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=false)
	Copy 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
	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	ScalarMultiply (const Point &P, const Integer &k) const
	Performs a scalar multiplication. More...

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

void	SimultaneousMultiply (Point results, const Point &base, const Integer exponents, unsigned int exponentsCount) const
	Multiplies a base to multiple exponents in a 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 ECP &rhs) const

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

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 = `false`
	)

Copy construct an ECP.

Parameters

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

See also: ModularArithmetic, MontgomeryRepresentation

Definition at line 46 of file ecp.cpp.

◆ 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 48 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 the fields fieldID and curve of the sequence ECParameters

Definition at line 58 of file ecp.cpp.

Member Function Documentation

◆ DEREncode()

void ECP::DEREncode ( BufferedTransformation & bt ) const

Encode the fields fieldID and curve of the sequence ECParameters.

Parameters

bt	BufferedTransformation derived object

Definition at line 74 of file ecp.cpp.

◆ Equal()

bool ECP::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< ECPPoint >.

Definition at line 205 of file ecp.cpp.

◆ Identity()

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

virtual

Provides the Identity element.

Returns: the Identity element

Implements AbstractGroup< ECPPoint >.

Definition at line 219 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 231 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 63 of file ecp.h.

◆ 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 244 of file ecp.cpp.

◆ Double()

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

virtual

Doubles an element in the group.

Parameters

a	the element

Returns: the element doubled

Reimplemented from AbstractGroup< ECPPoint >.

Definition at line 261 of file ecp.cpp.

◆ ScalarMultiply()

ECP::Point ECP::ScalarMultiply	(	const Point &	a,
		const Integer &	e
	)		const

virtual

Performs a scalar multiplication.

Parameters

a	multiplicand
e	multiplier

Returns: the product

Reimplemented from AbstractGroup< ECPPoint >.

Definition at line 378 of file ecp.cpp.

◆ CascadeScalarMultiply()

ECP::Point ECP::CascadeScalarMultiply	(	const Point &	x,
		const Integer &	e1,
		const Point &	y,
		const Integer &	e2
	)		const

virtual

TODO.

Parameters

x	first multiplicand
e1	the first multiplier
y	second multiplicand
e2	the second multiplier

Returns: TODO

Reimplemented from AbstractGroup< ECPPoint >.

Definition at line 486 of file ecp.cpp.

◆ SimultaneousMultiply()

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

virtual

Multiplies a base to multiple exponents in a group.

Parameters

results	an array of Elements
base	the base to raise to the exponents
exponents	an array of exponents
exponentsCount	the number of exponents in the array

SimultaneousMultiply() multiplies the base to each exponent in the exponents array and stores the result at the respective position in the results array.

SimultaneousMultiply() must be implemented in a derived class.

Precondition: COUNTOF(results) == exponentsCount; COUNTOF(exponents) == exponentsCount

Reimplemented from AbstractGroup< ECPPoint >.

Definition at line 388 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 196 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 78 of file ecp.h.

◆ 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 89 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 83 of file ecp.cpp.

◆ 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 >.

Definition at line 156 of file ecp.cpp.

◆ 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 >.

Definition at line 138 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 163 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 173 of file ecp.cpp.

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

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()

◆ Double()

◆ ScalarMultiply()

◆ CascadeScalarMultiply()

◆ SimultaneousMultiply()

◆ VerifyPoint()

◆ EncodedPointSize()

◆ DecodePoint() [1/2]

◆ DecodePoint() [2/2]

◆ EncodePoint() [1/2]

◆ EncodePoint() [2/2]

◆ BERDecodePoint()

◆ DEREncodePoint()