Class ECFieldElement.F2m

java.lang.Object

org.gudy.bouncycastle.math.ec.ECFieldElement

org.gudy.bouncycastle.math.ec.ECFieldElement.F2m

All Implemented Interfaces:

ECConstants

Enclosing class:

ECFieldElement

public static class ECFieldElement.F2m
extends ECFieldElement

Class representing the Elements of the finite field F2m in polynomial basis (PB) representation. Both trinomial (TPB) and pentanomial (PPB) polynomial basis representations are supported. Gaussian normal basis (GNB) representation is not supported.

Nested Class Summary

Nested classes/interfaces inherited from class ECFieldElement

ECFieldElement.F2m, ECFieldElement.Fp

Field Summary

Fields

Modifier and Type	Field	Description
static final int	GNB	Indicates gaussian normal basis representation (GNB).
private int	k1	TPB: The integer k where xm + xk + 1 represents the reduction polynomial f(z). PPB: The integer k1 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).
private int	k2	TPB: Always set to 0 PPB: The integer k2 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).
private int	k3	TPB: Always set to 0 PPB: The integer k3 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).
private int	m	The exponent m of F2m.
static final int	PPB	Indicates pentanomial basis representation (PPB).
private int	representation	TPB or PPB.
private int	t	The number of ints required to hold m bits.
static final int	TPB	Indicates trinomial basis representation (TPB).
private IntArray	x	The IntArray holding the bits.

Fields inherited from interface ECConstants

FOUR, ONE, THREE, TWO, ZERO

Constructor Summary

Constructors

Modifier	Constructor	Description
	F2m(int m, int k1, int k2, int k3, BigInteger x)	Constructor for PPB.
private	F2m(int m, int k1, int k2, int k3, IntArray x)
	F2m(int m, int k, BigInteger x)	Constructor for TPB.

Method Summary

Modifier and Type	Method	Description
ECFieldElement	add(ECFieldElement b)
static void	checkFieldElements(ECFieldElement a, ECFieldElement b)	Checks, if the ECFieldElements a and b are elements of the same field F2m (having the same representation).
ECFieldElement	divide(ECFieldElement b)
boolean	equals(Object anObject)
String	getFieldName()
int	getFieldSize()
int	getK1()
int	getK2()
int	getK3()
int	getM()
int	getRepresentation()
int	hashCode()
ECFieldElement	invert()
ECFieldElement	multiply(ECFieldElement b)
ECFieldElement	negate()
ECFieldElement	sqrt()
ECFieldElement	square()
ECFieldElement	subtract(ECFieldElement b)
BigInteger	toBigInteger()

Methods inherited from class ECFieldElement

toString

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details

GNB

public static final int GNB

Indicates gaussian normal basis representation (GNB). Number chosen according to X9.62. GNB is not implemented at present.

See Also:

• Constant Field Values

TPB

public static final int TPB

Indicates trinomial basis representation (TPB). Number chosen according to X9.62.

See Also:

• Constant Field Values

PPB

public static final int PPB

Indicates pentanomial basis representation (PPB). Number chosen according to X9.62.

See Also:

• Constant Field Values

representation

private int representation

TPB or PPB.

m

private int m

The exponent m of F2m.

k1

private int k1

TPB: The integer k where xm + xk + 1 represents the reduction polynomial f(z).
PPB: The integer k1 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k2

private int k2

TPB: Always set to 0
PPB: The integer k2 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k3

private int k3

TPB: Always set to 0
PPB: The integer k3 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

x

private IntArray x

The IntArray holding the bits.

t

private int t

The number of ints required to hold m bits.

Constructor Details

F2m

public F2m(int m,
 int k1,
 int k2,
 int k3,
 BigInteger x)

Constructor for PPB.

Parameters:

m - The exponent m of F2m.

k1 - The integer k1 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k2 - The integer k2 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k3 - The integer k3 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

x - The BigInteger representing the value of the field element.

F2m

public F2m(int m,
 int k,
 BigInteger x)

Constructor for TPB.

Parameters:

m - The exponent m of F2m.

k - The integer k where xm + xk + 1 represents the reduction polynomial f(z).

x - The BigInteger representing the value of the field element.

F2m

private F2m(int m,
 int k1,
 int k2,
 int k3,
 IntArray x)

Method Details

toBigInteger

public BigInteger toBigInteger()

Specified by:

toBigInteger in class ECFieldElement

getFieldName

public String getFieldName()

Specified by:

getFieldName in class ECFieldElement

getFieldSize

public int getFieldSize()

Specified by:

getFieldSize in class ECFieldElement

checkFieldElements

public static void checkFieldElements(ECFieldElement a,
 ECFieldElement b)

Checks, if the ECFieldElements a and b are elements of the same field F2m (having the same representation).

Parameters:

a - field element.

b - field element to be compared.

Throws:

IllegalArgumentException - if a and b are not elements of the same field F2m (having the same representation).

add

public ECFieldElement add(ECFieldElement b)

Specified by:

add in class ECFieldElement

subtract

public ECFieldElement subtract(ECFieldElement b)

Specified by:

subtract in class ECFieldElement

multiply

public ECFieldElement multiply(ECFieldElement b)

Specified by:

multiply in class ECFieldElement

divide

public ECFieldElement divide(ECFieldElement b)

Specified by:

divide in class ECFieldElement

negate

public ECFieldElement negate()

Specified by:

negate in class ECFieldElement

square

public ECFieldElement square()

Specified by:

square in class ECFieldElement

invert

public ECFieldElement invert()

Specified by:

invert in class ECFieldElement

sqrt

public ECFieldElement sqrt()

Specified by:

sqrt in class ECFieldElement

getRepresentation

public int getRepresentation()

Returns:

the representation of the field F2m, either of TPB (trinomial basis representation) or PPB (pentanomial basis representation).

getM

public int getM()

Returns:

the degree m of the reduction polynomial f(z).

getK1

public int getK1()

Returns:

TPB: The integer k where xm + xk + 1 represents the reduction polynomial f(z).
PPB: The integer k1 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

getK2

public int getK2()

Returns:

TPB: Always returns 0
PPB: The integer k2 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

getK3

public int getK3()

Returns:

TPB: Always set to 0
PPB: The integer k3 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

equals

public boolean equals(Object anObject)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object