::EncodePoint	(	byte *	encodedPoint,
		const Point &	P,
		bool	compressed
	)		const

virtual

Encodes an elliptic curve point.

Parameters

P	point which is decoded
encodedPoint	byte array for the encoded point
compressed	flag indicating if the point is compressed

encodedPoint must be at least EncodedPointSize() in length

Implements EncodedPoint< EC2NPoint >.

◆ EncodePoint() [2/2]

void EC2N::EncodePoint	(	BufferedTransformation &	bt,
		const Point &	P,
		bool	compressed
	)		const

virtual

Encodes an elliptic curve point.

Parameters

bt	target BufferedTransformation
P	point which is encoded
compressed	flag indicating if the point is compressed

Implements EncodedPoint< EC2NPoint >.

◆ BERDecodePoint()

Point EC2N::BERDecodePoint ( BufferedTransformation & bt ) const

virtual

BER Decodes an elliptic curve point.

Parameters

bt	source BufferedTransformation

Returns: the decoded elliptic curve point

Implements EncodedPoint< EC2NPoint >.

◆ DEREncodePoint()

void EC2N::DEREncodePoint	(	BufferedTransformation &	bt,
		const Point &	P,
		bool	compressed
	)		const

virtual

DER Encodes an elliptic curve point.

Parameters

bt	target BufferedTransformation
P	point which is encoded
compressed	flag indicating if the point is compressed

Implements EncodedPoint< EC2NPoint >.

◆ FieldSize()

Integer EC2N::FieldSize ( ) const

inline

Definition at line 80 of file ec2n.h.

◆ GetField()

const Field & EC2N::GetField ( ) const

inline

Definition at line 81 of file ec2n.h.

◆ GetA()

const FieldElement & EC2N::GetA ( ) const

inline

Definition at line 82 of file ec2n.h.

◆ GetB()

const FieldElement & EC2N::GetB ( ) const

inline

Definition at line 83 of file ec2n.h.

◆ operator==()

bool EC2N::operator== ( const EC2N & rhs ) const

inline

Definition at line 85 of file ec2n.h.

The documentation for this class was generated from the following file:

ec2n.h

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Field

◆ FieldElement

◆ Point

Constructor & Destructor Documentation

◆ ~EC2N()

◆ EC2N() [1/3]

◆ EC2N() [2/3]

◆ EC2N() [3/3]

Member Function Documentation

◆ DEREncode()

◆ Equal()

◆ Identity()

◆ Inverse()

◆ InversionIsFast()

◆ Add()

◆ Double()

◆ Multiply()

◆ CascadeMultiply()

◆ VerifyPoint()

◆ EncodedPointSize()

◆ DecodePoint() [1/2]

◆ DecodePoint() [2/2]

◆ EncodePoint() [1/2]

◆ EncodePoint() [2/2]

◆ BERDecodePoint()

◆ DEREncodePoint()

◆ FieldSize()

◆ GetField()

◆ GetA()

◆ GetB()

◆ operator==()