iaik.security.ec.math.field

Class BinaryFieldElement

java.lang.Object

iaik.security.ec.math.field.BinaryFieldElement

All Implemented Interfaces:

FieldElement, GenericFieldElement, Cloneable

public final class BinaryFieldElement
extends Object
implements FieldElement

This class represents a mutable binary field element. It can be used in combination with arbitrary binary fields.

Also note that (almost) all methods in this class work in-place. So, there is no guarantee that values input to methods in this class will not be overridden. In case of doubt and if values need to be reused, always clone the value, before inputting it to a method.

Author:

Christian Hanser

See Also:

FieldElement, BinaryField

Method Summary

Modifier and Type	Method and Description
BinaryFieldElement	add(BinaryFieldElement b, boolean preserveB) Performs either the addition a += b or b += a, if preserveB is set to false.
BinaryFieldElement	add(GenericFieldElement b) Adds b to this.
BinaryFieldElement	addBase(GenericFieldElement b) Adds b to this where b is an element of the underlying base field.
BinaryFieldElement	addOutOfPlace(GenericFieldElement b) Adds this with b which is an element of the base field, where a new object holding the result is created.
BinaryFieldElement	clone() Clones the value of this field element.
BinaryFieldElement	divide(GenericFieldElement b) Divides this and another field elements.
boolean	equals(Object obj)
BinaryFieldElement	exponentiate(BigInteger n) Raises this to the power n.
BinaryFieldElement	exponentiate(int n) Raises this to the power n.
BinaryFieldElement	exponentiateByPowerOf2(int n) Raises this element to the power 2n.
BinaryFieldElement	exponentiateOutOfPlace(BigInteger n) Raises this to the power n.
BinaryFieldElement	exponentiateOutOfPlace(int n) Raises this to the power n.
int	getBit(int index) Returns the value of a certain bit of this.
PrecomputationData	getExtendedPrecomputationData() Compiles 256 precomputed values for the multiplication algorithm.
BinaryField	getField() Returns the associated finite field.
PrecomputationData	getPrecomputationData() Compiles 16 precomputed values for the multiplication algorithm.
int	getTrace() Determines the trace of this.
int	hashCode()
BinaryFieldElement	invert() Sets this to its inverse.
boolean	isOne() Determines whether this is one.
boolean	isZero() Determines whether this is zero.
BinaryFieldElement	multiply(BigInteger n) Multiples this by n.
BinaryFieldElement	multiply(GenericFieldElement b) Multiplies this with b which is an element of the same field.
BinaryFieldElement	multiply(PrecomputationData data) Multiplies this with the already available precomputation data of b, where a new object holding the result is created.
BinaryFieldElement	multiplyByBase(GenericFieldElement b) Multiplies this with b which is an element of the base field.
BinaryFieldElement	multiplyByBaseOutOfPlace(GenericFieldElement b) Multiplies this with b which is an element of the base field, where a new object holding the result is created.
BinaryFieldElement	multiplyOutOfPlace(BigInteger n) Multiples this by n, where a new object holding the result is created.
BinaryFieldElement	multiplyOutOfPlace(GenericFieldElement b) Multiplies this with b which is an element of the same field, where a new object holding the result is created.
BinaryFieldElement	multiplyOutOfPlace(PrecomputationData data) Multiplies this with the already available precomputation data of b.
BinaryFieldElement	negate() Returns the negative of this.
BinaryFieldElement	negateOutOfPlace() Returns the negative of this, where a new object holding the result is created.
BinaryFieldElement	square() Computes the square of this in-place.
BinaryFieldElement	squareOutOfPlace() Computes the square of this, where a new object holding the result is created.
BinaryFieldElement	squareRoot() Computes the square root of this.
BinaryFieldElement	subtract(GenericFieldElement b) Subtracts b from this.
BinaryFieldElement	subtractOutOfPlace(GenericFieldElement b) Subtracts b from this which is an element of the base field, where a new object holding the result is created.
boolean	testBit(int index) Tests whether a certain bit of this is set.
BigInteger	toBigInteger() Returns the BigInteger-representation of this instance.
byte[]	toByteArray() Returns the byte[] representation of this instance.
String	toString()

Methods inherited from class java.lang.Object

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

Method Detail

negate

public BinaryFieldElement negate()

Description copied from interface: GenericFieldElement

Returns the negative of this. This functions works in-place.

Specified by:

negate in interface FieldElement

Specified by:

negate in interface GenericFieldElement

Returns:

the negative of this

negateOutOfPlace

public BinaryFieldElement negateOutOfPlace()

Description copied from interface: GenericFieldElement

Returns the negative of this, where a new object holding the result is created.

Specified by:

negateOutOfPlace in interface GenericFieldElement

Returns:

the negative of this

add

public BinaryFieldElement add(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Adds b to this. This functions works in-place.

