org.bouncycastle.math.ec
Class ECCurve.F2m

java.lang.Object
  org.bouncycastle.math.ec.ECCurve
      org.bouncycastle.math.ec.ECCurve.AbstractF2m
          org.bouncycastle.math.ec.ECCurve.F2m

Enclosing class:

ECCurve

public static class ECCurve.F2m

extends ECCurve.AbstractF2m

Elliptic curves over F2m. The Weierstrass equation is given by y 2 + xy = x 3 + ax 2 + b.

Nested Class Summary

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

ECCurve.AbstractF2m, ECCurve.AbstractFp, ECCurve.Config, ECCurve.F2m, ECCurve.Fp

Field Summary

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

a, b, cofactor, coord, COORD_AFFINE, COORD_HOMOGENEOUS, COORD_JACOBIAN, COORD_JACOBIAN_CHUDNOVSKY, COORD_JACOBIAN_MODIFIED, COORD_LAMBDA_AFFINE, COORD_LAMBDA_PROJECTIVE, COORD_SKEWED, endomorphism, field, multiplier, order

Constructor Summary

	ECCurve.F2m(int m, int k, java.math.BigInteger a, java.math.BigInteger b) Deprecated. use constructor taking order/cofactor
	ECCurve.F2m(int m, int k, java.math.BigInteger a, java.math.BigInteger b, java.math.BigInteger order, java.math.BigInteger cofactor) Constructor for Trinomial Polynomial Basis (TPB).
	ECCurve.F2m(int m, int k1, int k2, int k3, java.math.BigInteger a, java.math.BigInteger b) Deprecated. use constructor taking order/cofactor
	ECCurve.F2m(int m, int k1, int k2, int k3, java.math.BigInteger a, java.math.BigInteger b, java.math.BigInteger order, java.math.BigInteger cofactor) Constructor for Pentanomial Polynomial Basis (PPB).
protected	ECCurve.F2m(int m, int k1, int k2, int k3, ECFieldElement a, ECFieldElement b, java.math.BigInteger order, java.math.BigInteger cofactor)

Method Summary

protected ECCurve	cloneCurve()
ECLookupTable	createCacheSafeLookupTable(ECPoint[] points, int off, int len) Create a cache-safe lookup table for the specified sequence of points.
protected ECMultiplier	createDefaultMultiplier()
protected ECPoint	createRawPoint(ECFieldElement x, ECFieldElement y)
protected ECPoint	createRawPoint(ECFieldElement x, ECFieldElement y, ECFieldElement[] zs)
ECFieldElement	fromBigInteger(java.math.BigInteger x)
int	getFieldSize()
ECPoint	getInfinity()
int	getK1()
int	getK2()
int	getK3()
int	getM()
boolean	isTrinomial() Return true if curve uses a Trinomial basis.
boolean	supportsCoordinateSystem(int coord)

Methods inherited from class org.bouncycastle.math.ec.ECCurve.AbstractF2m

createPoint, decompressPoint, inverse, isKoblitz, isValidFieldElement, randomFieldElement, randomFieldElementMult, solveQuadraticEquation

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

checkPoint, checkPoints, checkPoints, configure, decodePoint, equals, equals, getA, getAffinePointEncodingLength, getAllCoordinateSystems, getB, getCofactor, getCoordinateSystem, getEndomorphism, getField, getFieldElementEncodingLength, getMultiplier, getOrder, getPreCompInfo, hashCode, importPoint, normalizeAll, normalizeAll, precompute, validatePoint

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)

Deprecated. use constructor taking order/cofactor

Constructor for Trinomial Polynomial Basis (TPB).

Parameters:

m - The exponent m of F 2 m.

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

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

ECCurve.F2m

public ECCurve.F2m(int m,
                   int k,
                   java.math.BigInteger a,
                   java.math.BigInteger b,
                   java.math.BigInteger order,
                   java.math.BigInteger cofactor)

Constructor for Trinomial Polynomial Basis (TPB).

Parameters:

m - The exponent m of F 2 m.

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

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

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

cofactor - The cofactor of the elliptic curve, i.e. #E a(F 2 m) = h * n.

ECCurve.F2m

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

Deprecated. use constructor taking order/cofactor

Constructor for Pentanomial Polynomial Basis (PPB).

Parameters:

m - The exponent m of F 2 m.

k1 - The integer k1 where x m + x k3 + x k2 + x k1 + 1 represents the reduction polynomial f(z).

k2 - The integer k2 where x m + x k3 + x k2 + x k1 + 1 represents the reduction polynomial f(z).

k3 - The integer k3 where x m + x k3 + x k2 + x k1 + 1 represents the reduction polynomial f(z).

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

ECCurve.F2m

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

Constructor for Pentanomial Polynomial Basis (PPB).

Parameters:

m - The exponent m of F 2 m.

k1 - The integer k1 where x m + x k3 + x k2 + x k1 + 1 represents the reduction polynomial f(z).

k2 - The integer k2 where x m + x k3 + x k2 + x k1 + 1 represents the reduction polynomial f(z).

k3 - The integer k3 where x m + x k3 + x k2 + x k1 + 1 represents the reduction polynomial f(z).

a - The coefficient a in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

b - The coefficient b in the Weierstrass equation for non-supersingular elliptic curves over F 2 m.

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

cofactor - The cofactor of the elliptic curve, i.e. #E a(F 2 m) = h * n.

ECCurve.F2m

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

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

createRawPoint

protected ECPoint createRawPoint(ECFieldElement x,
                                 ECFieldElement y)

Specified by:

createRawPoint in class ECCurve

createRawPoint

protected ECPoint createRawPoint(ECFieldElement x,
                                 ECFieldElement y,
                                 ECFieldElement[] zs)

Specified by:

createRawPoint in class ECCurve

getInfinity

public ECPoint getInfinity()

Specified by:

getInfinity in class ECCurve

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()

createCacheSafeLookupTable

public ECLookupTable createCacheSafeLookupTable(ECPoint[] points,
                                                int off,
                                                int len)

Description copied from class: ECCurve

Create a cache-safe lookup table for the specified sequence of points. All the points MUST belong to this ECCurve instance, and MUST already be normalized.

Overrides:

createCacheSafeLookupTable in class ECCurve