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

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 the hash code value for this characteristic 2 finite field.

Methods declared in class Object

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

Modifier and Type	Method	Description
protected Object	clone()	Answers a new instance of the same class as the receiver, whose slots have been filled in with the values in the slots of the receiver.
protected void	finalize()	Deprecated, for removal: This API element is subject to removal in a future version. May cause performance issues, deadlocks and hangs.
final Class<? extends Object>	getClass()	Answers the unique instance of java.lang.Class which represents the class of the receiver.
final void	notify()	Causes one thread which is waiting on the receiver to be made ready to run.
final void	notifyAll()	Causes all threads which are waiting on the receiver to be made ready to run.
String	toString()	Answers a string containing a concise, human-readable description of the receiver.
final void	wait()	Causes the thread which sent this message to be made not ready to run pending some change in the receiver (as indicated by notify or notifyAll).
final void	wait(long time)	Causes the thread which sent this message to be made not ready to run either pending some change in the receiver (as indicated by notify or notifyAll) or the expiration of the timeout.
final void	wait(long time, int frac)	Causes the thread which sent this message to be made not ready to run either pending some change in the receiver (as indicated by notify or notifyAll) or the expiration of the timeout.

Constructor Details

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 Details

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()

hashCode

public int hashCode()

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

Overrides:

hashCode in class Object

Returns:

the hash code value for this characteristic 2 finite field

See Also:

• Object.equals(Object)