de.flexiprovider.common.math.finitefields
Class GF2nONBElement

java.lang.Object
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  +--de.flexiprovider.common.math.finitefields.GF2nElement
        |
        +--de.flexiprovider.common.math.finitefields.GF2nONBElement

All Implemented Interfaces:

GFElement

public class GF2nONBElement

extends GF2nElement

This class implements an element of the finite field GF(2ⁿ ). It is represented in an optimal normal basis representation and holds the pointer mField to its corresponding field.

Author:

Birgit Henhapl, Martin Döring

See Also:

GF2nField, GF2nElement

Fields inherited from class de.flexiprovider.common.math.finitefields.GF2nElement

mDegree, mField

Constructor Summary

GF2nONBElement(GF2nONBElement gf2n)
Copy constructor.

GF2nONBElement(GF2nONBField gf2n, byte[] e)
Construct a new GF2nONBElement from its encoding.

GF2nONBElement(GF2nONBField gf2n, FlexiBigInt val)
Construct the element of the field gf2n with the specified value val.

GF2nONBElement(GF2nONBField gf2n, java.util.Random rand)
Construct a random element over the field gf2n, using the specified source of randomness.

Method Summary

GFElement	add(GFElement addend) Compute the sum of this element and addend.
void	addToThis(GFElement addend) Compute this + addend (overwrite this).
(package private) void	assignOne() assigns to this element the one element
(package private) void	assignZero() assigns to this element the zero element
java.lang.Object	clone() Create a new GF2nONBElement by cloning this GF2nPolynomialElement.
boolean	equals(java.lang.Object other) Compare this element with another object.
int	hashCode()
GF2nElement	increase() returns this element + 1.
void	increaseThis() increases this element.
GFElement	invert() Compute the multiplicative inverse of this element.
void	invertThis() Multiplicatively invert of this element (overwrite this).
boolean	isOne() Checks whether this element is one.
boolean	isZero() Checks whether this element is zero.
GFElement	multiply(GFElement factor) Compute the product of this element and factor.
void	multiplyThisBy(GFElement factor) Compute this * factor (overwrite this).
static GF2nONBElement	ONE(GF2nONBField gf2n) Create the one element.
(package private) void	reverseOrder() Reverses the bit-order in this element(according to 1363).
GF2nElement	solveQuadraticEquation() Solves a quadratic equation. Let z2 + z = this.
GF2nElement	square() returns this element to the power of 2.
GF2nElement	squareRoot() returns the root ofthis element.
void	squareRootThis() square roots this element.
void	squareThis() squares this element.
(package private) boolean	testBit(int index) Checks whether the indexed bit of the bit representation is set.
boolean	testRightmostBit() Returns whether the highest bit of the bit representation is set
byte[]	toByteArray() Returns this element as byte array.
FlexiBigInt	toFlexiBigInt() Returns this element as FlexiBigInt.
java.lang.String	toString() Returns a String representation of this element.
java.lang.String	toString(int radix) Returns a String representation of this element.
int	trace() Returns the trace of this element.
static GF2nONBElement	ZERO(GF2nONBField gf2n) Create the zero element.

Methods inherited from class de.flexiprovider.common.math.finitefields.GF2nElement

convert, getField, subtract, subtractFromThis

Methods inherited from class java.lang.Object

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

Constructor Detail

GF2nONBElement

public GF2nONBElement(GF2nONBField gf2n,
                      java.util.Random rand)

Construct a random element over the field gf2n, using the specified source of randomness.

Parameters:

gf2n - the field

rand - the source of randomness

GF2nONBElement

public GF2nONBElement(GF2nONBField gf2n,
                      byte[] e)

Construct a new GF2nONBElement from its encoding.

Parameters:

gf2n - the field

e - the encoded element

GF2nONBElement

public GF2nONBElement(GF2nONBField gf2n,
                      FlexiBigInt val)

Construct the element of the field gf2n with the specified value val.

Parameters:

gf2n - the field

val - the value represented by a FlexiBigInt

GF2nONBElement

public GF2nONBElement(GF2nONBElement gf2n)

Copy constructor.

Parameters:

gf2n - the field

Method Detail

clone

public java.lang.Object clone()

Create a new GF2nONBElement by cloning this GF2nPolynomialElement.

Overrides:

clone in class GF2nElement

Returns:

a copy of this element

ZERO

public static GF2nONBElement ZERO(GF2nONBField gf2n)

Create the zero element.

Parameters:

gf2n - the finite field

Returns:

the zero element in the given finite field

ONE

public static GF2nONBElement ONE(GF2nONBField gf2n)

Create the one element.

