QuadraticExtensionFieldElement (ECCelerate 6.2 API)

java.lang.Object
- iaik.security.ec.math.field.QuadraticExtensionFieldElement

All Implemented Interfaces:

ExtensionFieldElement, GenericFieldElement, PrimeCharacteristicFieldElement, Cloneable
```
public final class QuadraticExtensionFieldElement
extends Object
```
This class represents elements of quadratic extension fields.

Author:

Christian Hanser, Sebastian Ramacher

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`QuadraticExtensionFieldElement`	`add(GenericFieldElement b)` Adds `b` to `this`.
`QuadraticExtensionFieldElement`	`addBase(GenericFieldElement b)` Adds `b` to `this` where `b` is an element of the underlying base field.
`QuadraticExtensionFieldElement`	`addOutOfPlace(ExtensionFieldElement b)` Adds two elements and returns a new object holding the result.
`QuadraticExtensionFieldElement`	`addOutOfPlace(GenericFieldElement b)` Adds two elements and returns a new object holding the result.
`QuadraticExtensionFieldElement`	`addOutOfPlace(PrimeCharacteristicFieldElement b)` Adds two elements and returns a new object holding the result.
`QuadraticExtensionFieldElement`	`applyFrobenius(int i)` Compute the `i`-th Frobenius of `this`.
`QuadraticExtensionFieldElement`	`clone()` Clones the value of this field element.
`QuadraticExtensionFieldElement`	`conjugate()` Conjugate this element.
`QuadraticExtensionFieldElement`	`conjugate(int i)` Conjugate this element `i` times.
`QuadraticExtensionFieldElement`	`divide(GenericFieldElement b)` Divides `this` and another field elements.
`QuadraticExtensionFieldElement`	`divideBy2()` Divides `this` by 2.
`boolean`	`equals(Object obj)`
`QuadraticExtensionFieldElement`	`exponentiate(BigInteger n)` Raises `this` to the power `n`.
`QuadraticExtensionFieldElement`	`exponentiate(int n)` Raises `this` to the power `n`.
`QuadraticExtensionFieldElement`	`exponentiateByPowerOf2(int exponent)` Raise `this` to the power of 2^`n`.
`QuadraticExtensionFieldElement`	`exponentiateOutOfPlace(BigInteger n)` Raises `this` to the power `n`.
`QuadraticExtensionFieldElement`	`exponentiateOutOfPlace(int n)` Raises `this` to the power `n`.
`iaik.security.ec.math.field.AbstractQuadraticExtensionField`	`getField()` Returns the associated finite field.
`PrimeFieldElement`	`getNorm()` Computes the norm of `this`, which is an element of the base field.
`int`	`getQuadraticCharacter()` Implements a quadratic character, which returns -1,0,1 depending on whether `this` is a quadratic non-residue, a multiple of the modulus, or a quadratic residue.
`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`.
`int`	`hashCode()`
`QuadraticExtensionFieldElement`	`invert()` Sets `this` to its inverse.
`boolean`	`isOne()` Determines whether `this` is one.
`boolean`	`isZero()` Determines whether `this` is zero.
`QuadraticExtensionFieldElement`	`multiply(BigInteger n)` Multiples `this` by `n`.
`QuadraticExtensionFieldElement`	`multiply(GenericFieldElement b)` Multiplies `this` with `b` which is an element of the same field.
`QuadraticExtensionFieldElement`	`multiply(PrimeFieldElement b)` Multiply `this` by a prime field element.
`QuadraticExtensionFieldElement`	`multiplyBy2()` Multiplies `this` with 2.
`QuadraticExtensionFieldElement`	`multiplyBy2OutOfPlace()` Multiplies `this` with 2 and returns a new object holding the result.
`QuadraticExtensionFieldElement`	`multiplyBy3()` Multiplies `this` with 3.
`QuadraticExtensionFieldElement`	`multiplyBy3OutOfPlace()` Multiplies `this` with 3 and returns a new object holding the result.
`QuadraticExtensionFieldElement`	`multiplyByAdjointRoot()` Multiply `this` by the root used to obtain the extension field.
`QuadraticExtensionFieldElement`	`multiplyByAdjointRootOutOfPlace()` Multiply with adjoint root out of place
`QuadraticExtensionFieldElement`	`multiplyByBase(GenericFieldElement b)` Multiplies `this` with `b` which is an element of the base field.
`QuadraticExtensionFieldElement`	`multiplyByBaseOutOfPlace(GenericFieldElement b)` Multiplies `this` with `b` which is an element of the base field, where a new object holding the result is created.
`QuadraticExtensionFieldElement`	`multiplyByPowerOf2(int exponent)` Multiplies `this` by 2^`n`.
`QuadraticExtensionFieldElement`	`multiplyByPowerOf2OutOfPlace(int exponent)` Multiplies `this` by 2^`n` and returns a new object holding the result.
`QuadraticExtensionFieldElement`	`multiplyOutOfPlace(BigInteger n)` Multiples `this` by `n`, where a new object holding the result is created.
`QuadraticExtensionFieldElement`	`multiplyOutOfPlace(GenericFieldElement b)` Multiplies `this` with `b` which is an element of the same field, where a new object holding the result is created.
`QuadraticExtensionFieldElement`	`multiplyOutOfPlace(PrimeFieldElement b)` Multiply `this` by a prime field element, where a new object holding the result is created.
`QuadraticExtensionFieldElement`	`negate()` Returns the negative of `this`.
`QuadraticExtensionFieldElement`	`negateOutOfPlace()` Returns the negative of `this`, where a new object holding the result is created.
`QuadraticExtensionFieldElement`	`square()` Computes the square of `this` in-place.
`QuadraticExtensionFieldElement`	`squareOutOfPlace()` Computes the square of `this`, where a new object holding the result is created.
`QuadraticExtensionFieldElement`	`squareRoot()` Computes the square root of `this` in-place.
`QuadraticExtensionFieldElement`	`squareRoot(boolean checkSquare)` Computes the square root of `this`.
`QuadraticExtensionFieldElement`	`subtract(GenericFieldElement b)` Subtracts `b` from `this`.
`QuadraticExtensionFieldElement`	`subtractOutOfPlace(ExtensionFieldElement b)` Subtract two elements and returns a new object holding the result.
`QuadraticExtensionFieldElement`	`subtractOutOfPlace(GenericFieldElement b)` Subtracts `b` from `this` which is an element of the base field, where a new object holding the result is created.
`QuadraticExtensionFieldElement`	`subtractOutOfPlace(PrimeCharacteristicFieldElement b)` Subtracts `b` from `this` and returns a new object holding the result.
`Object`	`toBigIntegers()` Returns the (multi-dimensional) `BigInteger`-array representation of this instance.
`byte[]`	`toByteArray()` Returns `byte`-array representation of this instance.
`String`	`toString()`

