iaik.security.ec.math.field

Interface ExtensionFieldElement

All Superinterfaces:

Cloneable, GenericFieldElement, PrimeCharacteristicFieldElement

All Known Implementing Classes:

QuadraticExtensionFieldElement, SexticExtensionFieldElement

public interface ExtensionFieldElement
extends PrimeCharacteristicFieldElement

This interface describes the methods every field element of an extension field has to provide.

Author:

Christian Hanser, Sebastian Ramacher

Method Summary

Modifier and Type	Method and Description
ExtensionFieldElement	add(GenericFieldElement b) Adds b to this.
ExtensionFieldElement	addBase(GenericFieldElement b) Adds b to this where b is an element of the underlying base field.
ExtensionFieldElement	addOutOfPlace(ExtensionFieldElement b) Adds two elements and returns a new object holding the result.
ExtensionFieldElement	addOutOfPlace(GenericFieldElement b) Adds two elements and returns a new object holding the result.
ExtensionFieldElement	applyFrobenius(int i) Compute the i-th Frobenius of this.
ExtensionFieldElement	clone() Clones the value of this field element.
ExtensionFieldElement	conjugate() Conjugate this element.
ExtensionFieldElement	conjugate(int i) Conjugate this element i times.
ExtensionFieldElement	divide(GenericFieldElement b) Divides this and another field elements.
ExtensionFieldElement	divideBy2() Divides this by 2.
ExtensionFieldElement	exponentiate(BigInteger n) Raises this to the power n.
ExtensionFieldElement	exponentiate(int n) Raises this to the power n.
ExtensionFieldElement	exponentiateByPowerOf2(int n) Raise this to the power of 2^n.
ExtensionFieldElement	exponentiateOutOfPlace(BigInteger n) Raises this to the power n.
ExtensionFieldElement	exponentiateOutOfPlace(int n) Raises this to the power n.
PrimeFieldElement	getNorm() Computes the norm of this, which is an element of the base field.
PrimeCharacteristicFieldElement	getValue(int index) Get index-th subfield element used to represent this.
GenericFieldElement[]	getValues() Get subfield elements used to represent this.
PrimeFieldElement[]	getValuesRecursive() Get prime field elements used to represent this.
ExtensionFieldElement	invert() Sets this to its inverse.
ExtensionFieldElement	multiply(BigInteger n) Multiples this by n.
ExtensionFieldElement	multiply(GenericFieldElement b) Multiplies this with b which is an element of the same field.
ExtensionFieldElement	multiplyBy2() Multiplies this with 2.
ExtensionFieldElement	multiplyBy3() Multiplies this with 3.
ExtensionFieldElement	multiplyByAdjointRoot() Multiply this by the root used to obtain the extension field.
ExtensionFieldElement	multiplyByBase(GenericFieldElement b) Multiplies this with b which is an element of the base field.
ExtensionFieldElement	multiplyByPowerOf2(int exponent) Multiplies this by 2^n.
ExtensionFieldElement	multiplyOutOfPlace(GenericFieldElement b) Multiplies this with b which is an element of the same field, where a new object holding the result is created.
ExtensionFieldElement	negate() Returns the negative of this.
ExtensionFieldElement	square() Computes the square of this in-place.
ExtensionFieldElement	squareOutOfPlace() Computes the square of this, where a new object holding the result is created.
ExtensionFieldElement	squareRoot() Computes the square root of this in-place.
ExtensionFieldElement	subtract(GenericFieldElement b) Subtracts b from this.
ExtensionFieldElement	subtractOutOfPlace(ExtensionFieldElement b) Subtract two elements and returns a new object holding the result.
ExtensionFieldElement	subtractOutOfPlace(GenericFieldElement b) Subtracts b from this which is an element of the base field, where a new object holding the result is created.
Object	toBigIntegers() Returns the (multi-dimensional) BigInteger-array representation of this instance.
byte[]	toByteArray() Returns byte-array representation of this instance.

