Performs modular arithmetic in Montgomery representation for increased speed. More...

#include <modarith.h>

Inheritance diagram for MontgomeryRepresentation:

Public Member Functions
	MontgomeryRepresentation (const Integer &modulus)
	Construct a MontgomeryRepresentation. More...

virtual ModularArithmetic *	Clone () const
	Clone a MontgomeryRepresentation. More...

bool	IsMontgomeryRepresentation () const
	Retrieves the representation. More...

Integer	ConvertIn (const Integer &a) const
	Reduces an element in the congruence class. More...

Integer	ConvertOut (const Integer &a) const
	Reduces an element in the congruence class. More...

const Integer &	MultiplicativeIdentity () const
	Retrieves the multiplicative identity. More...

const Integer &	Multiply (const Integer &a, const Integer &b) const
	Multiplies elements in the ring. More...

const Integer &	Square (const Integer &a) const
	Square an element in the ring. More...

const Integer &	MultiplicativeInverse (const Integer &a) const
	Calculate the multiplicative inverse of an element in the ring. More...

Integer	CascadeExponentiate (const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
	TODO. More...

void	SimultaneousExponentiate (Element results, const Element &base, const Integer exponents, unsigned int exponentsCount) const
	Exponentiates a base to multiple exponents in the ring. More...

Public Member Functions inherited from ModularArithmetic
	ModularArithmetic (const Integer &modulus=Integer::One())
	Construct a ModularArithmetic. More...

	ModularArithmetic (const ModularArithmetic &ma)
	Copy construct a ModularArithmetic. More...

ModularArithmetic &	operator= (const ModularArithmetic &ma)
	Assign a ModularArithmetic. More...

	ModularArithmetic (BufferedTransformation &bt)
	Construct a ModularArithmetic. More...

virtual ModularArithmetic *	Clone () const
	Clone a ModularArithmetic. More...

void	DEREncode (BufferedTransformation &bt) const
	Encodes in DER format. More...

void	DEREncodeElement (BufferedTransformation &out, const Element &a) const
	Encodes element in DER format. More...

void	BERDecodeElement (BufferedTransformation &in, Element &a) const
	Decodes element in DER format. More...

const Integer &	GetModulus () const
	Retrieves the modulus. More...

void	SetModulus (const Integer &newModulus)
	Sets the modulus. More...

virtual bool	IsMontgomeryRepresentation () const
	Retrieves the representation. More...

virtual Integer	ConvertIn (const Integer &a) const
	Reduces an element in the congruence class. More...

virtual Integer	ConvertOut (const Integer &a) const
	Reduces an element in the congruence class. More...

const Integer &	Half (const Integer &a) const
	Divides an element by 2. More...

bool	Equal (const Integer &a, const Integer &b) const
	Compare two elements for equality. More...

const Integer &	Identity () const
	Provides the Identity element. More...

const Integer &	Add (const Integer &a, const Integer &b) const
	Adds elements in the ring. More...

Integer &	Accumulate (Integer &a, const Integer &b) const
	TODO. More...

const Integer &	Inverse (const Integer &a) const
	Inverts the element in the ring. More...

const Integer &	Subtract (const Integer &a, const Integer &b) const
	Subtracts elements in the ring. More...

Integer &	Reduce (Integer &a, const Integer &b) const
	TODO. More...

const Integer &	Double (const Integer &a) const
	Doubles an element in the ring. More...

const Integer &	MultiplicativeIdentity () const
	Retrieves the multiplicative identity. More...

const Integer &	Multiply (const Integer &a, const Integer &b) const
	Multiplies elements in the ring. More...

const Integer &	Square (const Integer &a) const
	Square an element in the ring. More...

bool	IsUnit (const Integer &a) const
	Determines whether an element is a unit in the ring. More...

const Integer &	MultiplicativeInverse (const Integer &a) const
	Calculate the multiplicative inverse of an element in the ring. More...

const Integer &	Divide (const Integer &a, const Integer &b) const
	Divides elements in the ring. More...

