Overview  Package   Class  Tree  Deprecated  Index  Help 
 PREV CLASS   NEXT CLASS FRAMES    NO FRAMES
SUMMARY:  INNER | FIELD | CONSTR | METHOD DETAIL:  FIELD | CONSTR | METHOD

de.flexiprovider.common.math.finitefields
Class GF2nPolynomialElement

java.lang.Object
  |
  +--de.flexiprovider.common.math.finitefields.GF2nElement
        |
        +--de.flexiprovider.common.math.finitefields.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.

Author:
Oliver Seiler
See Also:
"GF2nField", GF2nPolynomialField, GF2nONBElement, GF2Polynomial

Fields inherited from class de.flexiprovider.common.math.finitefields.GF2nElement
mDegree, mField
 
Constructor Summary
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, GF2Polynomial bs)
          Creates a new GF2nPolynomialElement using the given field and Bitstring.
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.
 
Method Summary
 GFElement add(GFElement addend)
          Compute the sum of this element and addend.
 void addToThis(GFElement addend)
          Compute this + addend (overwrite this).
(package private)  void assignOne()
          Assigns the value 'one' to this Polynomial.
(package private)  void assignZero()
          Assigns the value 'zero' to this Polynomial.
 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.
(package private)  boolean testBit(int index)
          Checks whether the indexed bit of the bit representation is set.
 boolean testRightmostBit()
          Returns whether the rightmost bit of the bit representation is set.
 byte[] toByteArray()
          Converts this GF2nPolynomialElement to a byte[] according to 1363.
 FlexiBigInt 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 de.flexiprovider.common.math.finitefields.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.
Overrides:
clone in class GF2nElement
Returns:
a copy of this element

assignZero

void assignZero()
Assigns the value 'zero' to this Polynomial.
Overrides:
assignZero in class GF2nElement

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

assignOne

void assignOne()
Assigns the value 'one' to this Polynomial.
Overrides:
assignOne in class GF2nElement

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.
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()
Overrides:
hashCode in class java.lang.Object
Returns:
the hash code of this element

testBit

boolean testBit(int index)
Checks whether the indexed bit of the bit representation is set.
Overrides:
testBit in class GF2nElement
Parameters:
index - the index of the bit to test
Returns:
true if the indexed bit is set

testRightmostBit

public boolean testRightmostBit()
Returns whether the rightmost bit of the bit representation is set. This is needed for data conversion according to 1363.
Overrides:
testRightmostBit in class GF2nElement
Returns:
true if the rightmost bit of this element is set

add

public GFElement add(GFElement addend)
              throws DifferentFieldsException
Compute the sum of this element and addend.
Parameters:
addend - the addend
Returns:
this + other (newly created)
Throws:
DifferentFieldsException - if the elements are of different fields.

addToThis

public void addToThis(GFElement addend)
               throws DifferentFieldsException
Compute this + addend (overwrite this).
Parameters:
addend - the addend
Throws:
DifferentFieldsException - if the elements are of different fields.

increase

public GF2nElement increase()
Returns this element + 'one".
Overrides:
increase in class GF2nElement
Returns:
this + 'one'

increaseThis

public void increaseThis()
Increases this element by 'one'.
Overrides:
increaseThis in class GF2nElement

multiply

public GFElement multiply(GFElement factor)
                   throws DifferentFieldsException
Compute the product of this element and factor.
Parameters:
factor - the factor
Returns:
this * factor (newly created)
Throws:
DifferentFieldsException - if the elements are of different fields.

multiplyThisBy

public void multiplyThisBy(GFElement factor)
                    throws DifferentFieldsException
Compute this * factor (overwrite this).
Parameters:
factor - the factor
Throws:
DifferentFieldsException - if the elements are of different fields.

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.
Overrides:
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.
Overrides:
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(de.flexiprovider.common.math.finitefields.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(de.flexiprovider.common.math.finitefields.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.
Overrides:
squareRoot in class GF2nElement
Returns:
this1/2 (newly created)

squareRootThis

public void squareRootThis()
Compute the square root of this element.
Overrides:
squareRootThis in class GF2nElement

solveQuadraticEquation

public GF2nElement solveQuadraticEquation()
                                   throws NoSolutionException
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.
Overrides:
solveQuadraticEquation in class GF2nElement
Returns:
a GF2nPolynomialElement representing one z satisfying the equation z2 + z = this
Throws:
NoSolutionException - if no solution exists
See Also:
"IEEE 1363, Annex A.4.7"

trace

public int trace()
Returns the trace of this GF2nPolynomialElement.
Overrides:
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.
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 FlexiBigInt toFlexiBigInt()
Converts this GF2nPolynomialElement to an integer according to 1363.
Returns:
a FlexiBigInt representing the value of this GF2nPolynomialElement
See Also:
"P1363 5.5.1 p22 BS2IP"
Overview  Package   Class  Tree  Deprecated  Index  Help 
 PREV CLASS   NEXT CLASS FRAMES    NO FRAMES
SUMMARY:  INNER | FIELD | CONSTR | METHOD DETAIL:  FIELD | CONSTR | METHOD