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class:ECFieldF2m [NONE]
  • 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:
    ECField

constructor:<init>(int) [NONE]

  • 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.

constructor:<init>(int,java.math.BigInteger) [NONE]

  • 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.

constructor:<init>(int,int[]) [NONE]

  • 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:getFieldSize() [NONE]

  • 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.

method:getM() [NONE]

  • getM

    public int getM()
    Returns the value m of this characteristic 2 finite field.
    Returns:
    m with 2^m being the number of elements.

method:getReductionPolynomial() [NONE]

  • 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.

method:getMidTermsOfReductionPolynomial() [NONE]

  • 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.

method:equals(java.lang.Object) [NONE]

  • 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

method:hashCode() [NONE]

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