java.lang.Object
- org.bouncycastle.pqc.math.linearalgebra.GF2nElement
- - org.bouncycastle.pqc.math.linearalgebra.GF2nPolynomialElement

All Implemented Interfaces:

GFElement
```
public class GF2nPolynomialElement
extends GF2nElement
```
This class implements elements of finite binary fields GF(2ⁿ) using polynomial representation. For more information on the arithmetic see for example IEEE Standard 1363 or Certicom online-tutorial.

See Also:

"GF2nField", GF2nPolynomialField, GF2nONBElement, GF2Polynomial

Field Summary
- Fields inherited from class org.bouncycastle.pqc.math.linearalgebra.GF2nElement
  mDegree, mField

Constructor Summary

Constructors
Constructor	Description
`GF2nPolynomialElement(GF2nPolynomialElement other)`	Creates a new GF2nPolynomialElement by cloning the given GF2nPolynomialElement b.
`GF2nPolynomialElement(GF2nPolynomialField f, byte[] os)`	Creates a new GF2nPolynomialElement using the given field f and byte[] os as value.
`GF2nPolynomialElement(GF2nPolynomialField f, int[] is)`	Creates a new GF2nPolynomialElement using the given field f and int[] is as value.
`GF2nPolynomialElement(GF2nPolynomialField f, java.util.Random rand)`	Create a new random GF2nPolynomialElement using the given field and source of randomness.
`GF2nPolynomialElement(GF2nPolynomialField f, GF2Polynomial bs)`	Creates a new GF2nPolynomialElement using the given field and Bitstring.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`GFElement`	`add(GFElement addend)`	Compute the sum of this element and `addend`.
`void`	`addToThis(GFElement addend)`	Compute `this + addend` (overwrite `this`).
`java.lang.Object`	`clone()`	Creates a new GF2nPolynomialElement by cloning this GF2nPolynomialElement.
`boolean`	`equals(java.lang.Object other)`	Compare this element with another object.
`int`	`hashCode()`
`GF2nElement`	`increase()`	Returns `this` element + 'one".
`void`	`increaseThis()`	Increases this element by 'one'.
`GFElement`	`invert()`	Compute the multiplicative inverse of this element.
`GF2nPolynomialElement`	`invertEEA()`	Calculates the multiplicative inverse of this and returns the result in a new GF2nPolynomialElement.
`GF2nPolynomialElement`	`invertMAIA()`	Calculates the multiplicative inverse of this using the modified almost inverse algorithm and returns the result in a new GF2nPolynomialElement.
`GF2nPolynomialElement`	`invertSquare()`	Calculates the multiplicative inverse of this and returns the result in a new GF2nPolynomialElement.
`boolean`	`isOne()`	Tests if the GF2nPolynomialElement has 'one' as value.
`boolean`	`isZero()`	Checks whether this element is zero.
`GFElement`	`multiply(GFElement factor)`	Compute the product of this element and `factor`.
`void`	`multiplyThisBy(GFElement factor)`	Compute `this * factor` (overwrite `this`).
`static GF2nPolynomialElement`	`ONE(GF2nPolynomialField f)`	Create the one element.
`GF2nPolynomialElement`	`power(int k)`	Calculates this to the power of k and returns the result in a new GF2nPolynomialElement.
`GF2nElement`	`solveQuadraticEquation()`	Solves the quadratic equation `z² + z = this` if such a solution exists.
`GF2nElement`	`square()`	This method is used internally to map the square()-calls within GF2nPolynomialElement to one of the possible squaring methods.
`GF2nPolynomialElement`	`squareBitwise()`	Squares this GF2nPolynomialElement by shifting left its Bitstring and reducing.
`GF2nPolynomialElement`	`squareMatrix()`	Squares this GF2nPolynomialElement using GF2nField's squaring matrix.
`GF2nPolynomialElement`	`squarePreCalc()`	Squares this GF2nPolynomialElement by using precalculated values and reducing.
`GF2nElement`	`squareRoot()`	Compute the square root of this element and return the result in a new `GF2nPolynomialElement`.
`void`	`squareRootThis()`	Compute the square root of this element.
`void`	`squareThis()`	This method is used internally to map the square()-calls within GF2nPolynomialElement to one of the possible squaring methods.
`void`	`squareThisBitwise()`	Squares this GF2nPolynomialElement by shifting left its Bitstring and reducing.
`void`	`squareThisMatrix()`	Squares this GF2nPolynomialElement using GF2nFields squaring matrix.
`void`	`squareThisPreCalc()`	Squares this GF2nPolynomialElement by using precalculated values and reducing.
`boolean`	`testRightmostBit()`	Returns whether the rightmost bit of the bit representation is set.
`byte[]`	`toByteArray()`	Converts this GF2nPolynomialElement to a byte[] according to 1363.
`java.math.BigInteger`	`toFlexiBigInt()`	Converts this GF2nPolynomialElement to an integer according to 1363.
`java.lang.String`	`toString()`	Returns a string representing this Bitstrings value using hexadecimal radix in MSB-first order.
`java.lang.String`	`toString(int radix)`	Returns a string representing this Bitstrings value using hexadecimal or binary radix in MSB-first order.
`int`	`trace()`	Returns the trace of this GF2nPolynomialElement.
`static GF2nPolynomialElement`	`ZERO(GF2nPolynomialField f)`	Create the zero element.

