java.lang.Object
- org.bouncycastle.pqc.math.linearalgebra.GF2nElement

All Implemented Interfaces:

GFElement

Direct Known Subclasses:

GF2nONBElement, GF2nPolynomialElement
```
public abstract class GF2nElement
extends java.lang.Object
implements GFElement
```
This abstract class implements an element of the finite field GF(2)ⁿ in either optimal normal basis representation (ONB) or in polynomial representation. It is extended by the classes GF2nONBElement and GF2nPolynomialElement .

See Also:

GF2nPolynomialElement, GF2nONBElement, GF2nONBField

Field Summary

Fields
Modifier and Type	Field	Description
`protected int`	`mDegree`	holds the extension degree n of this element's corresponding field.
`protected GF2nField`	`mField`	holds a pointer to this element's corresponding field.

Constructor Summary

Constructors
Constructor Description

GF2nElement()

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method	Description
`abstract java.lang.Object`	`clone()`
`GF2nElement`	`convert(GF2nField basis)`	Performs a basis transformation of this element to the given GF2nField `basis`.
`GF2nField`	`getField()`	Returns the field of this element.
`abstract GF2nElement`	`increase()`	Returns `this` element + 1.
`abstract void`	`increaseThis()`	Increases this element by one.
`abstract GF2nElement`	`solveQuadraticEquation()`	Solves a quadratic equation. Let z² + z = `this`.
`abstract GF2nElement`	`square()`	Returns `this` element to the power of 2.
`abstract GF2nElement`	`squareRoot()`	Compute the square root of this element and return the result in a new `GF2nElement`.
`abstract void`	`squareRootThis()`	Compute the square root of this element.
`abstract void`	`squareThis()`	Squares `this` element.
`GFElement`	`subtract(GFElement minuend)`	Compute the difference of this element and `minuend`.
`void`	`subtractFromThis(GFElement minuend)`	Compute the difference of this element and `minuend`, overwriting this element.
`abstract boolean`	`testRightmostBit()`	Returns whether the rightmost bit of the bit representation is set.
`abstract int`	`trace()`	Returns the trace of this element.

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

Methods inherited from interface org.bouncycastle.pqc.math.linearalgebra.GFElement
add, addToThis, equals, hashCode, invert, isOne, isZero, multiply, multiplyThisBy, toByteArray, toFlexiBigInt, toString, toString

- Field Detail
  - mField
```
protected GF2nField mField
```
    holds a pointer to this element's corresponding field.
  - mDegree
```
protected int mDegree
```
    holds the extension degree n of this element's corresponding field.
- Constructor Detail
  - GF2nElement
```
public GF2nElement()
```
- Method Detail
  - clone
```
public abstract java.lang.Object clone()
```
    Specified by:
    
    clone in interface GFElement
    
    Overrides:
    
    clone in class java.lang.Object
    
    Returns:
    
    a copy of this GF2nElement
  - testRightmostBit
```
public abstract boolean testRightmostBit()
```
    Returns whether the rightmost bit of the bit representation is set. This is needed for data conversion according to 1363.
    
    Returns:
    
    true if the rightmost bit of this element is set
  - getField
```
public final GF2nField getField()
```
    Returns the field of this element.
    
    Returns:
    
    the field of this element
  - increase
```
public abstract GF2nElement increase()
```
    Returns this element + 1.
    
    Returns:
    
    this + 1
  - increaseThis
```
public abstract void increaseThis()
```
    Increases this element by one.
  - subtract
```
public final GFElement subtract(GFElement minuend)
```
    Compute the difference of this element and minuend.
    
    Specified by:
    
    subtract in interface GFElement
    
    Parameters:
    
    minuend - the minuend
    
    Returns:
    
    this - minuend (newly created)
  - subtractFromThis
```
public final void subtractFromThis(GFElement minuend)
```
    Compute the difference of this element and minuend, overwriting this element.
    
    Specified by:
    
    subtractFromThis in interface GFElement
    
    Parameters:
    
    minuend - the minuend
  - square
```
public abstract GF2nElement square()
```
    Returns this element to the power of 2.
    
    Returns:
    
    this²
  - squareThis
```
public abstract void squareThis()
```
    Squares this element.
  - squareRoot
```
public abstract GF2nElement squareRoot()
```
    Compute the square root of this element and return the result in a new GF2nElement.
    
    Returns:
    
    this^1/2 (newly created)
  - squareRootThis
```
public abstract void squareRootThis()
```
    Compute the square root of this element.
  - convert
```
public final GF2nElement convert(GF2nField basis)
```
    Performs a basis transformation of this element to the given GF2nField basis.
    
    Parameters:
    
    basis - the GF2nField representation to transform this element to
    
    Returns:
    
    this element in the representation of basis
  - trace
```
public abstract int trace()
```
    Returns the trace of this element.
    
    Returns:
    
    the trace of this element
  - solveQuadraticEquation
```
public abstract GF2nElement solveQuadraticEquation()
                                            throws java.lang.RuntimeException
```
    Solves a quadratic equation.
    Let z² + z = this. Then this method returns z.
    
    Returns:
    
    z with z² + z = this
    
    Throws:
    
    java.lang.RuntimeException

Class GF2nElement

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.bouncycastle.pqc.math.linearalgebra.GFElement

Field Detail

mField

mDegree

Constructor Detail

GF2nElement

Method Detail

clone

testRightmostBit

getField

increase

increaseThis

subtract

subtractFromThis

square

squareThis

squareRoot

squareRootThis

convert

trace

solveQuadraticEquation