klefki.algebra.groups.ecg.elliptic

Module Contents

Classes

EllipticCurveGroup	A monoid in which every element has an inverse is called group.
PairFriendlyEllipticCurveGroup	A monoid in which every element has an inverse is called group.
EllipicCyclicSubgroup	With Lagrange’s therem
JacobianGroup	A monoid in which every element has an inverse is called group.

class klefki.algebra.groups.ecg.elliptic.EllipticCurveGroup(*args)

Bases: klefki.algebra.abstract.Group

A monoid in which every element has an inverse is called group.

A

B

from_JacobianGroup(self, o)

from_list(self, o)

from_int(self, o)

from_tuple(self, o)

op(self, g)

The Operator for obeying axiom associativity (2)

inverse(self)

Implement for axiom inverse

classmethod identity(cls)

The value for obeying axiom identity (3)

property x(self)

property y(self)

class klefki.algebra.groups.ecg.elliptic.PairFriendlyEllipticCurveGroup(*args)

Bases: klefki.algebra.groups.ecg.elliptic.EllipticCurveGroup

A monoid in which every element has an inverse is called group.

e

F

property pairing(cls, P, Q)

classmethod e(cls, P, Q)

class klefki.algebra.groups.ecg.elliptic.EllipicCyclicSubgroup(*args)

Bases: klefki.algebra.groups.ecg.elliptic.EllipticCurveGroup

With Lagrange’s therem the order of a subgroup is a divisor of the order of the parent group

N

scalar(self, times)

class klefki.algebra.groups.ecg.elliptic.JacobianGroup(*args)

Bases: klefki.algebra.abstract.Group

A monoid in which every element has an inverse is called group.

A

B

craft(self, o)

Automatic lookup method like from_{type} of Class Object.

double(self, n=None)

classmethod identity(cls)

The value for obeying axiom identity (3)

inverse(self)

Implement for axiom inverse

op(self, g)

The Operator for obeying axiom associativity (2)