Class ECFieldF2m

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 correspondes 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)