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 y² + xy = x³ + ax² + b.

Nested Class Summary
- Nested classes/interfaces 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

Constructors
Modifier	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 order, BigInteger cofactor)`	Constructor for Pentanomial Polynomial Basis (PPB).
`protected`	`F2m(int m, int k1, int k2, int k3, ECFieldElement a, ECFieldElement b, BigInteger order, BigInteger cofactor)`
	`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 order, BigInteger cofactor)`	Constructor for Trinomial Polynomial Basis (TPB).

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method	Description
`protected ECCurve`	`cloneCurve()`
`protected ECMultiplier`	`createDefaultMultiplier()`
`ECPoint`	`createPoint(BigInteger x, BigInteger y, boolean withCompression)`
`protected ECPoint`	`createRawPoint(ECFieldElement x, ECFieldElement y, boolean withCompression)`
`protected ECPoint`	`createRawPoint(ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, boolean withCompression)`
`protected ECPoint`	`decompressPoint(int yTilde, BigInteger X1)`	Decompresses a compressed point P = (xp, yp) (X9.62 s 4.2.2).
`ECFieldElement`	`fromBigInteger(BigInteger x)`
`int`	`getFieldSize()`
`BigInteger`	`getH()`	Deprecated. use `ECCurve.getCofactor()` instead
`ECPoint`	`getInfinity()`
`int`	`getK1()`
`int`	`getK2()`
`int`	`getK3()`
`int`	`getM()`
`BigInteger`	`getN()`	Deprecated. use `ECCurve.getOrder()` instead
`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, checkPoints, configure, createPoint, decodePoint, equals, equals, getA, getAllCoordinateSystems, getB, getCofactor, getCoordinateSystem, getEndomorphism, getField, getMultiplier, getOrder, getPreCompInfo, hashCode, importPoint, normalizeAll, normalizeAll, setPreCompInfo, validatePoint, validatePoint

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - F2m
```
public F2m(int m,
           int k,
           BigInteger a,
           BigInteger b)
```
    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.
  - F2m
```
public F2m(int m,
           int k,
           BigInteger a,
           BigInteger b,
           BigInteger order,
           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.
  - 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 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.
  - F2m
```
public F2m(int m,
           int k1,
           int k2,
           int k3,
           BigInteger a,
           BigInteger b,
           BigInteger order,
           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.
  - F2m
```
protected F2m(int m,
              int k1,
              int k2,
              int k3,
              ECFieldElement a,
              ECFieldElement b,
              BigInteger order,
              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(BigInteger x)
```
    Specified by:
    
    fromBigInteger in class ECCurve
  - createPoint
```
public ECPoint createPoint(BigInteger x,
                           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
  - createRawPoint
```
protected ECPoint createRawPoint(ECFieldElement x,
                                 ECFieldElement y,
                                 ECFieldElement[] zs,
                                 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,
                                  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.
  - 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()
```
    Deprecated.
    use ECCurve.getOrder() instead
  - getH
```
public BigInteger getH()
```
    Deprecated.
    use ECCurve.getCofactor() instead

Class ECCurve.F2m

Nested Class Summary

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

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

F2m

F2m

F2m

F2m

F2m

Method Detail

cloneCurve

supportsCoordinateSystem

createDefaultMultiplier

getFieldSize

fromBigInteger

createPoint

createRawPoint

createRawPoint

getInfinity

isKoblitz

decompressPoint

getM

isTrinomial

getK1

getK2

getK3

getN

getH