Crypto++  5.6.5
Free C++ class library of cryptographic schemes
Public Types | Public Member Functions | List of all members
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=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 PointIdentity () const
 Provides the Identity element. More...
 
const PointInverse (const Point &P) const
 Inverts the element in the group. More...
 
bool InversionIsFast () const
 Determine if inversion is fast. More...
 
const PointAdd (const Point &P, const Point &Q) const
 Adds elements in the group. More...
 
const PointDouble (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 FieldGetField () const
 
const FieldElementGetA () const
 
const FieldElementGetB () const
 
bool operator== (const ECP &rhs) const
 
- Public Member Functions inherited from AbstractGroup< ECPPoint >
virtual const ElementSubtract (const Element &a, const Element &b) const
 Subtracts elements in the group. More...
 
virtual ElementAccumulate (Element &a, const Element &b) const
 TODO. More...
 
virtual ElementReduce (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 22 of file ecp.h.

Constructor & Destructor Documentation

ECP::ECP ( const ECP ecp,
bool  convertToMontgomeryRepresentation = false 
)

Copy construct an ECP.

Parameters
ecpthe other ECP object
convertToMontgomeryRepresentationflag indicating if the curve should be converted to a MontgomeryRepresentation
See also
ModularArithmetic, MontgomeryRepresentation
ECP::ECP ( const Integer modulus,
const FieldElement a,
const FieldElement b 
)
inline

Construct an ECP.

Parameters
modulusthe prime modulus
aField::Element
bField::Element

Definition at line 44 of file ecp.h.

ECP::ECP ( BufferedTransformation bt)

Construct an ECP from BER encoded parameters.

Parameters
btBufferedTransformation derived object

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

Member Function Documentation

void ECP::DEREncode ( BufferedTransformation bt) const

Encode the fields fieldID and curve of the sequence ECParameters.

Parameters
btBufferedTransformation derived object
bool ECP::Equal ( const Point a,
const Point b 
) const
virtual

Compare two elements for equality.

Parameters
afirst element
bsecond element
Returns
true if the elements are equal, false otherwise

Equal() tests the elements for equality using a==b

Implements AbstractGroup< ECPPoint >.

const Point& ECP::Identity ( ) const
virtual

Provides the Identity element.

Returns
the Identity element

Implements AbstractGroup< ECPPoint >.

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

Inverts the element in the group.

Parameters
afirst element
Returns
the inverse of the element

Implements AbstractGroup< ECPPoint >.

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 59 of file ecp.h.

const Point& ECP::Add ( const Point a,
const Point b 
) const
virtual

Adds elements in the group.

Parameters
afirst element
bsecond element
Returns
the sum of a and b

Implements AbstractGroup< ECPPoint >.

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

Doubles an element in the group.

Parameters
athe element
Returns
the element doubled

Reimplemented from AbstractGroup< ECPPoint >.

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

Performs a scalar multiplication.

Parameters
amultiplicand
emultiplier
Returns
the product

Reimplemented from AbstractGroup< ECPPoint >.

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

TODO.

Parameters
xfirst multiplicand
e1the first multiplier
ysecond multiplicand
e2the second multiplier
Returns
TODO

Reimplemented from AbstractGroup< ECPPoint >.

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

Multiplies a base to multiple exponents in a group.

Parameters
resultsan array of Elements
basethe base to raise to the exponents
exponentsan array of exponents
exponentsCountthe 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 >.

bool ECP::VerifyPoint ( const Point P) const
virtual

Verifies points on elliptic curve.

Parameters
Ppoint to verify
Returns
true if the point is valid, false otherwise

Implements EncodedPoint< ECPPoint >.

unsigned int ECP::EncodedPointSize ( bool  compressed = false) const
inlinevirtual

Determines encoded point size.

Parameters
compressedflag indicating if the point is compressed
Returns
the minimum number of bytes required to encode the point

Implements EncodedPoint< ECPPoint >.

Definition at line 74 of file ecp.h.

bool ECP::DecodePoint ( Point P,
BufferedTransformation bt,
size_t  len 
) const
virtual

Decodes an elliptic curve point.

Parameters
Ppoint which is decoded
btsource BufferedTransformation
lennumber of bytes to read from the BufferedTransformation
Returns
true if a point was decoded, false otherwise

Implements EncodedPoint< ECPPoint >.

bool ECP::DecodePoint ( Point P,
const byte *  encodedPoint,
size_t  len 
) const
virtual

Decodes an elliptic curve point.

Parameters
Ppoint which is decoded
encodedPointbyte array with the encoded point
lenthe size of the array
Returns
true if a point was decoded, false otherwise

Implements EncodedPoint< ECPPoint >.

void ECP::EncodePoint ( byte *  encodedPoint,
const Point P,
bool  compressed 
) const
virtual

Encodes an elliptic curve point.

Parameters
Ppoint which is decoded
encodedPointbyte array for the encoded point
compressedflag indicating if the point is compressed

encodedPoint must be at least EncodedPointSize() in length

Implements EncodedPoint< ECPPoint >.

void ECP::EncodePoint ( BufferedTransformation bt,
const Point P,
bool  compressed 
) const
virtual

Encodes an elliptic curve point.

Parameters
bttarget BufferedTransformation
Ppoint which is encoded
compressedflag indicating if the point is compressed

Implements EncodedPoint< ECPPoint >.

Point ECP::BERDecodePoint ( BufferedTransformation bt) const
virtual

BER Decodes an elliptic curve point.

Parameters
btsource BufferedTransformation
Returns
the decoded elliptic curve point

Implements EncodedPoint< ECPPoint >.

void ECP::DEREncodePoint ( BufferedTransformation bt,
const Point P,
bool  compressed 
) const
virtual

DER Encodes an elliptic curve point.

Parameters
bttarget BufferedTransformation
Ppoint which is encoded
compressedflag indicating if the point is compressed

Implements EncodedPoint< ECPPoint >.


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