Methods inherited from class org.bouncycastle.pqc.math.linearalgebra.GF2nElement
convert, getField, subtract, subtractFromThis

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

- Constructor Detail
  - GF2nPolynomialElement
```
public GF2nPolynomialElement(GF2nPolynomialField f,
                             java.util.Random rand)
```
    Create a new random GF2nPolynomialElement using the given field and source of randomness.
    
    Parameters:
    
    f - the GF2nField to use
    
    rand - the source of randomness
  - GF2nPolynomialElement
```
public GF2nPolynomialElement(GF2nPolynomialField f,
                             GF2Polynomial bs)
```
    Creates a new GF2nPolynomialElement using the given field and Bitstring.
    
    Parameters:
    
    f - the GF2nPolynomialField to use
    
    bs - the desired value as Bitstring
  - GF2nPolynomialElement
```
public GF2nPolynomialElement(GF2nPolynomialField f,
                             byte[] os)
```
    Creates a new GF2nPolynomialElement using the given field f and byte[] os as value. The conversion is done according to 1363.
    
    Parameters:
    
    f - the GF2nField to use
    
    os - the octet string to assign to this GF2nPolynomialElement
    
    See Also:
    
    "P1363 5.5.5 p23, OS2FEP/OS2BSP"
  - GF2nPolynomialElement
```
public GF2nPolynomialElement(GF2nPolynomialField f,
                             int[] is)
```
    Creates a new GF2nPolynomialElement using the given field f and int[] is as value.
    
    Parameters:
    
    f - the GF2nField to use
    
    is - the integer string to assign to this GF2nPolynomialElement
  - GF2nPolynomialElement
```
public GF2nPolynomialElement(GF2nPolynomialElement other)
```
    Creates a new GF2nPolynomialElement by cloning the given GF2nPolynomialElement b.
    
    Parameters:
    
    other - the GF2nPolynomialElement to clone
- Method Detail
  - clone
```
public java.lang.Object clone()
```
    Creates a new GF2nPolynomialElement by cloning this GF2nPolynomialElement.
    
    Specified by:
    
    clone in interface GFElement
    
    Specified by:
    
    clone in class GF2nElement
    
    Returns:
    
    a copy of this element
  - ZERO
```
public static GF2nPolynomialElement ZERO(GF2nPolynomialField f)
```
    Create the zero element.
    
    Parameters:
    
    f - the finite field
    
    Returns:
    
    the zero element in the given finite field
  - ONE
```
public static GF2nPolynomialElement ONE(GF2nPolynomialField f)
```
    Create the one element.
    
    Parameters:
    
    f - the finite field
    
    Returns:
    
    the one element in the given finite field
  - isZero
```
public boolean isZero()
```
    Checks whether this element is zero.
    
    Returns:
    
    true if this is the zero element
  - isOne
```
public boolean isOne()
```
    Tests if the GF2nPolynomialElement has 'one' as value.
    
    Returns:
    
    true if this equals one (this == 1)
  - equals
```
public boolean equals(java.lang.Object other)
```
    Compare this element with another object.
    
    Specified by:
    
    equals in interface GFElement
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    other - the other object
    
    Returns:
    
    true if the two objects are equal, false otherwise
  - hashCode
```
public int hashCode()
```
    Specified by:
    
    hashCode in interface GFElement
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hash code of this element
  - testRightmostBit
```
public boolean testRightmostBit()
```
    Returns whether the rightmost bit of the bit representation is set. This is needed for data conversion according to 1363.
    
    Specified by:
    
    testRightmostBit in class GF2nElement
    
    Returns:
    
    true if the rightmost bit of this element is set
  - add
```
public GFElement add(GFElement addend)
              throws java.lang.RuntimeException
```
    Compute the sum of this element and addend.
    
    Parameters:
    
    addend - the addend
    
    Returns:
    
    this + other (newly created)
    
    Throws:
    
    java.lang.RuntimeException
  - addToThis
```
public void addToThis(GFElement addend)
               throws java.lang.RuntimeException
```
    Compute this + addend (overwrite this).
    
