ECP Class Reference

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

inline virtual

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

inline virtual

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