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

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

All Methods Instance Methods Concrete Methods
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 a hash code value for this characteristic 2 finite field.

Methods declared in class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

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 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 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)