    Parameters:
    
    addend - the addend
    
    Throws:
    
    java.lang.RuntimeException
  - increase
```
public GF2nElement increase()
```
    Returns this element + 'one".
    
    Specified by:
    
    increase in class GF2nElement
    
    Returns:
    
    this + 'one'
  - increaseThis
```
public void increaseThis()
```
    Increases this element by 'one'.
    
    Specified by:
    
    increaseThis in class GF2nElement
  - multiply
```
public GFElement multiply(GFElement factor)
                   throws java.lang.RuntimeException
```
    Compute the product of this element and factor.
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this * factor (newly created)
    
    Throws:
    
    java.lang.RuntimeException
  - multiplyThisBy
```
public void multiplyThisBy(GFElement factor)
                    throws java.lang.RuntimeException
```
    Compute this * factor (overwrite this).
    
    Parameters:
    
    factor - the factor
    
    Throws:
    
    java.lang.RuntimeException
  - invert
```
public GFElement invert()
                 throws java.lang.ArithmeticException
```
    Compute the multiplicative inverse of this element.
    
    Returns:
    
    this^-1 (newly created)
    
    Throws:
    
    java.lang.ArithmeticException - if this is the zero element.
    
    See Also:
    
    invertMAIA(), invertEEA(), invertSquare()
  - invertEEA
```
public GF2nPolynomialElement invertEEA()
                                throws java.lang.ArithmeticException
```
    Calculates the multiplicative inverse of this and returns the result in a new GF2nPolynomialElement.
    
    Returns:
    
    this^(-1)
    
    Throws:
    
    java.lang.ArithmeticException - if this equals zero
  - invertSquare
```
public GF2nPolynomialElement invertSquare()
                                   throws java.lang.ArithmeticException
```
    Calculates the multiplicative inverse of this and returns the result in a new GF2nPolynomialElement.
    
    Returns:
    
    this^(-1)
    
    Throws:
    
    java.lang.ArithmeticException - if this equals zero
  - invertMAIA
```
public GF2nPolynomialElement invertMAIA()
                                 throws java.lang.ArithmeticException
```
    Calculates the multiplicative inverse of this using the modified almost inverse algorithm and returns the result in a new GF2nPolynomialElement.
    
    Returns:
    
    this^(-1)
    
    Throws:
    
    java.lang.ArithmeticException - if this equals zero
  - square
```
public GF2nElement square()
```
    This method is used internally to map the square()-calls within GF2nPolynomialElement to one of the possible squaring methods.
    
    Specified by:
    
    square in class GF2nElement
    
    Returns:
    
    this² (newly created)
    
    See Also:
    
    squarePreCalc()
  - squareThis
```
public void squareThis()
```
    This method is used internally to map the square()-calls within GF2nPolynomialElement to one of the possible squaring methods.
    
    Specified by:
    
    squareThis in class GF2nElement
  - squareMatrix
```
public GF2nPolynomialElement squareMatrix()
```
    Squares this GF2nPolynomialElement using GF2nField's squaring matrix. This is supposed to be fast when using a polynomial (no tri- or pentanomial) as fieldpolynomial. Use squarePreCalc when using a tri- or pentanomial as fieldpolynomial instead.
    
    Returns:
    
    this² (newly created)
    
    See Also:
    
    GF2Polynomial.vectorMult(org.bouncycastle.pqc.math.linearalgebra.GF2Polynomial), squarePreCalc(), squareBitwise()
  - squareThisMatrix
```
public void squareThisMatrix()
```
    Squares this GF2nPolynomialElement using GF2nFields squaring matrix. This is supposed to be fast when using a polynomial (no tri- or pentanomial) as fieldpolynomial. Use squarePreCalc when using a tri- or pentanomial as fieldpolynomial instead.
    
    See Also:
    
    GF2Polynomial.vectorMult(org.bouncycastle.pqc.math.linearalgebra.GF2Polynomial), squarePreCalc(), squareBitwise()
  - squareBitwise
```
public GF2nPolynomialElement squareBitwise()
```
    Squares this GF2nPolynomialElement by shifting left its Bitstring and reducing. This is supposed to be the slowest method. Use squarePreCalc or squareMatrix instead.
    
    Returns:
    
    this² (newly created)
    
    See Also:
    
    squareMatrix(), squarePreCalc(), GF2Polynomial.squareThisBitwise()
  - squareThisBitwise
```
public void squareThisBitwise()
```
    Squares this GF2nPolynomialElement by shifting left its Bitstring and reducing. This is supposed to be the slowest method. Use squarePreCalc or squareMatrix instead.
    
