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.Config, ECCurve.F2m, ECCurve.Fp

Field Summary

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

a, b, coord, COORD_AFFINE, COORD_HOMOGENEOUS, COORD_JACOBIAN, COORD_JACOBIAN_CHUDNOVSKY, COORD_JACOBIAN_MODIFIED, COORD_LAMBDA_AFFINE, COORD_LAMBDA_PROJECTIVE, COORD_SKEWED, multiplier

Constructor Summary

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

Method Summary

protected ECCurve	cloneCurve()
protected ECMultiplier	createDefaultMultiplier()
ECPoint	createPoint(java.math.BigInteger x, java.math.BigInteger y, boolean withCompression)
protected ECPoint	createRawPoint(ECFieldElement x, ECFieldElement y, boolean withCompression)
protected ECPoint	decompressPoint(int yTilde, java.math.BigInteger X1) Decompresses a compressed point P = (xp, yp) (X9.62 s 4.2.2).
boolean	equals(java.lang.Object anObject)
ECFieldElement	fromBigInteger(java.math.BigInteger x)
int	getFieldSize()
java.math.BigInteger	getH()
ECPoint	getInfinity()
int	getK1()
int	getK2()
int	getK3()
int	getM()
java.math.BigInteger	getN()
int	hashCode()
boolean	isKoblitz() Returns true if this is a Koblitz curve (ABC curve).
boolean	isTrinomial() Return true if curve uses a Trinomial basis.
boolean	supportsCoordinateSystem(int coord)

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

checkPoint, checkPoints, configure, createPoint, decodePoint, getA, getAllCoordinateSystems, getB, getCoordinateSystem, getMultiplier, getPreCompInfo, importPoint, normalizeAll, setPreCompInfo

Methods inherited from class java.lang.Object

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

Constructor Detail

ECCurve.F2m

public ECCurve.F2m(int m,
                   int k,
                   java.math.BigInteger a,
                   java.math.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.

ECCurve.F2m

public ECCurve.F2m(int m,
                   int k,
                   java.math.BigInteger a,
                   java.math.BigInteger b,
                   java.math.BigInteger n,
                   java.math.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.

ECCurve.F2m

public ECCurve.F2m(int m,
                   int k1,
                   int k2,
                   int k3,
                   java.math.BigInteger a,
                   java.math.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.

ECCurve.F2m

public ECCurve.F2m(int m,
                   int k1,
                   int k2,
                   int k3,
                   java.math.BigInteger a,
                   java.math.BigInteger b,
                   java.math.BigInteger n,
                   java.math.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.

ECCurve.F2m

protected ECCurve.F2m(int m,
                      int k1,
                      int k2,
                      int k3,
                      ECFieldElement a,
                      ECFieldElement b,
                      java.math.BigInteger n,
                      java.math.BigInteger h)

Method Detail

cloneCurve

protected ECCurve cloneCurve()

Specified by:

cloneCurve in class ECCurve

supportsCoordinateSystem

public boolean supportsCoordinateSystem(int coord)

Overrides:

supportsCoordinateSystem in class ECCurve

createDefaultMultiplier

protected ECMultiplier createDefaultMultiplier()

Overrides:

createDefaultMultiplier in class ECCurve

getFieldSize

public int getFieldSize()

Specified by:

getFieldSize in class ECCurve

fromBigInteger

public ECFieldElement fromBigInteger(java.math.BigInteger x)

Specified by:

fromBigInteger in class ECCurve

createPoint

public ECPoint createPoint(java.math.BigInteger x,
                           java.math.BigInteger y,
                           boolean withCompression)

Overrides:

createPoint in class ECCurve

createRawPoint

protected ECPoint createRawPoint(ECFieldElement x,
                                 ECFieldElement y,
                                 boolean withCompression)

Specified by:

createRawPoint 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,
                                  java.math.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(java.lang.Object anObject)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class 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 java.math.BigInteger getN()

getH

public java.math.BigInteger getH()