Methods inherited from class java.lang.Object
finalize, getClass, notify, notifyAll, wait, wait, wait

- Method Detail
  - getValues
```
public GenericFieldElement[] getValues()
```
    Description copied from interface: ExtensionFieldElement
    
    Get subfield elements used to represent this.
    
    Returns:
    
    subfield elements used to represent this
  - getValue
```
public PrimeCharacteristicFieldElement getValue(int index)
```
    Description copied from interface: ExtensionFieldElement
    
    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
  - invert
```
public QuadraticExtensionFieldElement invert()
```
    Description copied from interface: GenericFieldElement
    
    Sets this to its inverse.
    
    Returns:
    
    the inverse of this
  - multiply
```
public QuadraticExtensionFieldElement multiply(GenericFieldElement b)
```
    Description copied from interface: GenericFieldElement
    
    Multiplies this with b which is an element of the same field.
    
    Parameters:
    
    b - the second factor
    
    Returns:
    
    the product of this and b
  - multiplyOutOfPlace
```
public QuadraticExtensionFieldElement 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.
    
    Parameters:
    
    b - the second factor
    
    Returns:
    
    the product of this and b
  - multiply
```
public QuadraticExtensionFieldElement multiply(PrimeFieldElement b)
```
    Multiply this by a prime field element.
    
    Parameters:
    
    b - prime field element
    
    Returns:
    
    product of this and b
  - multiplyOutOfPlace
```
public QuadraticExtensionFieldElement multiplyOutOfPlace(PrimeFieldElement b)
```
    Multiply this by a prime field element, where a new object holding the result is created.
    
    Parameters:
    
    b - prime field element
    
    Returns:
    
    product of this and b
  - multiply
```
public QuadraticExtensionFieldElement multiply(BigInteger n)
```
    Description copied from interface: GenericFieldElement
    
    Multiples this by n.
    
    Parameters:
    
    n - the factor
    
    Returns:
    
    the product of this and n
  - multiplyOutOfPlace
```
public QuadraticExtensionFieldElement multiplyOutOfPlace(BigInteger n)
```
    Description copied from interface: GenericFieldElement
    
    Multiples this by n, where a new object holding the result is created.
    
    Parameters:
    
    n - the factor
    
    Returns:
    
    the product of this and n
  - multiplyByBase
```
public QuadraticExtensionFieldElement multiplyByBase(GenericFieldElement b)
```
    Description copied from interface: GenericFieldElement
    
    Multiplies this with b which is an element of the base field.
    
    Parameters:
    
    b - the second factor
    
    Returns:
    
    the product of this and b
  - multiplyByBaseOutOfPlace
```
public QuadraticExtensionFieldElement 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.
    
