Class ECFieldF2m

java.lang.Object
java.security.spec.ECFieldF2m
All Implemented Interfaces:
ECField
public class ECFieldF2m extends Object implements ECField
This immutable class defines an elliptic curve (EC) characteristic 2 finite field.
Since:
1.5
See Also:

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

  • Method Summary

    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 the hash code value for this characteristic 2 finite field.

    Methods declared in class Object

    clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait
    Modifier and Type
    Method
    Description
    protected Object
    clone()
    Creates and returns a copy of this object.
    protected void
    finalize()
    Deprecated, for removal: This API element is subject to removal in a future version.
    Finalization is deprecated and subject to removal in a future release.
    final Class<?>
    getClass()
    Returns the runtime class of this Object.
    final void
    notify()
    Wakes up a single thread that is waiting on this object's monitor.
    final void
    notifyAll()
    Wakes up all threads that are waiting on this object's monitor.
    String
    toString()
    Returns a string representation of the object.
    final void
    wait()
    Causes the current thread to wait until it is awakened, typically by being notified or interrupted.
    final void
    wait(long timeoutMillis)
    Causes the current thread to wait until it is awakened, typically by being notified or interrupted, or until a certain amount of real time has elapsed.
    final void
    wait(long timeoutMillis, int nanos)
    Causes the current thread to wait until it is awakened, typically by being notified or interrupted, or until a certain amount of real time has elapsed.

  • Constructor Details

    • 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 Details

    • 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:

    • hashCode

      public int hashCode()
      Returns the hash code value for this characteristic 2 finite field.
      Overrides:
      hashCode in class Object
      Returns:
      the hash code value for this characteristic 2 finite field
      See Also: