Package org.gudy.bouncycastle.math.ec
Class ECCurve.F2m
java.lang.Object
org.gudy.bouncycastle.math.ec.ECCurve
org.gudy.bouncycastle.math.ec.ECCurve.F2m
- Enclosing class:
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.gudy.bouncycastle.math.ec.ECCurve
ECCurve.F2m, ECCurve.Fp
-
Field Summary
FieldsModifier and TypeFieldDescriptionprivate BigInteger
The cofactor of the curve.private ECPoint.F2m
The point at infinity on this curve.private int
TPB: The integerk
wherexm + xk + 1
represents the reduction polynomialf(z)
.
PPB: The integerk1
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.private int
TPB: Always set to0
PPB: The integerk2
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.private int
TPB: Always set to0
PPB: The integerk3
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.private int
The exponentm
ofF2m
.private byte
The parameterμ
of the elliptic curve if this is a Koblitz curve.private BigInteger
The order of the base point of the curve.private BigInteger[]
The auxiliary valuess0
ands1
used for partial modular reduction for Koblitz curves. -
Constructor Summary
ConstructorsConstructorDescriptionF2m
(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 TypeMethodDescriptioncreatePoint
(BigInteger x, BigInteger y, boolean withCompression) decodePoint
(byte[] encoded) private ECPoint
decompressPoint
(byte[] xEnc, int ypBit) Decompresses a compressed point P = (xp, yp) (X9.62 s 4.2.2).boolean
int
getH()
int
getK1()
int
getK2()
int
getK3()
int
getM()
(package private) byte
getMu()
Returns the parameterμ
of the elliptic curve.getN()
(package private) BigInteger[]
getSi()
int
hashCode()
boolean
Returns true if this is a Koblitz curve (ABC curve).boolean
Return true if curve uses a Trinomial basis.private ECFieldElement
Solves a quadratic equationz2 + z = beta
(X9.62 D.1.6) The other solution isz + 1
.
-
Field Details
-
m
private int mThe exponentm
ofF2m
. -
k1
private int k1TPB: The integerk
wherexm + xk + 1
represents the reduction polynomialf(z)
.
PPB: The integerk1
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
. -
k2
private int k2TPB: Always set to0
PPB: The integerk2
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
. -
k3
private int k3TPB: Always set to0
PPB: The integerk3
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
. -
n
The order of the base point of the curve. -
h
The cofactor of the curve. -
infinity
The point at infinity on this curve. -
mu
private byte muThe parameterμ
of the elliptic curve if this is a Koblitz curve. -
si
The auxiliary valuess0
ands1
used for partial modular reduction for Koblitz curves.
-
-
Constructor Details
-
F2m
Constructor for Trinomial Polynomial Basis (TPB).- Parameters:
m
- The exponentm
ofF2m
.k
- The integerk
wherexm + xk + 1
represents the reduction polynomialf(z)
.a
- The coefficienta
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.b
- The coefficientb
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.
-
F2m
Constructor for Trinomial Polynomial Basis (TPB).- Parameters:
m
- The exponentm
ofF2m
.k
- The integerk
wherexm + xk + 1
represents the reduction polynomialf(z)
.a
- The coefficienta
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.b
- The coefficientb
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.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
Constructor for Pentanomial Polynomial Basis (PPB).- Parameters:
m
- The exponentm
ofF2m
.k1
- The integerk1
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.k2
- The integerk2
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.k3
- The integerk3
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.a
- The coefficienta
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.b
- The coefficientb
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.
-
F2m
Constructor for Pentanomial Polynomial Basis (PPB).- Parameters:
m
- The exponentm
ofF2m
.k1
- The integerk1
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.k2
- The integerk2
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.k3
- The integerk3
wherexm + xk3 + xk2 + xk1 + 1
represents the reduction polynomialf(z)
.a
- The coefficienta
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.b
- The coefficientb
in the Weierstrass equation for non-supersingular elliptic curves overF2m
.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 classECCurve
-
fromBigInteger
- Specified by:
fromBigInteger
in classECCurve
-
createPoint
- Specified by:
createPoint
in classECCurve
-
decodePoint
- Specified by:
decodePoint
in classECCurve
-
getInfinity
- Specified by:
getInfinity
in classECCurve
-
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
-
getMu
byte getMu()Returns the parameterμ
of the elliptic curve.- Returns:
μ
of the elliptic curve.- Throws:
IllegalArgumentException
- if the given ECCurve is not a Koblitz curve.
-
getSi
BigInteger[] getSi()- Returns:
- the auxiliary values
s0
ands1
used for partial modular reduction for Koblitz curves.
-
decompressPoint
Decompresses a compressed point P = (xp, yp) (X9.62 s 4.2.2).- Parameters:
xEnc
- The encoding of field element xp.ypBit
- ~yp, an indication bit for the decompression of yp.- Returns:
- the decompressed point.
-
solveQuadradicEquation
Solves a quadratic equationz2 + z = beta
(X9.62 D.1.6) The other solution isz + 1
.- Parameters:
beta
- The value to solve the qradratic equation for.- Returns:
- the solution for
z2 + z = beta
ornull
if no solution exists.
-
equals
-
hashCode
public int hashCode() -
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
-
getH
-