Class 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

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.

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

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)

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.

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)

© 1993, 2020, Oracle and/or its affiliates. All rights reserved.
Documentation extracted from Debian's OpenJDK Development Kit package.
Licensed under the GNU General Public License, version 2, with the Classpath Exception.
Various third party code in OpenJDK is licensed under different licenses (see Debian package).
Java and OpenJDK are trademarks or registered trademarks of Oracle and/or its affiliates.
https://docs.oracle.com/en/java/javase/11/docs/api/java.base/java/security/spec/ECFieldF2m.html