Package org.bouncycastle.math.ec

Class ECCurve.F2m

java.lang.Object

org.bouncycastle.math.ec.ECCurve

org.bouncycastle.math.ec.ECCurve.F2m

Enclosing class:

ECCurve

public static class ECCurve.F2m
extends ECCurve

Elliptic curves over F2m. The Weierstrass equation is given by y2 + xy = x3 + ax2 + b.

Nested Class Summary

Nested classes/interfaces inherited from class org.bouncycastle.math.ec.ECCurve

ECCurve.F2m, ECCurve.Fp

Constructor Summary

Constructors

Constructor	Description
F2m(int m, int k1, int k2, int k3, BigInteger a, BigInteger b)	Constructor for Pentanomial Polynomial Basis (PPB).
F2m(int m, int k1, int k2, int k3, BigInteger a, BigInteger b, BigInteger n, BigInteger h)	Constructor for Pentanomial Polynomial Basis (PPB).
F2m(int m, int k, BigInteger a, BigInteger b)	Constructor for Trinomial Polynomial Basis (TPB).
F2m(int m, int k, BigInteger a, BigInteger b, BigInteger n, BigInteger h)	Constructor for Trinomial Polynomial Basis (TPB).

Method Summary

Modifier and Type	Method	Description
ECPoint	createPoint(BigInteger x, BigInteger y, boolean withCompression)
protected ECPoint	decompressPoint(int yTilde, BigInteger X1)	Decompresses a compressed point P = (xp, yp) (X9.62 s 4.2.2).
boolean	equals(Object anObject)	Compares this instance with the specified object and indicates if they are equal.
ECFieldElement	fromBigInteger(BigInteger x)
int	getFieldSize()
BigInteger	getH()
ECPoint	getInfinity()
int	getK1()
int	getK2()
int	getK3()
int	getM()
BigInteger	getN()
int	hashCode()	Returns an integer hash code for this object.
boolean	isKoblitz()	Returns true if this is a Koblitz curve (ABC curve).
boolean	isTrinomial()	Return true if curve uses a Trinomial basis.

Methods inherited from class org.bouncycastle.math.ec.ECCurve

decodePoint, getA, getB

Methods inherited from class java.lang.Object

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

Constructor Details

F2m

public F2m(int m,
int k,
BigInteger a,
BigInteger b)

Constructor for Trinomial Polynomial Basis (TPB).

Parameters:

m - The exponent m of F2m.

k - The integer k where xm + xk + 1 represents the reduction polynomial f(z).

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F2m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F2m.

F2m

public F2m(int m,
int k,
BigInteger a,
BigInteger b,
BigInteger n,
BigInteger h)

Constructor for Trinomial Polynomial Basis (TPB).

Parameters:

m - The exponent m of F2m.

k - The integer k where xm + xk + 1 represents the reduction polynomial f(z).

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F2m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F2m.

n - The order of the main subgroup of the elliptic curve.

h - The cofactor of the elliptic curve, i.e. #Ea(F2m) = h * n.

F2m

public F2m(int m,
int k1,
int k2,
int k3,
BigInteger a,
BigInteger b)

Constructor for Pentanomial Polynomial Basis (PPB).

Parameters:

m - The exponent m of F2m.

k1 - The integer k1 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k2 - The integer k2 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k3 - The integer k3 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F2m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F2m.

F2m

public F2m(int m,
int k1,
int k2,
int k3,
BigInteger a,
BigInteger b,
BigInteger n,
BigInteger h)

Constructor for Pentanomial Polynomial Basis (PPB).

Parameters:

m - The exponent m of F2m.

k1 - The integer k1 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k2 - The integer k2 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

k3 - The integer k3 where xm + xk3 + xk2 + xk1 + 1 represents the reduction polynomial f(z).

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F2m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F2m.

n - The order of the main subgroup of the elliptic curve.

h - The cofactor of the elliptic curve, i.e. #Ea(F2m) = h * n.

Method Details

getFieldSize

public int getFieldSize()

Specified by:

getFieldSize in class ECCurve

fromBigInteger

public ECFieldElement fromBigInteger(BigInteger x)

Specified by:

fromBigInteger in class ECCurve

createPoint

public ECPoint createPoint(BigInteger x,
BigInteger y,
boolean withCompression)

Specified by:

createPoint in class ECCurve

getInfinity

public ECPoint getInfinity()

Specified by:

getInfinity in class ECCurve

isKoblitz

public boolean isKoblitz()

Returns true if this is a Koblitz curve (ABC curve).

Returns:

true if this is a Koblitz curve (ABC curve), false otherwise

decompressPoint

protected ECPoint decompressPoint(int yTilde,
BigInteger X1)

Decompresses a compressed point P = (xp, yp) (X9.62 s 4.2.2).

Specified by:

decompressPoint in class ECCurve

Parameters:

yTilde - ~yp, an indication bit for the decompression of yp.

X1 - The field element xp.

Returns:

the decompressed point.

equals

public boolean equals(Object anObject)

Description copied from class: Object

Compares this instance with the specified object and indicates if they are equal. In order to be equal, o must represent the same object as this instance using a class-specific comparison. The general contract is that this comparison should be reflexive, symmetric, and transitive. Also, no object reference other than null is equal to null.

The default implementation returns true only if this == o. See Writing a correct equals method if you intend implementing your own equals method.

The general contract for the equals and Object.hashCode() methods is that if equals returns true for any two objects, then hashCode() must return the same value for these objects. This means that subclasses of Object usually override either both methods or neither of them.

Overrides:

equals in class Object

Parameters:

anObject - the object to compare this instance with.

Returns:

true if the specified object is equal to this Object; false otherwise.

See Also:

Object.hashCode()

hashCode

public int hashCode()

Description copied from class: Object

Returns an integer hash code for this object. By contract, any two objects for which Object.equals(java.lang.Object) returns true must return the same hash code value. This means that subclasses of Object usually override both methods or neither method.

Note that hash values must not change over time unless information used in equals comparisons also changes.

See Writing a correct hashCode method if you intend implementing your own hashCode method.

Overrides:

hashCode in class Object

Returns:

this object's hash code.

See Also:

Object.equals(java.lang.Object)

getM

public int getM()

isTrinomial

public boolean isTrinomial()

Return true if curve uses a Trinomial basis.

Returns:

true if curve Trinomial, false otherwise.

getK1

public int getK1()

getK2

public int getK2()

getK3

public int getK3()

getN

public BigInteger getN()

getH

public BigInteger getH()