Integer	CascadeExponentiate (const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
	TODO. More...

void	SimultaneousExponentiate (Element results, const Element &base, const Integer exponents, unsigned int exponentsCount) const
	Exponentiates a base to multiple exponents in the ring. More...

unsigned int	MaxElementBitLength () const
	Provides the maximum bit size of an element in the ring. More...

unsigned int	MaxElementByteLength () const
	Provides the maximum byte size of an element in the ring. More...

Element	RandomElement (RandomNumberGenerator &rng, const RandomizationParameter &ignore_for_now=0) const
	Provides a random element in the ring. More...

bool	operator== (const ModularArithmetic &rhs) const
	Compares two ModularArithmetic for equality. More...

Public Member Functions inherited from AbstractRing< Integer >
	AbstractRing ()
	Construct an AbstractRing. More...

	AbstractRing (const AbstractRing &source)
	Copy construct an AbstractRing. More...

AbstractRing &	operator= (const AbstractRing &source)
	Assign an AbstractRing. More...

virtual bool	IsUnit (const Element &a) const=0
	Determines whether an element is a unit in the group. More...

virtual const Element &	MultiplicativeIdentity () const=0
	Retrieves the multiplicative identity. More...

virtual const Element &	Multiply (const Element &a, const Element &b) const=0
	Multiplies elements in the group. More...

virtual const Element &	MultiplicativeInverse (const Element &a) const=0
	Calculate the multiplicative inverse of an element in the group. More...

virtual const Element &	Square (const Element &a) const
	Square an element in the group. More...

virtual const Element &	Divide (const Element &a, const Element &b) const
	Divides elements in the group. More...

virtual Element	Exponentiate (const Element &a, const Integer &e) const
	Raises a base to an exponent in the group. More...

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

virtual void	SimultaneousExponentiate (Element results, const Element &base, const Integer exponents, unsigned int exponentsCount) const
	Exponentiates a base to multiple exponents in the Ring. More...

virtual const AbstractGroup< Integer > &	MultiplicativeGroup () const
	Retrieves the multiplicative group. More...

Public Member Functions inherited from AbstractGroup< Integer >
virtual bool	Equal (const Element &a, const Element &b) const=0
	Compare two elements for equality. More...

virtual const Element &	Identity () const=0
	Provides the Identity element. More...

virtual const Element &	Add (const Element &a, const Element &b) const=0
	Adds elements in the group. More...

virtual const Element &	Inverse (const Element &a) const=0
	Inverts the element in the group. More...

virtual bool	InversionIsFast () const
	Determine if inversion is fast. More...

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...

Additional Inherited Members
Public Types inherited from ModularArithmetic
typedef int	RandomizationParameter

typedef Integer	Element

Public Types inherited from AbstractRing< Integer >
typedef Integer	Element

Public Types inherited from AbstractGroup< Integer >
typedef Integer	Element

Static Public Attributes inherited from ModularArithmetic
static const RandomizationParameter	DefaultRandomizationParameter

Detailed Description

Performs modular arithmetic in Montgomery representation for increased speed.

The Montgomery representation represents each congruence class [a] as a*r%n, where r is a convenient power of 2.

const Element& returned by member functions are references to internal data members. Since each object may have only one such data member for holding results, the following code will produce incorrect results:

    abcd = group.Add(group.Add(a,b), group.Add(c,d));

But this should be fine:

    abcd = group.Add(a, group.Add(b, group.Add(c,d));

Definition at line 295 of file modarith.h.

Constructor & Destructor Documentation

◆ ~MontgomeryRepresentation()

virtual MontgomeryRepresentation::~MontgomeryRepresentation ( )

inlinevirtual

Definition at line 298 of file modarith.h.

◆ MontgomeryRepresentation()

MontgomeryRepresentation::MontgomeryRepresentation ( const Integer & modulus )

Construct a MontgomeryRepresentation.

Parameters

modulus congruence class modulus

Note: The modulus must be odd.

Member Function Documentation

◆ Clone()

virtual ModularArithmetic * MontgomeryRepresentation::Clone ( ) const

inlinevirtual

Clone a MontgomeryRepresentation.