    See Also:
    
    squareMatrix(), squarePreCalc(), GF2Polynomial.squareThisBitwise()
  - squarePreCalc
```
public GF2nPolynomialElement squarePreCalc()
```
    Squares this GF2nPolynomialElement by using precalculated values and reducing. This is supposed to de fastest when using a trinomial or pentanomial as field polynomial. Use squareMatrix when using a ordinary polynomial as field polynomial.
    
    Returns:
    
    this² (newly created)
    
    See Also:
    
    squareMatrix(), GF2Polynomial.squareThisPreCalc()
  - squareThisPreCalc
```
public void squareThisPreCalc()
```
    Squares this GF2nPolynomialElement by using precalculated values and reducing. This is supposed to de fastest when using a tri- or pentanomial as fieldpolynomial. Use squareMatrix when using a ordinary polynomial as fieldpolynomial.
    
    See Also:
    
    squareMatrix(), GF2Polynomial.squareThisPreCalc()
  - power
```
public GF2nPolynomialElement power(int k)
```
    Calculates this to the power of k and returns the result in a new GF2nPolynomialElement.
    
    Parameters:
    
    k - the power
    
    Returns:
    
    this^k in a new GF2nPolynomialElement
  - squareRoot
```
public GF2nElement squareRoot()
```
    Compute the square root of this element and return the result in a new GF2nPolynomialElement.
    
    Specified by:
    
    squareRoot in class GF2nElement
    
    Returns:
    
    this^1/2 (newly created)
  - squareRootThis
```
public void squareRootThis()
```
    Compute the square root of this element.
    
    Specified by:
    
    squareRootThis in class GF2nElement
  - solveQuadraticEquation
```
public GF2nElement solveQuadraticEquation()
                                   throws java.lang.RuntimeException
```
    Solves the quadratic equation z² + z = this if such a solution exists. This method returns one of the two possible solutions. The other solution is z + 1. Use z.increase() to compute this solution.
    
    Specified by:
    
    solveQuadraticEquation in class GF2nElement
    
    Returns:
    
    a GF2nPolynomialElement representing one z satisfying the equation z² + z = this
    
    Throws:
    
    java.lang.RuntimeException
    
    See Also:
    
    "IEEE 1363, Annex A.4.7"
  - trace
```
public int trace()
```
    Returns the trace of this GF2nPolynomialElement.
    
    Specified by:
    
    trace in class GF2nElement
    
    Returns:
    
    the trace of this GF2nPolynomialElement
  - toString
```
public java.lang.String toString()
```
    Returns a string representing this Bitstrings value using hexadecimal radix in MSB-first order.
    
    Specified by:
    
    toString in interface GFElement
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    a String representing this Bitstrings value.
  - toString
```
public java.lang.String toString(int radix)
```
    Returns a string representing this Bitstrings value using hexadecimal or binary radix in MSB-first order.
    
    Parameters:
    
    radix - the radix to use (2 or 16, otherwise 2 is used)
    
    Returns:
    
    a String representing this Bitstrings value.
  - toByteArray
```
public byte[] toByteArray()
```
    Converts this GF2nPolynomialElement to a byte[] according to 1363.
    
    Returns:
    
    a byte[] representing the value of this GF2nPolynomialElement
    
    See Also:
    
    "P1363 5.5.2 p22f BS2OSP, FE2OSP"
  - toFlexiBigInt
```
public java.math.BigInteger toFlexiBigInt()
```
    Converts this GF2nPolynomialElement to an integer according to 1363.
    
    Returns:
    
    a BigInteger representing the value of this GF2nPolynomialElement
    
    See Also:
    
    "P1363 5.5.1 p22 BS2IP"

Class GF2nPolynomialElement

Field Summary

Fields inherited from class org.bouncycastle.pqc.math.linearalgebra.GF2nElement

Constructor Summary

Method Summary

Methods inherited from class org.bouncycastle.pqc.math.linearalgebra.GF2nElement

Methods inherited from class java.lang.Object

Constructor Detail

GF2nPolynomialElement

GF2nPolynomialElement

GF2nPolynomialElement

GF2nPolynomialElement

GF2nPolynomialElement

Method Detail

clone

ZERO

ONE

isZero

isOne

equals

hashCode

testRightmostBit

add

addToThis

increase

increaseThis

multiply

multiplyThisBy

invert

invertEEA

invertSquare

invertMAIA

square

squareThis

squareMatrix

squareThisMatrix

squareBitwise

squareThisBitwise

squarePreCalc

squareThisPreCalc

power

squareRoot

squareRootThis

solveQuadraticEquation

trace

toString

toString

toByteArray

toFlexiBigInt