Specified by:

add in interface FieldElement

Specified by:

add in interface GenericFieldElement

Parameters:

b - the second addend

Returns:

the sum of this and b

addOutOfPlace

public BinaryFieldElement addOutOfPlace(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Adds this with b which is an element of the base field, where a new object holding the result is created.

Specified by:

addOutOfPlace in interface GenericFieldElement

Parameters:

b - the second factor

Returns:

the sum of this and b

addBase

public BinaryFieldElement addBase(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Adds b to this where b is an element of the underlying base field.

Specified by:

addBase in interface FieldElement

Specified by:

addBase in interface GenericFieldElement

Parameters:

b - the second addend

Returns:

the sum of this and b

add

public BinaryFieldElement add(BinaryFieldElement b,
                              boolean preserveB)

Performs either the addition a += b or b += a, if preserveB is set to false. Otherwise, it acts as add(GenericFieldElement).

Parameters:

b - the addend

preserveB - if true, b will be preserved, otherwise its content may be exchanged by the result

Returns:

the result

subtract

public BinaryFieldElement subtract(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Subtracts b from this. This functions works in-place.

Specified by:

subtract in interface FieldElement

Specified by:

subtract in interface GenericFieldElement

Parameters:

b - the subtrahend

Returns:

the difference of this and b

subtractOutOfPlace

public BinaryFieldElement subtractOutOfPlace(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Subtracts b from this which is an element of the base field, where a new object holding the result is created.

Specified by:

subtractOutOfPlace in interface GenericFieldElement

Parameters:

b - the second factor

Returns:

the difference of this and b

invert

public BinaryFieldElement invert()

Description copied from interface: GenericFieldElement

Sets this to its inverse.

Specified by:

invert in interface FieldElement

Specified by:

invert in interface GenericFieldElement

Returns:

the inverse of this

multiply

public BinaryFieldElement multiply(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Multiplies this with b which is an element of the same field.

Specified by:

multiply in interface FieldElement

Specified by:

multiply in interface GenericFieldElement

Parameters:

b - the second factor

Returns:

the product of this and b

multiplyOutOfPlace

public BinaryFieldElement multiplyOutOfPlace(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Multiplies this with b which is an element of the same field, where a new object holding the result is created.

Specified by:

multiplyOutOfPlace in interface FieldElement

Specified by:

multiplyOutOfPlace in interface GenericFieldElement

Parameters:

b - the second factor

Returns:

the product of this and b

multiply

public BinaryFieldElement multiply(BigInteger n)

Description copied from interface: GenericFieldElement

Multiples this by n.

Specified by:

multiply in interface FieldElement

Specified by:

multiply in interface GenericFieldElement

Parameters:

n - the factor

Returns:

the product of this and n

multiplyOutOfPlace

public BinaryFieldElement multiplyOutOfPlace(BigInteger n)

Description copied from interface: GenericFieldElement

Multiples this by n, where a new object holding the result is created.

Specified by:

multiplyOutOfPlace in interface FieldElement

Specified by:

multiplyOutOfPlace in interface GenericFieldElement

Parameters:

n - the factor

Returns:

the product of this and n

multiplyByBase

public BinaryFieldElement multiplyByBase(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Multiplies this with b which is an element of the base field.

Specified by:

multiplyByBase in interface FieldElement

Specified by:

multiplyByBase in interface GenericFieldElement

Parameters:

b - the second factor

Returns:

the product of this and b

multiplyByBaseOutOfPlace

public BinaryFieldElement multiplyByBaseOutOfPlace(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Multiplies this with b which is an element of the base field, where a new object holding the result is created.

Specified by:

multiplyByBaseOutOfPlace in interface FieldElement

Specified by:

multiplyByBaseOutOfPlace in interface GenericFieldElement

Parameters:

b - the second factor

Returns:

the product of this and b

multiply

public BinaryFieldElement multiply(PrecomputationData data)

Multiplies this with the already available precomputation data of b, where a new object holding the result is created.

Parameters:

data - the precomputation data for the factor b

Returns:

the product of this and b

multiplyOutOfPlace

public BinaryFieldElement multiplyOutOfPlace(PrecomputationData data)

Multiplies this with the already available precomputation data of b.

Parameters:

data - the precomputation data for the factor b

Returns:

the product of this and b

getExtendedPrecomputationData

public PrecomputationData getExtendedPrecomputationData()

Compiles 256 precomputed values for the multiplication algorithm. Note: the raw value of this is referenced inside the precomputation data. Hence, if it is changed afterwards, also the precomputation data changes!!

Returns:

an object holding the precomputed values

getPrecomputationData

public PrecomputationData getPrecomputationData()

Compiles 16 precomputed values for the multiplication algorithm. Note: the raw value of this is referenced inside the precomputation data. Hence, if it is changed afterwards, also the precomputation data changes!!