Returns: pointer to a new MontgomeryRepresentation

Clone effectively copy constructs a new MontgomeryRepresentation. The caller is responsible for deleting the pointer returned from this method.

Reimplemented from ModularArithmetic.

Definition at line 309 of file modarith.h.

◆ IsMontgomeryRepresentation()

bool MontgomeryRepresentation::IsMontgomeryRepresentation ( ) const

inlinevirtual

Retrieves the representation.

Returns: true if the if the modulus is in Montgomery form for multiplication, false otherwise

Reimplemented from ModularArithmetic.

Definition at line 311 of file modarith.h.

◆ ConvertIn()

Integer MontgomeryRepresentation::ConvertIn ( const Integer & a ) const

inlinevirtual

Reduces an element in the congruence class.

Parameters

a	element to convert

Returns: the reduced element

ConvertIn is useful for derived classes, like MontgomeryRepresentation, which must convert between representations.

Reimplemented from ModularArithmetic.

Definition at line 313 of file modarith.h.

◆ ConvertOut()

Integer MontgomeryRepresentation::ConvertOut ( const Integer & a ) const

virtual

Reduces an element in the congruence class.

Parameters

a	element to convert

Returns: the reduced element

ConvertOut is useful for derived classes, like MontgomeryRepresentation, which must convert between representations.

Reimplemented from ModularArithmetic.

◆ MultiplicativeIdentity()

const Integer & MontgomeryRepresentation::MultiplicativeIdentity ( ) const

inlinevirtual

Retrieves the multiplicative identity.

Returns: the multiplicative identity

the base class implementations returns 1.

Reimplemented from ModularArithmetic.

Definition at line 318 of file modarith.h.

◆ Multiply()

const Integer & MontgomeryRepresentation::Multiply	(	const Integer &	a,
		const Integer &	b
	)		const

virtual

Multiplies elements in the ring.

Parameters

a	the multiplicand
b	the multiplier

Returns: the product of a and b

Multiply returns a*b%n.

Reimplemented from ModularArithmetic.

◆ Square()

const Integer & MontgomeryRepresentation::Square ( const Integer & a ) const

virtual

Square an element in the ring.

Parameters

a	the element

Returns: the element squared

Square returns a*a%n. The element a must provide a Square member function.

Reimplemented from ModularArithmetic.

◆ MultiplicativeInverse()

const Integer & MontgomeryRepresentation::MultiplicativeInverse ( const Integer & a ) const

virtual

Calculate the multiplicative inverse of an element in the ring.

Parameters

a	the element

MultiplicativeInverse returns a^-1%n. The element a must provide a InverseMod member function.

Reimplemented from ModularArithmetic.

◆ CascadeExponentiate()

Integer MontgomeryRepresentation::CascadeExponentiate	(	const Integer &	x,
		const Integer &	e1,
		const Integer &	y,
		const Integer &	e2
	)		const

inlinevirtual

TODO.

Parameters

x	first element
e1	first exponent
y	second element
e2	second exponent

Returns: TODO

Reimplemented from ModularArithmetic.

Definition at line 327 of file modarith.h.

◆ SimultaneousExponentiate()

void MontgomeryRepresentation::SimultaneousExponentiate	(	Element *	results,
		const Element &	base,
		const Integer *	exponents,
		unsigned int	exponentsCount
	)		const

inlinevirtual

Exponentiates a base to multiple exponents in the ring.

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

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

SimultaneousExponentiate() must be implemented in a derived class.

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

Reimplemented from ModularArithmetic.

Definition at line 330 of file modarith.h.

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

modarith.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ~MontgomeryRepresentation()

◆ MontgomeryRepresentation()

Member Function Documentation

◆ Clone()

◆ IsMontgomeryRepresentation()

◆ ConvertIn()

◆ ConvertOut()

◆ MultiplicativeIdentity()

◆ Multiply()

◆ Square()

◆ MultiplicativeInverse()

◆ CascadeExponentiate()

◆ SimultaneousExponentiate()