java.lang.Object
- org.bouncycastle.pqc.math.linearalgebra.GF2nField

Direct Known Subclasses:

GF2nONBField, GF2nPolynomialField
```
public abstract class GF2nField
extends java.lang.Object
```
This abstract class defines the finite field GF(2ⁿ). It holds the extension degree n, the characteristic, the irreducible fieldpolynomial and conversion matrices. GF2nField is implemented by the classes GF2nPolynomialField and GF2nONBField.

See Also:

GF2nONBField, GF2nPolynomialField

Field Summary

Fields
Modifier and Type	Field	Description
`protected GF2Polynomial`	`fieldPolynomial`	the irreducible fieldPolynomial stored in normal order (also for ONB)
`protected java.util.Vector`	`fields`	holds a list of GF2nFields to which elements have been converted and thus a COB-Matrix exists
`protected java.util.Vector`	`matrices`	the COB matrices
`protected int`	`mDegree`	the degree of this field
`protected java.security.SecureRandom`	`random`

Constructor Summary

Constructors
Modifier Constructor Description

protected GF2nField(java.security.SecureRandom random)

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method	Description
`protected abstract void`	`computeCOBMatrix(GF2nField B1)`	Computes the change-of-basis matrix for basis conversion according to 1363.
`protected abstract void`	`computeFieldPolynomial()`	Computes the fieldpolynomial.
`GF2nElement`	`convert(GF2nElement elem, GF2nField basis)`	Converts the given element in representation according to this field to a new element in representation according to B1 using the change-of-basis matrix calculated by computeCOBMatrix.
`boolean`	`equals(java.lang.Object other)`	Decides whether the given object `other` is the same as this field.
`int`	`getDegree()`	Returns the degree n of this field.
`GF2Polynomial`	`getFieldPolynomial()`	Returns the fieldpolynomial as a new Bitstring.
`protected abstract GF2nElement`	`getRandomRoot(GF2Polynomial B0FieldPolynomial)`	Computes a random root from the given irreducible fieldpolynomial according to IEEE 1363 algorithm A.5.6.
`int`	`hashCode()`
`protected GF2Polynomial[]`	`invertMatrix(GF2Polynomial[] matrix)`	Inverts the given matrix represented as bitstrings.

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

- Field Detail
  - random
```
protected final java.security.SecureRandom random
```
  - mDegree
```
protected int mDegree
```
    the degree of this field
  - fieldPolynomial
```
protected GF2Polynomial fieldPolynomial
```
    the irreducible fieldPolynomial stored in normal order (also for ONB)
  - fields
```
protected java.util.Vector fields
```
    holds a list of GF2nFields to which elements have been converted and thus a COB-Matrix exists
  - matrices
```
protected java.util.Vector matrices
```
    the COB matrices
- Constructor Detail
  - GF2nField
```
protected GF2nField(java.security.SecureRandom random)
```
- Method Detail
  - getDegree
```
public final int getDegree()
```
    Returns the degree n of this field.
    
    Returns:
    
    the degree n of this field
  - getFieldPolynomial
```
public final GF2Polynomial getFieldPolynomial()
```
    Returns the fieldpolynomial as a new Bitstring.
    
    Returns:
    
    a copy of the fieldpolynomial as a new Bitstring
  - equals
```
public final boolean equals(java.lang.Object other)
```
    Decides whether the given object other is the same as this field.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    other - another object
    
    Returns:
    
    (this == other)
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hash code of this field
  - getRandomRoot
```
protected abstract GF2nElement getRandomRoot(GF2Polynomial B0FieldPolynomial)
```
    Computes a random root from the given irreducible fieldpolynomial according to IEEE 1363 algorithm A.5.6. This cal take very long for big degrees.
    
    Parameters:
    
    B0FieldPolynomial - the fieldpolynomial if the other basis as a Bitstring
    
    Returns:
    
    a random root of BOFieldPolynomial in representation according to this field
    
    See Also:
    
    "P1363 A.5.6, p103f"
  - computeCOBMatrix
```
protected abstract void computeCOBMatrix(GF2nField B1)
```
    Computes the change-of-basis matrix for basis conversion according to 1363. The result is stored in the lists fields and matrices.
    
    Parameters:
    
    B1 - the GF2nField to convert to
    
    See Also:
    
    "P1363 A.7.3, p111ff"
  - computeFieldPolynomial
```
protected abstract void computeFieldPolynomial()
```
    Computes the fieldpolynomial. This can take a long time for big degrees.
  - invertMatrix
```
protected final GF2Polynomial[] invertMatrix(GF2Polynomial[] matrix)
```
    Inverts the given matrix represented as bitstrings.
    
    Parameters:
    
    matrix - the matrix to invert as a Bitstring[]
    
    Returns:
    
    matrix^(-1)
  - convert
```
public final GF2nElement convert(GF2nElement elem,
                                 GF2nField basis)
                          throws java.lang.RuntimeException
```
    Converts the given element in representation according to this field to a new element in representation according to B1 using the change-of-basis matrix calculated by computeCOBMatrix.
    
    Parameters:
    
    elem - the GF2nElement to convert
    
    basis - the basis to convert elem to
    
    Returns:
    
    elem converted to a new element representation according to basis
    
    Throws:
    
    java.lang.RuntimeException
    
    See Also:
    
    computeCOBMatrix(org.bouncycastle.pqc.math.linearalgebra.GF2nField), getRandomRoot(org.bouncycastle.pqc.math.linearalgebra.GF2Polynomial), GF2nPolynomial, "P1363 A.7 p109ff"

Class GF2nField

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

random

mDegree

fieldPolynomial

fields

matrices

Constructor Detail

GF2nField

Method Detail

getDegree

getFieldPolynomial

equals

hashCode

getRandomRoot

computeCOBMatrix

computeFieldPolynomial

invertMatrix

convert