ECFieldF2m

AI-generated Key Takeaways

• ECFieldF2m defines an elliptic curve over a characteristic 2 finite field with 2^m elements.

• It supports both normal and polynomial basis representations, with constructors allowing specification of the field size (m) and reduction polynomial.

• Provides methods to retrieve field size, representation parameters (m, reduction polynomial details), and perform equality checks.

• Inherits methods from Object for basic object operations and implements ECField to provide the field size.

• Instances of ECFieldF2m are immutable, ensuring their properties remain constant after creation.

public class ECFieldF2m extends Object
implements ECField

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

See Also

• ECField

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

From class java.lang.Object

Object	clone() Creates and returns a copy of this Object.
boolean	equals(Object obj) Compares this instance with the specified object and indicates if they are equal.
void	finalize() Invoked when the garbage collector has detected that this instance is no longer reachable.
final Class<?>	getClass() Returns the unique instance of Class that represents this object's class.
int	hashCode() Returns an integer hash code for this object.
final void	notify() Causes a thread which is waiting on this object's monitor (by means of calling one of the wait() methods) to be woken up.
final void	notifyAll() Causes all threads which are waiting on this object's monitor (by means of calling one of the wait() methods) to be woken up.
String	toString() Returns a string containing a concise, human-readable description of this object.
final void	wait(long timeout, int nanos) Causes the calling thread to wait until another thread calls the notify() or notifyAll() method of this object or until the specified timeout expires.
final void	wait(long timeout) Causes the calling thread to wait until another thread calls the notify() or notifyAll() method of this object or until the specified timeout expires.
final void	wait() Causes the calling thread to wait until another thread calls the notify() or notifyAll() method of this object.

From interface java.security.spec.ECField

abstract int

getFieldSize() Returns the field size in bits.

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 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.

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.