Returns:

an object holding the precomputed values

divide

public BinaryFieldElement divide(GenericFieldElement b)

Description copied from interface: GenericFieldElement

Divides this and another field elements.

Specified by:

divide in interface FieldElement

Specified by:

divide in interface GenericFieldElement

Parameters:

b - the divisor

Returns:

the quotient of this and b

squareRoot

public BinaryFieldElement squareRoot()

Description copied from interface: FieldElement

Computes the square root of this.

Specified by:

squareRoot in interface FieldElement

Specified by:

squareRoot in interface GenericFieldElement

Returns:

a field element representing the square root of this

square

public BinaryFieldElement square()

Description copied from interface: GenericFieldElement

Computes the square of this in-place.

Specified by:

square in interface FieldElement

Specified by:

square in interface GenericFieldElement

Returns:

the square of this

squareOutOfPlace

public BinaryFieldElement squareOutOfPlace()

Description copied from interface: GenericFieldElement

Computes the square of this, where a new object holding the result is created.

Specified by:

squareOutOfPlace in interface FieldElement

Specified by:

squareOutOfPlace in interface GenericFieldElement

Returns:

the square of this

exponentiate

public BinaryFieldElement exponentiate(BigInteger n)

Description copied from interface: GenericFieldElement

Raises this to the power n. Works in-place.

Specified by:

exponentiate in interface FieldElement

Specified by:

exponentiate in interface GenericFieldElement

Parameters:

n - the exponent

Returns:

the nth power of this

exponentiate

public BinaryFieldElement exponentiate(int n)

Description copied from interface: GenericFieldElement

Raises this to the power n. Works in-place.

Specified by:

exponentiate in interface GenericFieldElement

Parameters:

n - the exponent

Returns:

the nth power of this

exponentiateOutOfPlace

public BinaryFieldElement exponentiateOutOfPlace(BigInteger n)

Description copied from interface: GenericFieldElement

Raises this to the power n.

Specified by:

exponentiateOutOfPlace in interface GenericFieldElement

Parameters:

n - the exponent

Returns:

the nth power of this

exponentiateOutOfPlace

public BinaryFieldElement exponentiateOutOfPlace(int n)

Description copied from interface: GenericFieldElement

Raises this to the power n.

Specified by:

exponentiateOutOfPlace in interface GenericFieldElement

Parameters:

n - the exponent

Returns:

the nth power of this

exponentiateByPowerOf2

public BinaryFieldElement exponentiateByPowerOf2(int n)

Raises this element to the power 2n.

Specified by:

exponentiateByPowerOf2 in interface GenericFieldElement

Parameters:

n - the power of 2

Returns:

2nth power of this

getTrace

public int getTrace()

Determines the trace of this.

Returns:

the trace t in F2 of this

getField

public BinaryField getField()

Description copied from interface: GenericFieldElement

Returns the associated finite field.

Specified by:

getField in interface GenericFieldElement

Returns:

the associated finite field

testBit

public boolean testBit(int index)

Description copied from interface: FieldElement

Tests whether a certain bit of this is set.

Specified by:

testBit in interface FieldElement

Parameters:

index - the index of the bit

Returns:

true if the bit is 1; false otherwise

getBit

public int getBit(int index)

Description copied from interface: FieldElement

Returns the value of a certain bit of this.

Specified by:

getBit in interface FieldElement

Parameters:

index - the index of the bit

Returns:

the value of a certain bit, i.e. 0 or 1

isOne

public boolean isOne()

Description copied from interface: GenericFieldElement

Determines whether this is one.

Specified by:

isOne in interface GenericFieldElement

Returns:

true iff this is the one element

isZero

public boolean isZero()

Description copied from interface: GenericFieldElement

Determines whether this is zero.

Specified by:

isZero in interface GenericFieldElement

Returns:

true iff this is the zero element

toBigInteger

public BigInteger toBigInteger()

Description copied from interface: FieldElement

Returns the BigInteger-representation of this instance.

Specified by:

toBigInteger in interface FieldElement

Returns:

the BigInteger-representation

toByteArray

public byte[] toByteArray()

Description copied from interface: GenericFieldElement

Returns the byte[] representation of this instance.

Specified by:

toByteArray in interface GenericFieldElement

Returns:

the byte[] representation

clone

public BinaryFieldElement clone()

Description copied from interface: FieldElement

Clones the value of this field element.

Specified by:

clone in interface FieldElement

Specified by:

clone in interface GenericFieldElement

Overrides:

clone in class Object

Returns:

the clone

equals

public boolean equals(Object obj)

Specified by:

equals in interface GenericFieldElement

Overrides:

equals in class Object

hashCode

public int hashCode()

Specified by:

hashCode in interface GenericFieldElement

Overrides:

hashCode in class Object

toString

public String toString()

Specified by:

toString in interface GenericFieldElement

Overrides:

toString in class Object