GF2mField (Bouncy Castle Library 1.60 API Specification)

java.lang.Object
- org.bouncycastle.pqc.math.linearalgebra.GF2mField

```
public class GF2mField
extends java.lang.Object
```
This class describes operations with elements from the finite field F = GF(2^m). ( GF(2^m)= GF(2)[A] where A is a root of irreducible polynomial with degree m, each field element B has a polynomial basis representation, i.e. it is represented by a different binary polynomial of degree less than m, B = poly(A) ) All operations are defined only for field with 1< m <32. For the representation of field elements the map f: F->Z, poly(A)->poly(2) is used, where integers have the binary representation. For example: A^7+A^3+A+1 -> (00...0010001011)=139 Also for elements type Integer is used.

See Also:

PolynomialRingGF2

Constructor Summary

Constructors
Constructor	Description
`GF2mField(byte[] enc)`
`GF2mField(int degree)`	create a finite field GF(2^m)
`GF2mField(int degree, int poly)`	create a finite field GF(2^m) with the fixed field polynomial
`GF2mField(GF2mField field)`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`int`	`add(int a, int b)`	Return sum of two elements
`java.lang.String`	`elementToStr(int a)`
`boolean`	`equals(java.lang.Object other)`	checks if given object is equal to this field.
`int`	`exp(int a, int k)`	compute exponentiation a^k
`int`	`getDegree()`	return degree of the field
`byte[]`	`getEncoded()`	return the encoded form of this field
`int`	`getPolynomial()`	return the field polynomial
`int`	`getRandomElement(java.security.SecureRandom sr)`	create a random field element using PRNG sr
`int`	`getRandomNonZeroElement()`	create a random non-zero field element
`int`	`getRandomNonZeroElement(java.security.SecureRandom sr)`	create a random non-zero field element using PRNG sr
`int`	`hashCode()`
`int`	`inverse(int a)`	compute the multiplicative inverse of a
`boolean`	`isElementOfThisField(int e)`
`int`	`mult(int a, int b)`	Return product of two elements
`int`	`sqRoot(int a)`	compute the square root of an integer
`java.lang.String`	`toString()`	Returns a human readable form of this field.

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

- Constructor Detail
  - GF2mField
```
public GF2mField(int degree)
```
    create a finite field GF(2^m)
    
    Parameters:
    
    degree - the degree of the field
  - GF2mField
```
public GF2mField(int degree,
                 int poly)
```
    create a finite field GF(2^m) with the fixed field polynomial
    
    Parameters:
    
    degree - the degree of the field
    
    poly - the field polynomial
  - GF2mField
```
public GF2mField(byte[] enc)
```
  - GF2mField
```
public GF2mField(GF2mField field)
```
- Method Detail
  - getDegree
```
public int getDegree()
```
    return degree of the field
    
    Returns:
    
    degree of the field
  - getPolynomial
```
public int getPolynomial()
```
    return the field polynomial
    
    Returns:
    
    the field polynomial
  - getEncoded
```
public byte[] getEncoded()
```
    return the encoded form of this field
    
    Returns:
    
    the field in byte array form
  - add
```
public int add(int a,
               int b)
```
    Return sum of two elements
    
    Parameters:
    
    a -
    
    b -
    
    Returns:
    
    a+b
  - mult
```
public int mult(int a,
                int b)
```
    Return product of two elements
    
    Parameters:
    
    a -
    
    b -
    
    Returns:
    
    a*b
  - exp
```
public int exp(int a,
               int k)
```
    compute exponentiation a^k
    
    Parameters:
    
    a - a field element a
    
    k - k degree
    
    Returns:
    
    a^k
  - inverse
```
public int inverse(int a)
```
    compute the multiplicative inverse of a
    
    Parameters:
    
    a - a field element a
    
    Returns:
    
    a^-1
  - sqRoot
```
public int sqRoot(int a)
```
    compute the square root of an integer
    
    Parameters:
    
    a - a field element a
    
    Returns:
    
    a^1/2
  - getRandomElement
```
public int getRandomElement(java.security.SecureRandom sr)
```
    create a random field element using PRNG sr
    
    Parameters:
    
    sr - SecureRandom
    
    Returns:
    
    a random element
  - getRandomNonZeroElement
```
public int getRandomNonZeroElement()
```
    create a random non-zero field element
    
    Returns:
    
    a random element
  - getRandomNonZeroElement
```
public int getRandomNonZeroElement(java.security.SecureRandom sr)
```
    create a random non-zero field element using PRNG sr
    
    Parameters:
    
    sr - SecureRandom
    
    Returns:
    
    a random non-zero element
  - isElementOfThisField
```
public boolean isElementOfThisField(int e)
```
    Returns:
    
    true if e is encoded element of this field and false otherwise
  - elementToStr
```
public java.lang.String elementToStr(int a)
```
  - equals
```
public boolean equals(java.lang.Object other)
```
    checks if given object is equal to this field.
    The method returns false whenever the given object is not GF2m.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    other - object
    
    Returns:
    
    true or false
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object
  - toString
```
public java.lang.String toString()
```
    Returns a human readable form of this field.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    a human readable form of this field.

Class GF2mField

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

GF2mField

GF2mField

GF2mField

GF2mField

Method Detail

getDegree

getPolynomial

getEncoded

add

mult

exp

inverse

sqRoot

getRandomElement

getRandomNonZeroElement

getRandomNonZeroElement

isElementOfThisField

elementToStr

equals

hashCode

toString