ECFieldF2m

public class ECFieldF2m extends Object
implements ECField

This immutable class defines an elliptic curve (EC) characteristic 2 finite field.

See Also

Public Constructor Summary

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.

Public Method Summary

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.

Inherited Method Summary

Public Constructors

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.

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.

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.

Public Methods

public boolean equals (Object obj)

Compares this finite field for equality with the specified 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.

public int getFieldSize ()

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

Returns
  • the field size in bits.

public int getM ()

Returns the value m of this characteristic 2 finite field.

Returns
  • m with 2^m being the number of elements.

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.

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.

public int hashCode ()

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

Returns
  • a hash code value.