Methods inherited from interface iaik.security.ec.math.field.PrimeCharacteristicFieldElement

addOutOfPlace, getQuadraticCharacter, multiplyBy2OutOfPlace, multiplyBy3OutOfPlace, multiplyByBaseOutOfPlace, multiplyByPowerOf2OutOfPlace, multiplyOutOfPlace, negateOutOfPlace, squareRoot, subtractOutOfPlace

Methods inherited from interface iaik.security.ec.math.field.GenericFieldElement

equals, getField, hashCode, isOne, isZero, toString

Method Detail

negate

ExtensionFieldElement negate()

Description copied from interface: GenericFieldElement

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

Specified by:

negate in interface GenericFieldElement

Specified by:

negate in interface PrimeCharacteristicFieldElement

Returns:

the negative of this

add

ExtensionFieldElement add(GenericFieldElement b)

Description copied from interface: GenericFieldElement

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

Specified by:

add in interface GenericFieldElement

Specified by:

add in interface PrimeCharacteristicFieldElement

Parameters:

b - the second addend

Returns:

the sum of this and b

addOutOfPlace

ExtensionFieldElement addOutOfPlace(GenericFieldElement b)

Description copied from interface: PrimeCharacteristicFieldElement

Adds two elements and returns a new object holding the result.

Specified by:

addOutOfPlace in interface GenericFieldElement

Specified by:

addOutOfPlace in interface PrimeCharacteristicFieldElement

Parameters:

b - the other value

Returns:

the sum

addOutOfPlace

ExtensionFieldElement addOutOfPlace(ExtensionFieldElement b)

Adds two elements and returns a new object holding the result.

Parameters:

b - the other value

Returns:

the sum

addBase

ExtensionFieldElement 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 GenericFieldElement

Specified by:

addBase in interface PrimeCharacteristicFieldElement

Parameters:

b - the second addend

Returns:

the sum of this and b

subtract

ExtensionFieldElement subtract(GenericFieldElement b)

Description copied from interface: GenericFieldElement

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

Specified by:

subtract in interface GenericFieldElement

Specified by:

subtract in interface PrimeCharacteristicFieldElement

Parameters:

b - the subtrahend

Returns:

the difference of this and b

subtractOutOfPlace

ExtensionFieldElement 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

Specified by:

subtractOutOfPlace in interface PrimeCharacteristicFieldElement

Parameters:

b - the second factor

Returns:

the difference of this and b

subtractOutOfPlace

ExtensionFieldElement subtractOutOfPlace(ExtensionFieldElement b)

Subtract two elements and returns a new object holding the result.

Parameters:

b - the other value

Returns:

the difference

invert

ExtensionFieldElement invert()

Description copied from interface: GenericFieldElement

Sets this to its inverse.

Specified by:

invert in interface GenericFieldElement

Specified by:

invert in interface PrimeCharacteristicFieldElement

Returns:

the inverse of this

multiply

ExtensionFieldElement 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 GenericFieldElement

Specified by:

multiply in interface PrimeCharacteristicFieldElement

Parameters:

b - the second factor

Returns:

the product of this and b

multiplyOutOfPlace

ExtensionFieldElement 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 GenericFieldElement

Specified by:

multiplyOutOfPlace in interface PrimeCharacteristicFieldElement

Parameters:

b - the second factor

Returns:

the product of this and b

multiplyByBase

ExtensionFieldElement 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 GenericFieldElement

Specified by:

multiplyByBase in interface PrimeCharacteristicFieldElement

Parameters:

b - the second factor

Returns:

the product of this and b

multiply

ExtensionFieldElement multiply(BigInteger n)

Description copied from interface: GenericFieldElement

Multiples this by n.

Specified by:

multiply in interface GenericFieldElement

Specified by:

multiply in interface PrimeCharacteristicFieldElement

Parameters:

n - the factor

Returns:

the product of this and n

multiplyBy2

ExtensionFieldElement multiplyBy2()

Description copied from interface: PrimeCharacteristicFieldElement

Multiplies this with 2.

Specified by:

multiplyBy2 in interface PrimeCharacteristicFieldElement

Returns:

the product of this and 2

multiplyBy3

ExtensionFieldElement multiplyBy3()

Description copied from interface: PrimeCharacteristicFieldElement

Multiplies this with 3.

Specified by:

multiplyBy3 in interface PrimeCharacteristicFieldElement

Returns:

the product of this and 3

multiplyByPowerOf2

ExtensionFieldElement multiplyByPowerOf2(int exponent)

Description copied from interface: PrimeCharacteristicFieldElement

Multiplies this by 2^n.

Specified by:

multiplyByPowerOf2 in interface PrimeCharacteristicFieldElement

Parameters:

exponent - the exponent

Returns:

the product of this and 2^n

multiplyByAdjointRoot

ExtensionFieldElement multiplyByAdjointRoot()

Multiply this by the root used to obtain the extension field.

