All Implemented Interfaces:

ECField

public class ECFieldF2m
extends Object
implements ECField 

Since:

1.5

See Also:

ECField

• Constructor Summary

  Constructors

  Constructor	Description
  ECFieldF2m (int m)	Creates an elliptic curve characteristic 2 finite field which has 2^m elements with normal basis.
  ECFieldF2m (int m, BigInteger rp)	Creates an elliptic curve characteristic 2 finite field which has 2^m elements with polynomial basis.
  ECFieldF2m (int m, int[] ks)	Creates an elliptic curve characteristic 2 finite field which has 2^m elements with polynomial basis.

• Method Summary

  All Methods

  Modifier and Type	Method	Description
  boolean	equals (Object obj)	Compares this finite field for equality with the specified object.
  int	getFieldSize ()	Returns the field size in bits which is m for this characteristic 2 finite field.
  int	getM ()	Returns the value m of this characteristic 2 finite field.
  int[]	getMidTermsOfReductionPolynomial ()	Returns an integer array which contains the order of the middle term(s) of the reduction polynomial for polynomial basis or null for normal basis.
  BigInteger	getReductionPolynomial ()	Returns a BigInteger whose i-th bit corresponds to the i-th coefficient of the reduction polynomial for polynomial basis or null for normal basis.
  int	hashCode ()	Returns a hash code value for this characteristic 2 finite field.

  • Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

• Constructor Detail

  • ECFieldF2m

    public ECFieldF2m(int m)

    Creates an elliptic curve characteristic 2 finite field which has 2^m elements with normal basis.

    Parameters:

    m - with 2^m being the number of elements.

    Throws:

    IllegalArgumentException - if m is not positive.

  • ECFieldF2m

    public ECFieldF2m(int m,
     BigInteger rp)

    Creates an elliptic curve characteristic 2 finite field which has 2^m elements with polynomial basis. The reduction polynomial for this field is based on rp whose i-th bit corresponds to the i-th coefficient of the reduction polynomial.

    Note: A valid reduction polynomial is either a trinomial (X^m + X^k + 1 with m > k >= 1) or a pentanomial (X^m + X^k3 + X^k2 + X^k1 + 1 with m > k3 > k2 > k1 >= 1).

    Parameters:

    m - with 2^m being the number of elements.

    rp - the BigInteger whose i-th bit corresponds to the i-th coefficient of the reduction polynomial.

    Throws:

    NullPointerException - if rp is null.

    IllegalArgumentException - if m is not positive, or rp does not represent a valid reduction polynomial.

  • ECFieldF2m

    public ECFieldF2m(int m,
     int[] ks)

    Creates an elliptic curve characteristic 2 finite field which has 2^m elements with polynomial basis. The reduction polynomial for this field is based on ks whose content contains the order of the middle term(s) of the reduction polynomial. Note: A valid reduction polynomial is either a trinomial (X^m + X^k + 1 with m > k >= 1) or a pentanomial (X^m + X^k3 + X^k2 + X^k1 + 1 with m > k3 > k2 > k1 >= 1), so ks should have length 1 or 3.

    Parameters:

    m - with 2^m being the number of elements.

    ks - the order of the middle term(s) of the reduction polynomial. Contents of this array are copied to protect against subsequent modification.

    Throws:

    NullPointerException - if ks is null.

    IllegalArgumentException - ifm is not positive, or the length of ks is neither 1 nor 3, or values in ks are not between m-1 and 1 (inclusive) and in descending order.

• Method Detail

  • getFieldSize

    public int getFieldSize()

    Returns the field size in bits which is m for this characteristic 2 finite field.

    Specified by:

    getFieldSize in interface ECField

    Returns:

    the field size in bits.

  • getM

    public int getM()

    Returns the value m of this characteristic 2 finite field.

    Returns:

    m with 2^m being the number of elements.

  • getReductionPolynomial

    public BigInteger getReductionPolynomial()

    Returns a BigInteger whose i-th bit corresponds to the i-th coefficient of the reduction polynomial for polynomial basis or null for normal basis.

    Returns:

    a BigInteger whose i-th bit corresponds to the i-th coefficient of the reduction polynomial for polynomial basis or null for normal basis.

  • getMidTermsOfReductionPolynomial

    public int[] getMidTermsOfReductionPolynomial()

    Returns an integer array which contains the order of the middle term(s) of the reduction polynomial for polynomial basis or null for normal basis.

    Returns:

    an integer array which contains the order of the middle term(s) of the reduction polynomial for polynomial basis or null for normal basis. A new array is returned each time this method is called.

  • equals

    public boolean equals(Object obj)

    Compares this finite field for equality with the specified object.

    Overrides:

    equals in class Object

    Parameters:

    obj - the object to be compared.

    Returns:

    true if obj is an instance of ECFieldF2m and both m and the reduction polynomial match, false otherwise.

    See Also:

    Object.hashCode(), HashMap

  • hashCode

    public int hashCode()

    Returns a hash code value for this characteristic 2 finite field.

    Overrides:

    hashCode in class Object

    Returns:

    a hash code value.

    See Also:

    Object.equals(java.lang.Object), System.identityHashCode(java.lang.Object)