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:

ECField

Constructors

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)

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.

Methods

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)