Parameters:

gf2n - the finite field

Returns:

the one element in the given finite field

assignZero

void assignZero()

assigns to this element the zero element

Overrides:

assignZero in class GF2nElement

assignOne

void assignOne()

assigns to this element the one element

Overrides:

assignOne in class GF2nElement

isZero

public boolean isZero()

Checks whether this element is zero.

Returns:

true if this is the zero element

isOne

public boolean isOne()

Checks whether this element is one.

Returns:

true if this is the one element

equals

public boolean equals(java.lang.Object other)

Compare this element with another object.

Overrides:

equals in class java.lang.Object

Parameters:

other - the other object

Returns:

true if the two objects are equal, false otherwise

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

Returns:

the hash code of this element

testRightmostBit

public boolean testRightmostBit()

Returns whether the highest bit of the bit representation is set

Overrides:

testRightmostBit in class GF2nElement

Returns:

true, if the highest bit of mPol is set, false, otherwise

testBit

boolean testBit(int index)

Checks whether the indexed bit of the bit representation is set. Warning: GF2nONBElement currently stores its bits in reverse order (compared to 1363) !!!

Overrides:

testBit in class GF2nElement

Parameters:

index - the index of the bit to test

Returns:

true if the indexed bit of mPol is set, false otherwise.

reverseOrder

void reverseOrder()

Reverses the bit-order in this element(according to 1363). This is a hack!

add

public GFElement add(GFElement addend)
              throws DifferentFieldsException

Compute the sum of this element and addend.

Parameters:

addend - the addend

Returns:

this + other (newly created)

Throws:

DifferentFieldsException - if the elements are of different fields.

addToThis

public void addToThis(GFElement addend)
               throws DifferentFieldsException

Compute this + addend (overwrite this).

Parameters:

addend - the addend

Throws:

DifferentFieldsException - if the elements are of different fields.

increase

public GF2nElement increase()

returns this element + 1.

Overrides:

increase in class GF2nElement

Returns:

this + 1

increaseThis

public void increaseThis()

increases this element.

Overrides:

increaseThis in class GF2nElement

multiply

public GFElement multiply(GFElement factor)
                   throws DifferentFieldsException

Compute the product of this element and factor.

Parameters:

factor - the factor

Returns:

this * factor (newly created)

Throws:

DifferentFieldsException - if the elements are of different fields.

multiplyThisBy

public void multiplyThisBy(GFElement factor)
                    throws DifferentFieldsException

Compute this * factor (overwrite this).

Parameters:

factor - the factor

Throws:

DifferentFieldsException - if the elements are of different fields.

square

public GF2nElement square()

returns this element to the power of 2.

Overrides:

square in class GF2nElement

Returns:

this²

squareThis

public void squareThis()

squares this element.

Overrides:

squareThis in class GF2nElement

invert

public GFElement invert()
                 throws java.lang.ArithmeticException

Compute the multiplicative inverse of this element.

Returns:

this^-1 (newly created)

Throws:

java.lang.ArithmeticException - if this is the zero element.

invertThis

public void invertThis()
                throws java.lang.ArithmeticException

Multiplicatively invert of this element (overwrite this).

Throws:

java.lang.ArithmeticException - if this is the zero element.

squareRoot

public GF2nElement squareRoot()

returns the root ofthis element.

Overrides:

squareRoot in class GF2nElement

Returns:

this^1/2

squareRootThis

public void squareRootThis()

square roots this element.

Overrides:

squareRootThis in class GF2nElement

trace

public int trace()

Returns the trace of this element.

Overrides:

trace in class GF2nElement

Returns:

the trace of this element

solveQuadraticEquation

public GF2nElement solveQuadraticEquation()
                                   throws NoSolutionException

Solves a quadratic equation.
Let z² + z = this. Then this method returns z.

Overrides:

solveQuadraticEquation in class GF2nElement

Returns:

z with z² + z = this

Throws:

NoSolutionException - if z² + z = this does not have a solution

toString

public java.lang.String toString()

Returns a String representation of this element.

Overrides:

toString in class java.lang.Object

Returns:

String representation of this element with the specified radix

toString

public java.lang.String toString(int radix)

Returns a String representation of this element. radix specifies the radix of the String representation.
NOTE: ONLY radix = 2 or radix = 16 IS IMPLEMENTED>

Parameters:

radix - specifies the radix of the String representation

Returns:

String representation of this element with the specified radix

toFlexiBigInt

public FlexiBigInt toFlexiBigInt()

Returns this element as FlexiBigInt. The conversion is P1363-conform.

Returns:

this element as FlexiBigInt

toByteArray

public byte[] toByteArray()

Returns this element as byte array. The conversion is P1363-conform.

Returns:

this element as byte array