Elliptic Curve over GF(p), where p is prime. More...

Inheritance diagram for ECP:

Public Types
typedef ModularArithmetic	Field

typedef Integer	FieldElement

typedef ECPPoint	Point

Public Types inherited from AbstractGroup< ECPPoint >
typedef ECPPoint	Element

Public Member Functions
	ECP ()
	Construct an ECP.

	ECP (const ECP &ecp, bool convertToMontgomeryRepresentation)
	Construct an ECP. More...

	ECP (const Integer &modulus, const FieldElement &a, const FieldElement &b)
	Construct an ECP. More...

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

void	DEREncode (BufferedTransformation &bt) const
	DER Encode. More...

bool	Equal (const Point &P, const Point &Q) const
	Compare two points. 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

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

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

void	SimultaneousMultiply (Point results, const Point &base, const Integer exponents, unsigned int exponentsCount) const

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 ECP &rhs) const

Public Member Functions inherited from AbstractGroup< ECPPoint >
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...

Detailed Description

Elliptic Curve over GF(p), where p is prime.

Definition at line 26 of file ecp.h.

Constructor & Destructor Documentation

◆ ECP() [1/3]

ECP::ECP	(	const ECP &	ecp,
		bool	convertToMontgomeryRepresentation
	)

Construct an ECP.

Parameters

ecp	the other ECP object
convertToMontgomeryRepresentation	flag indicating if the curve should be converted to a MontgomeryRepresentation.

Prior to Crypto++ 8.3 the default value for convertToMontgomeryRepresentation was false. it was changed due to two audit tools finding, "Signature-compatible with a copy constructor".

See also: ModularArithmetic, MontgomeryRepresentation

◆ ECP() [2/3]

ECP::ECP	(	const Integer &	modulus,
		const FieldElement &	a,
		const FieldElement &	b
	)

inline

Construct an ECP.

Parameters

modulus	the prime modulus
a	Field::Element
b	Field::Element

Definition at line 52 of file ecp.h.

◆ ECP() [3/3]

ECP::ECP ( BufferedTransformation & bt )

Construct an ECP 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 ECP::DEREncode ( BufferedTransformation & bt ) const

DER Encode.

Parameters

bt	BufferedTransformation derived object

DEREncode encode the fields fieldID and curve of the sequence ECParameters

◆ Equal()

bool ECP::Equal	(	const Point &	P,
		const Point &	Q
	)		const

virtual

Compare two points.

Parameters

P	the first point
Q	the second point

Returns: true if equal, false otherwise

Implements AbstractGroup< ECPPoint >.

◆ Identity()

const Point& ECP::Identity ( ) const

virtual

Provides the Identity element.

Returns: the Identity element

Implements AbstractGroup< ECPPoint >.

◆ Inverse()

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

virtual

Inverts the element in the group.

Parameters

a	first element

Returns: the inverse of the element

Implements AbstractGroup< ECPPoint >.

◆ InversionIsFast()

bool ECP::InversionIsFast ( ) const

inlinevirtual

Determine if inversion is fast.

Returns: true if inversion is fast, false otherwise

Reimplemented from AbstractGroup< ECPPoint >.

Definition at line 75 of file ecp.h.

◆ Add()

const Point& ECP::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< ECPPoint >.

◆ VerifyPoint()

bool ECP::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< ECPPoint >.

◆ EncodedPointSize()

unsigned int ECP::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< ECPPoint >.

Definition at line 90 of file ecp.h.

◆ DecodePoint() [1/2]

bool ECP::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< ECPPoint >.

◆ DecodePoint() [2/2]

bool ECP::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< ECPPoint >.

◆ EncodePoint() [1/2]

void ECP::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< ECPPoint >.

◆ EncodePoint() [2/2]

void ECP::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< ECPPoint >.

◆ BERDecodePoint()

Point ECP::BERDecodePoint ( BufferedTransformation & bt ) const

virtual

BER Decodes an elliptic curve point.

Parameters

bt	source BufferedTransformation

Returns: the decoded elliptic curve point

Implements EncodedPoint< ECPPoint >.

◆ DEREncodePoint()

void ECP::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< ECPPoint >.

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

ecp.h

Public Types

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ ECP() [1/3]

◆ ECP() [2/3]

◆ ECP() [3/3]

Member Function Documentation

◆ DEREncode()

◆ Equal()

◆ Identity()

◆ Inverse()

◆ InversionIsFast()

◆ Add()

◆ VerifyPoint()

◆ EncodedPointSize()

◆ DecodePoint() [1/2]

◆ DecodePoint() [2/2]

◆ EncodePoint() [1/2]

◆ EncodePoint() [2/2]

◆ BERDecodePoint()

◆ DEREncodePoint()