Returns:

this multiplied by the adjoint root.

divide

ExtensionFieldElement divide(GenericFieldElement b)

Divides this and another field elements.

You have no guarantee that b remains unchanged.

Specified by:

divide in interface GenericFieldElement

Specified by:

divide in interface PrimeCharacteristicFieldElement

Parameters:

b - the divisor

Returns:

the quotient of this and b

divideBy2

ExtensionFieldElement divideBy2()

Description copied from interface: PrimeCharacteristicFieldElement

Divides this by 2.

Specified by:

divideBy2 in interface PrimeCharacteristicFieldElement

Returns:

this divided by 2.

getValues

GenericFieldElement[] getValues()

Get subfield elements used to represent this.

Returns:

subfield elements used to represent this

getValuesRecursive

PrimeFieldElement[] getValuesRecursive()

Get prime field elements used to represent this. This calls getValues() recursively. They values are sorted from the coefficients of the lowest power to the the highest power.

Returns:

prime field elements used to represent this.

getValue

PrimeCharacteristicFieldElement getValue(int index)

Get index-th subfield element used to represent this.

Parameters:

index - index of the desired subfield element

Returns:

index-th subfield element used to represent this

getNorm

PrimeFieldElement getNorm()

Computes the norm of this, which is an element of the base field.

Returns:

the norm of a

conjugate

ExtensionFieldElement conjugate()

Conjugate this element.

Returns:

the conjugate of this

conjugate

ExtensionFieldElement conjugate(int i)

Conjugate this element i times.

Parameters:

i - number of times this should be conjugated

Returns:

the i-th conjugate of this

square

ExtensionFieldElement square()

Description copied from interface: GenericFieldElement

Computes the square of this in-place.

Specified by:

square in interface GenericFieldElement

Specified by:

square in interface PrimeCharacteristicFieldElement

Returns:

the square of this

squareOutOfPlace

ExtensionFieldElement 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 GenericFieldElement

Specified by:

squareOutOfPlace in interface PrimeCharacteristicFieldElement

Returns:

the square of this

squareRoot

ExtensionFieldElement squareRoot()

Description copied from interface: GenericFieldElement

Computes the square root of this in-place.

Specified by:

squareRoot in interface GenericFieldElement

Specified by:

squareRoot in interface PrimeCharacteristicFieldElement

Returns:

the square root of this or null if the square root does not exist.

exponentiate

ExtensionFieldElement exponentiate(int n)

Description copied from interface: GenericFieldElement

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

Specified by:

exponentiate in interface GenericFieldElement

Specified by:

exponentiate in interface PrimeCharacteristicFieldElement

Parameters:

n - the exponent

Returns:

the nth power of this

exponentiate

ExtensionFieldElement exponentiate(BigInteger n)

Description copied from interface: GenericFieldElement

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

Specified by:

exponentiate in interface GenericFieldElement

Specified by:

exponentiate in interface PrimeCharacteristicFieldElement

Parameters:

n - the exponent

Returns:

the nth power of this

exponentiateOutOfPlace

ExtensionFieldElement 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

exponentiateOutOfPlace

ExtensionFieldElement 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

exponentiateByPowerOf2

ExtensionFieldElement exponentiateByPowerOf2(int n)

Description copied from interface: GenericFieldElement

Raise this to the power of 2^n.

Specified by:

exponentiateByPowerOf2 in interface GenericFieldElement

Specified by:

exponentiateByPowerOf2 in interface PrimeCharacteristicFieldElement

Parameters:

n - the exponent

Returns:

the 2^n-th power of this.

applyFrobenius

ExtensionFieldElement applyFrobenius(int i)

Compute the i-th Frobenius of this.

Parameters:

i - number of times the Frobenius map should be applied

Returns:

the Frobenius map applied i-times to this ..

toBigIntegers

Object toBigIntegers()

Returns the (multi-dimensional) BigInteger-array representation of this instance.

Returns:

the BigInteger-array representation

toByteArray

byte[] toByteArray()

Returns byte-array representation of this instance.

Specified by:

toByteArray in interface GenericFieldElement

Returns:

the byte-array representation

clone

ExtensionFieldElement clone()

Clones the value of this field element.

Specified by:

clone in interface GenericFieldElement

Specified by:

clone in interface PrimeCharacteristicFieldElement

Returns:

the clone