    Parameters:
    
    b - the second factor
    
    Returns:
    
    the product of this and b
  - multiplyBy2
```
public QuadraticExtensionFieldElement multiplyBy2()
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Multiplies this with 2.
    
    Returns:
    
    the product of this and 2
  - multiplyBy2OutOfPlace
```
public QuadraticExtensionFieldElement multiplyBy2OutOfPlace()
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Multiplies this with 2 and returns a new object holding the result.
    
    Returns:
    
    the product of this and 2
  - multiplyBy3
```
public QuadraticExtensionFieldElement multiplyBy3()
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Multiplies this with 3.
    
    Returns:
    
    the product of this and 3
  - multiplyBy3OutOfPlace
```
public QuadraticExtensionFieldElement multiplyBy3OutOfPlace()
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Multiplies this with 3 and returns a new object holding the result.
    
    Returns:
    
    the product of this and 3
  - multiplyByPowerOf2
```
public QuadraticExtensionFieldElement multiplyByPowerOf2(int exponent)
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Multiplies this by 2^n.
    
    Parameters:
    
    exponent - the exponent
    
    Returns:
    
    the product of this and 2^n
  - multiplyByPowerOf2OutOfPlace
```
public QuadraticExtensionFieldElement multiplyByPowerOf2OutOfPlace(int exponent)
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Multiplies this by 2^n and returns a new object holding the result.
    
    Parameters:
    
    exponent - the exponent
    
    Returns:
    
    the product of this and 2^n
  - negate
```
public QuadraticExtensionFieldElement negate()
```
    Description copied from interface: GenericFieldElement
    
    Returns the negative of this. This functions works in-place.
    
    Returns:
    
    the negative of this
  - negateOutOfPlace
```
public QuadraticExtensionFieldElement negateOutOfPlace()
```
    Description copied from interface: GenericFieldElement
    
    Returns the negative of this, where a new object holding the result is created.
    
    Returns:
    
    the negative of this
  - add
```
public QuadraticExtensionFieldElement add(GenericFieldElement b)
```
    Description copied from interface: GenericFieldElement
    
    Adds b to this. This functions works in-place.
    
    Parameters:
    
    b - the second addend
    
    Returns:
    
    the sum of this and b
  - addOutOfPlace
```
public QuadraticExtensionFieldElement addOutOfPlace(GenericFieldElement b)
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Adds two elements and returns a new object holding the result.
    
    Parameters:
    
    b - the other value
    
    Returns:
    
    the sum
  - addOutOfPlace
```
public QuadraticExtensionFieldElement addOutOfPlace(PrimeCharacteristicFieldElement b)
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Adds two elements and returns a new object holding the result.
    
    Parameters:
    
    b - the other value
    
    Returns:
    
    the sum
  - addOutOfPlace
```
public QuadraticExtensionFieldElement addOutOfPlace(ExtensionFieldElement b)
```
    Description copied from interface: ExtensionFieldElement
    
    Adds two elements and returns a new object holding the result.
    
    Parameters:
    
    b - the other value
    
    Returns:
    
    the sum
  - addBase
```
public QuadraticExtensionFieldElement addBase(GenericFieldElement b)
```
    Description copied from interface: GenericFieldElement
    
    Adds b to this where b is an element of the underlying base field.
    
    Parameters:
    
    b - the second addend
    
    Returns:
    
    the sum of this and b
  - subtract
```
public QuadraticExtensionFieldElement subtract(GenericFieldElement b)
```
    Description copied from interface: GenericFieldElement
    
    Subtracts b from this. This functions works in-place.
    
