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

#include <ec2n.h>

Inheritance diagram for EC2N:

Collaboration 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
virtual	~EC2N ()

	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	~AbstractGroup ()

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...

Public Member Functions inherited from EncodedPoint< EC2NPoint >
virtual	~EncodedPoint ()

Private Attributes
clonable_ptr< Field >	m_field

FieldElement	m_a

FieldElement	m_b

Point	m_R

Detailed Description

Elliptic Curve over GF(2^n)

Definition at line 24 of file ec2n.h.

Member Typedef Documentation

typedef GF2NP EC2N::Field

Definition at line 27 of file ec2n.h.

typedef Field::Element EC2N::FieldElement

Definition at line 28 of file ec2n.h.

typedef EC2NPoint EC2N::Point

Definition at line 29 of file ec2n.h.

Constructor & Destructor Documentation

virtual EC2N::~EC2N ( )

inlinevirtual

Definition at line 31 of file ec2n.h.

EC2N::EC2N ( )

inline

Construct an EC2N.

Definition at line 34 of file ec2n.h.

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 40 of file ec2n.h.

EC2N::EC2N ( BufferedTransformation & bt )

Construct an EC2N from BER encoded parameters.

Parameters

bt	BufferedTransformation derived object

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

Definition at line 16 of file ec2n.cpp.

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Member Function Documentation

const EC2N::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 >.

Definition at line 196 of file ec2n.cpp.

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EC2N::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 >.

Definition at line 125 of file ec2n.cpp.

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

inline

Definition at line 61 of file ec2n.h.

bool EC2N::DecodePoint	(	EC2N::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 >.

Definition at line 47 of file ec2n.cpp.

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bool EC2N::DecodePoint	(	EC2N::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 >.

Definition at line 41 of file ec2n.cpp.

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void EC2N::DEREncode ( BufferedTransformation & bt ) const

Encode the fields fieldID and curve of the sequence ECParameters.

Parameters

bt	BufferedTransformation derived object

Definition at line 32 of file ec2n.cpp.

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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 >.

Definition at line 135 of file ec2n.cpp.

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const EC2N::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 >.

Definition at line 218 of file ec2n.cpp.

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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 67 of file ec2n.h.

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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 >.

Definition at line 118 of file ec2n.cpp.

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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 >.

Definition at line 100 of file ec2n.cpp.

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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 >.

Definition at line 164 of file ec2n.cpp.

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Integer EC2N::FieldSize ( ) const

inline

Definition at line 78 of file ec2n.h.

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const FieldElement& EC2N::GetA ( ) const

inline

Definition at line 80 of file ec2n.h.

const FieldElement& EC2N::GetB ( ) const

inline

Definition at line 81 of file ec2n.h.

const Field& EC2N::GetField ( ) const

inline

Definition at line 79 of file ec2n.h.

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const EC2N::Point & EC2N::Identity ( ) const

virtual

Provides the Identity element.

Returns: the Identity element

Implements AbstractGroup< EC2NPoint >.

Definition at line 178 of file ec2n.cpp.

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const EC2N::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 >.

Definition at line 183 of file ec2n.cpp.

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 55 of file ec2n.h.

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

inline

Definition at line 59 of file ec2n.h.

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

inline

Definition at line 83 of file ec2n.h.

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bool EC2N::ValidateParameters	(	RandomNumberGenerator &	rng,
		unsigned int	level = `3`
	)		const

Definition at line 142 of file ec2n.cpp.

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 >.

Definition at line 155 of file ec2n.cpp.

Member Data Documentation

FieldElement EC2N::m_a

private

Definition at line 88 of file ec2n.h.

FieldElement EC2N::m_b

private

Definition at line 88 of file ec2n.h.

clonable_ptr<Field> EC2N::m_field

private

Definition at line 87 of file ec2n.h.

Point EC2N::m_R

mutableprivate

Definition at line 89 of file ec2n.h.

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

src/cryptopp/ec2n.h
src/cryptopp/ec2n.cpp

Public Types

Public Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation