org.spongycastle.pqc.math.linearalgebra

Class GF2mField

java.lang.Object

org.spongycastle.pqc.math.linearalgebra.GF2mField

public class GF2mField
extends java.lang.Object

This class describes operations with elements from the finite field F = GF(2^m). ( GF(2^m)= GF(2)[A] where A is a root of irreducible polynomial with degree m, each field element B has a polynomial basis representation, i.e. it is represented by a different binary polynomial of degree less than m, B = poly(A) ) All operations are defined only for field with 1< m <32. For the representation of field elements the map f: F->Z, poly(A)->poly(2) is used, where integers have the binary representation. For example: A^7+A^3+A+1 -> (00...0010001011)=139 Also for elements type Integer is used.

See Also:

PolynomialRingGF2

Constructor Summary

Constructors

Constructor and Description
GF2mField(byte[] enc)
GF2mField(GF2mField field)
GF2mField(int degree) create a finite field GF(2^m)
GF2mField(int degree, int poly) create a finite field GF(2^m) with the fixed field polynomial

Method Summary

Modifier and Type	Method and Description
int	add(int a, int b) Return sum of two elements
java.lang.String	elementToStr(int a)
boolean	equals(java.lang.Object other) checks if given object is equal to this field.
int	exp(int a, int k) compute exponentiation a^k
int	getDegree() return degree of the field
byte[]	getEncoded() return the encoded form of this field
int	getPolynomial() return the field polynomial
int	getRandomElement(java.security.SecureRandom sr) create a random field element using PRNG sr
int	getRandomNonZeroElement() create a random non-zero field element
int	getRandomNonZeroElement(java.security.SecureRandom sr) create a random non-zero field element using PRNG sr
int	hashCode()
int	inverse(int a) compute the multiplicative inverse of a
boolean	isElementOfThisField(int e)
int	mult(int a, int b) Return product of two elements
int	sqRoot(int a) compute the square root of an integer
java.lang.String	toString() Returns a human readable form of this field.

Methods inherited from class java.lang.Object

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

Constructor Detail

GF2mField

public GF2mField(int degree)

create a finite field GF(2^m)

Parameters:

degree - the degree of the field

GF2mField

public GF2mField(int degree,
                 int poly)

create a finite field GF(2^m) with the fixed field polynomial

Parameters:

degree - the degree of the field

poly - the field polynomial

GF2mField

public GF2mField(byte[] enc)

GF2mField

public GF2mField(GF2mField field)

Method Detail

getDegree

public int getDegree()

return degree of the field

Returns:

degree of the field

getPolynomial

public int getPolynomial()

return the field polynomial

Returns:

the field polynomial

getEncoded

public byte[] getEncoded()

return the encoded form of this field

Returns:

the field in byte array form

add

public int add(int a,
               int b)

Return sum of two elements

Parameters:

a -

b -

Returns:

a+b

mult

public int mult(int a,
                int b)

Return product of two elements

Parameters:

a -

b -

Returns:

a*b

exp

public int exp(int a,
               int k)

compute exponentiation a^k

Parameters:

a - a field element a

k - k degree

Returns:

a^k

inverse

public int inverse(int a)

compute the multiplicative inverse of a

Parameters:

a - a field element a

Returns:

a^-1

sqRoot

public int sqRoot(int a)

compute the square root of an integer

Parameters:

a - a field element a

Returns:

a^1/2

getRandomElement

public int getRandomElement(java.security.SecureRandom sr)

create a random field element using PRNG sr

Parameters:

sr - SecureRandom

Returns:

a random element

getRandomNonZeroElement

public int getRandomNonZeroElement()

create a random non-zero field element

Returns:

a random element

getRandomNonZeroElement

public int getRandomNonZeroElement(java.security.SecureRandom sr)

create a random non-zero field element using PRNG sr

Parameters:

sr - SecureRandom

Returns:

a random non-zero element

isElementOfThisField

public boolean isElementOfThisField(int e)

Returns:

true if e is encoded element of this field and false otherwise

elementToStr

public java.lang.String elementToStr(int a)

equals

public boolean equals(java.lang.Object other)

checks if given object is equal to this field.

The method returns false whenever the given object is not GF2m.

Overrides:

equals in class java.lang.Object

Parameters:

other - object

Returns:

true or false

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

toString

public java.lang.String toString()

Returns a human readable form of this field.

Overrides:

toString in class java.lang.Object

Returns:

a human readable form of this field.