    Parameters:
    
    b - the subtrahend
    
    Returns:
    
    the difference of this and b
  - subtractOutOfPlace
```
public QuadraticExtensionFieldElement 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.
    
    Parameters:
    
    b - the second factor
    
    Returns:
    
    the difference of this and b
  - subtractOutOfPlace
```
public QuadraticExtensionFieldElement subtractOutOfPlace(ExtensionFieldElement b)
```
    Description copied from interface: ExtensionFieldElement
    
    Subtract two elements and returns a new object holding the result.
    
    Parameters:
    
    b - the other value
    
    Returns:
    
    the difference
  - subtractOutOfPlace
```
public QuadraticExtensionFieldElement subtractOutOfPlace(PrimeCharacteristicFieldElement b)
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Subtracts b from this and returns a new object holding the result.
    
    Parameters:
    
    b - the subtrahend
    
    Returns:
    
    the difference of this and b
  - conjugate
```
public QuadraticExtensionFieldElement conjugate()
```
    Description copied from interface: ExtensionFieldElement
    
    Conjugate this element.
    
    Returns:
    
    the conjugate of this
  - divide
```
public QuadraticExtensionFieldElement divide(GenericFieldElement b)
```
    Description copied from interface: ExtensionFieldElement
    
    Divides this and another field elements.
    You have no guarantee that b remains unchanged.
    
    Parameters:
    
    b - the divisor
    
    Returns:
    
    the quotient of this and b
  - divideBy2
```
public QuadraticExtensionFieldElement divideBy2()
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Divides this by 2.
    
    Returns:
    
    this divided by 2.
  - square
```
public QuadraticExtensionFieldElement square()
```
    Description copied from interface: GenericFieldElement
    
    Computes the square of this in-place.
    
    Returns:
    
    the square of this
  - squareOutOfPlace
```
public QuadraticExtensionFieldElement squareOutOfPlace()
```
    Description copied from interface: GenericFieldElement
    
    Computes the square of this, where a new object holding the result is created.
    
    Returns:
    
    the square of this
  - squareRoot
```
public QuadraticExtensionFieldElement squareRoot()
```
    Description copied from interface: GenericFieldElement
    
    Computes the square root of this in-place.
    
    Returns:
    
    the square root of this or null if the square root does not exist.
  - squareRoot
```
public QuadraticExtensionFieldElement squareRoot(boolean checkSquare)
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Computes the square root of this.
    
    Parameters:
    
    checkSquare - check if a is a square. If true, the return value is undefined for non-squares.
    
    Returns:
    
    square root of this
  - exponentiate
```
public QuadraticExtensionFieldElement exponentiate(BigInteger n)
```
    Description copied from interface: GenericFieldElement
    
    Raises this to the power n. Works in-place.
    
    Parameters:
    
    n - the exponent
    
    Returns:
    
    the nth power of this
  - exponentiate
```
public QuadraticExtensionFieldElement exponentiate(int n)
```
    Description copied from interface: GenericFieldElement
    
    Raises this to the power n. Works in-place.
    
    Parameters:
    
    n - the exponent
    
    Returns:
    
    the nth power of this
  - exponentiateOutOfPlace
```
public QuadraticExtensionFieldElement exponentiateOutOfPlace(BigInteger n)
```
    Description copied from interface: GenericFieldElement
    
    Raises this to the power n.
    
    Parameters:
    
    n - the exponent
    
    Returns:
    
    the nth power of this
  - exponentiateOutOfPlace
```
public QuadraticExtensionFieldElement exponentiateOutOfPlace(int n)
```
    Description copied from interface: GenericFieldElement
    
    Raises this to the power n.
    
    Parameters:
    
    n - the exponent
    
    Returns:
    
    the nth power of this
  - exponentiateByPowerOf2
```
public QuadraticExtensionFieldElement exponentiateByPowerOf2(int exponent)
```
    Description copied from interface: GenericFieldElement
    
    Raise this to the power of 2^n.
    
    Parameters:
    
    exponent - the exponent
    
    Returns:
    
    the 2^n-th power of this.
  - conjugate
```
public QuadraticExtensionFieldElement conjugate(int i)
```
    Description copied from interface: ExtensionFieldElement
    
    Conjugate this element i times.
    
    Parameters:
    
    i - number of times this should be conjugated
    
    Returns:
    
    the i-th conjugate of this
  - applyFrobenius
```
public QuadraticExtensionFieldElement applyFrobenius(int i)
```
    Description copied from interface: ExtensionFieldElement
    
    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 ..
  - getNorm
```
public PrimeFieldElement getNorm()
```
    Description copied from interface: ExtensionFieldElement
    
    Computes the norm of this, which is an element of the base field.
    
    Returns:
    
    the norm of a
  - multiplyByAdjointRoot
```
public QuadraticExtensionFieldElement multiplyByAdjointRoot()
```
    Description copied from interface: ExtensionFieldElement
    
    Multiply this by the root used to obtain the extension field.
    
