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

#include <ecp.h>

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.

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

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

void	DEREncode (BufferedTransformation &bt) const
	DER Encode.

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

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

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

bool	InversionIsFast () const
	Determine if inversion is fast.

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

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.

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

Detailed Description

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

Definition at line 26 of file ecp.h.

Member Typedef Documentation

◆ Field

typedef ModularArithmetic ECP::Field

Definition at line 29 of file ecp.h.

◆ FieldElement

typedef Integer ECP::FieldElement

Definition at line 30 of file ecp.h.

◆ Point

typedef ECPPoint ECP::Point

Definition at line 31 of file ecp.h.

Constructor & Destructor Documentation

◆ ~ECP()

virtual ECP::~ECP ( )

inlinevirtual

Definition at line 33 of file ecp.h.

◆ ECP() [1/4]

ECP::ECP ( )

inline

Construct an ECP.

Definition at line 36 of file ecp.h.

◆ ECP() [2/4]

ANONYMOUS_NAMESPACE_END 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

Definition at line 62 of file ecp.cpp.

◆ ECP() [3/4]

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() [4/4]

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

Definition at line 74 of file ecp.cpp.

Member Function Documentation

◆ Add()

const ECP::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 >.

Definition at line 260 of file ecp.cpp.

◆ BERDecodePoint()

ECP::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 >.

Definition at line 179 of file ecp.cpp.

◆ CascadeMultiply()

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

inline

Definition at line 84 of file ecp.h.

◆ CascadeScalarMultiply()

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

Definition at line 492 of file ecp.cpp.

◆ DecodePoint() [1/2]

bool ECP::DecodePoint	(	ECP::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 >.

Definition at line 105 of file ecp.cpp.

◆ DecodePoint() [2/2]

bool ECP::DecodePoint	(	ECP::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 >.

Definition at line 99 of file ecp.cpp.

◆ 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

Definition at line 90 of file ecp.cpp.

◆ 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 >.

Definition at line 189 of file ecp.cpp.

◆ Double()

const ECP::Point & ECP::Double ( const Point & P ) const

Definition at line 277 of file ecp.cpp.

◆ 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.

◆ EncodePoint() [1/2]

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 >.

Definition at line 154 of file ecp.cpp.

◆ EncodePoint() [2/2]

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 >.

Definition at line 172 of file ecp.cpp.

◆ 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 >.

Definition at line 221 of file ecp.cpp.

◆ FieldSize()

Integer ECP::FieldSize ( ) const

inline

Definition at line 101 of file ecp.h.

◆ GetA()

const FieldElement & ECP::GetA ( ) const

inline

Definition at line 103 of file ecp.h.

◆ GetB()

const FieldElement & ECP::GetB ( ) const

inline

Definition at line 104 of file ecp.h.

◆ GetField()

const Field & ECP::GetField ( ) const

inline

Definition at line 102 of file ecp.h.

◆ Identity()

const ECP::Point & ECP::Identity ( ) const

virtual

Provides the Identity element.

Returns: the Identity element

Implements AbstractGroup< ECPPoint >.

Definition at line 235 of file ecp.cpp.

◆ Inverse()

const ECP::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 >.

Definition at line 247 of file ecp.cpp.

◆ 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.

◆ Multiply()

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

inline

Definition at line 82 of file ecp.h.

◆ operator==()

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

inline

Definition at line 106 of file ecp.h.

◆ ScalarMultiply()

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

Definition at line 384 of file ecp.cpp.

◆ SimultaneousMultiply()

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

Definition at line 394 of file ecp.cpp.

◆ ValidateParameters()

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

Definition at line 196 of file ecp.cpp.

◆ 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 >.

Definition at line 212 of file ecp.cpp.

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

G:/work/subversion/scol-technologies/trunk/scol/plugins/security/cryptopp/ecp.h
G:/work/subversion/scol-technologies/trunk/scol/plugins/security/cryptopp/ecp.cpp

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Field

◆ FieldElement

◆ Point

Constructor & Destructor Documentation

◆ ~ECP()

◆ ECP() [1/4]

◆ ECP() [2/4]

◆ ECP() [3/4]

◆ ECP() [4/4]

Member Function Documentation

◆ Add()

◆ BERDecodePoint()

◆ CascadeMultiply()

◆ CascadeScalarMultiply()

◆ DecodePoint() [1/2]

◆ DecodePoint() [2/2]

◆ DEREncode()

◆ DEREncodePoint()

◆ Double()

◆ EncodedPointSize()

◆ EncodePoint() [1/2]

◆ EncodePoint() [2/2]

◆ Equal()

◆ FieldSize()

◆ GetA()

◆ GetB()

◆ GetField()

◆ Identity()

◆ Inverse()

◆ InversionIsFast()

◆ Multiply()

◆ operator==()

◆ ScalarMultiply()

◆ SimultaneousMultiply()

◆ ValidateParameters()

◆ VerifyPoint()