    Returns:
    
    this multiplied by the adjoint root.
  - multiplyByAdjointRootOutOfPlace
```
public QuadraticExtensionFieldElement multiplyByAdjointRootOutOfPlace()
```
    Multiply with adjoint root out of place
    
    Returns:
    
    product of this and the adjoint root
  - getQuadraticCharacter
```
public int getQuadraticCharacter()
```
    Description copied from interface: PrimeCharacteristicFieldElement
    
    Implements a quadratic character, which returns -1,0,1 depending on whether this is a quadratic non-residue, a multiple of the modulus, or a quadratic residue.
    
    Returns:
    
    the quadratic character (this/p)
  - isOne
```
public boolean isOne()
```
    Description copied from interface: GenericFieldElement
    
    Determines whether this is one.
    
    Returns:
    
    true iff this is the one element
  - isZero
```
public boolean isZero()
```
    Description copied from interface: GenericFieldElement
    
    Determines whether this is zero.
    
    Returns:
    
    true iff this is the zero element
  - toBigIntegers
```
public Object toBigIntegers()
```
    Description copied from interface: ExtensionFieldElement
    
    Returns the (multi-dimensional) BigInteger-array representation of this instance.
    
    Returns:
    
    the BigInteger-array representation
  - getField
```
public iaik.security.ec.math.field.AbstractQuadraticExtensionField getField()
```
    Description copied from interface: GenericFieldElement
    
    Returns the associated finite field.
    
    Returns:
    
    the associated finite field
  - hashCode
```
public int hashCode()
```
    Specified by:
    
    hashCode in interface GenericFieldElement
    
    Overrides:
    
    hashCode in class Object
  - equals
```
public boolean equals(Object obj)
```
    Specified by:
    
    equals in interface GenericFieldElement
    
    Overrides:
    
    equals in class Object
  - clone
```
public QuadraticExtensionFieldElement clone()
```
    Description copied from interface: ExtensionFieldElement
    
    Clones the value of this field element.
    
    Specified by:
    
    clone in interface ExtensionFieldElement
    
    Specified by:
    
    clone in interface GenericFieldElement
    
    Specified by:
    
    clone in interface PrimeCharacteristicFieldElement
    
    Returns:
    
    the clone
  - toString
```
public String toString()
```
    Specified by:
    
    toString in interface GenericFieldElement
    
    Overrides:
    
    toString in class Object
  - getValuesRecursive
```
public PrimeFieldElement[] getValuesRecursive()
```
    Description copied from interface: ExtensionFieldElement
    
    Get prime field elements used to represent this. This calls ExtensionFieldElement.getValues() recursively. They values are sorted from the coefficients of the lowest power to the the highest power.
    
    Specified by:
    
    getValuesRecursive in interface ExtensionFieldElement
    
    Returns:
    
    prime field elements used to represent this.
  - toByteArray
```
public byte[] toByteArray()
```
    Description copied from interface: ExtensionFieldElement
    
    Returns byte-array representation of this instance.
    
    Specified by:
    
    toByteArray in interface ExtensionFieldElement
    
    Specified by:
    
    toByteArray in interface GenericFieldElement
    
    Returns:
    
    the byte-array representation

Class QuadraticExtensionFieldElement

Method Summary

Methods inherited from class java.lang.Object

Method Detail

getValues

getValue

invert

multiply

multiplyOutOfPlace

multiply

multiplyOutOfPlace

multiply

multiplyOutOfPlace

multiplyByBase

multiplyByBaseOutOfPlace

multiplyBy2

multiplyBy2OutOfPlace

multiplyBy3

multiplyBy3OutOfPlace

multiplyByPowerOf2

multiplyByPowerOf2OutOfPlace

negate

negateOutOfPlace

add

addOutOfPlace

addOutOfPlace

addOutOfPlace

addBase

subtract

subtractOutOfPlace

subtractOutOfPlace

subtractOutOfPlace

conjugate

divide

divideBy2

square

squareOutOfPlace

squareRoot

squareRoot

exponentiate

exponentiate

exponentiateOutOfPlace

exponentiateOutOfPlace

exponentiateByPowerOf2

conjugate

applyFrobenius

getNorm

multiplyByAdjointRoot

multiplyByAdjointRootOutOfPlace

getQuadraticCharacter

isOne

isZero

toBigIntegers

getField

hashCode

equals

clone

toString

getValuesRecursive

toByteArray