klefki.algebra.concrete

Module Contents

Classes

FiniteFieldSecp256k1	A FIELD is a set F which is closed under two operations + and × s.t.
FiniteFieldCyclicSecp256k1	A FIELD is a set F which is closed under two operations + and × s.t.
EllipticCurveGroupSecp256k1	y^2 = x^3 + A * x + B
JacobianGroupSecp256k1	A monoid in which every element has an inverse is called group.
FiniteFieldSecp256r1	A FIELD is a set F which is closed under two operations + and × s.t.
FiniteFieldCyclicSecp256r1	A FIELD is a set F which is closed under two operations + and × s.t.
EllipticCurveGroupSecp256r1	A monoid in which every element has an inverse is called group.
JacobianGroupSecp256r1	A monoid in which every element has an inverse is called group.
EllipticCurveCyclicSubgroupSecp256r1	With Lagrange’s therem
EllipticCurveGroupSecp256r1	A monoid in which every element has an inverse is called group.

class klefki.algebra.concrete.FiniteFieldSecp256k1(*args)

Bases: klefki.algebra.fields.FiniteField

A FIELD is a set F which is closed under two operations + and × s.t. (1) Fis an abelian group under + and (2) F-{0} (the set F without the additive identity 0) is an abelian group under ×.

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class klefki.algebra.concrete.FiniteFieldCyclicSecp256k1(*args)

Bases: klefki.algebra.fields.FiniteField

A FIELD is a set F which is closed under two operations + and × s.t. (1) Fis an abelian group under + and (2) F-{0} (the set F without the additive identity 0) is an abelian group under ×.

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class klefki.algebra.concrete.EllipticCurveGroupSecp256k1(*args)

Bases: klefki.algebra.groups.EllipticCurveGroup

y^2 = x^3 + A * x + B

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op(self, g)

The Operator for obeying axiom associativity (2)

classmethod lift_x(cls, x: FiniteField)

class klefki.algebra.concrete.JacobianGroupSecp256k1(*args)

Bases: klefki.algebra.groups.JacobianGroup

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

__slots__ = []

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class klefki.algebra.concrete.FiniteFieldSecp256r1(*args)

Bases: klefki.algebra.fields.FiniteField

A FIELD is a set F which is closed under two operations + and × s.t. (1) Fis an abelian group under + and (2) F-{0} (the set F without the additive identity 0) is an abelian group under ×.

__slots__ = []

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class klefki.algebra.concrete.FiniteFieldCyclicSecp256r1(*args)

Bases: klefki.algebra.fields.FiniteField

A FIELD is a set F which is closed under two operations + and × s.t. (1) Fis an abelian group under + and (2) F-{0} (the set F without the additive identity 0) is an abelian group under ×.

__slots__ = []

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class klefki.algebra.concrete.EllipticCurveGroupSecp256r1(*args)

Bases: klefki.algebra.groups.EllipticCurveGroup

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

__slots__ = []

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class klefki.algebra.concrete.JacobianGroupSecp256r1(*args)

Bases: klefki.algebra.groups.JacobianGroup

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

__slots__ = []

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class klefki.algebra.concrete.EllipticCurveCyclicSubgroupSecp256r1(*args)

Bases: klefki.algebra.groups.EllipicCyclicSubgroup

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

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class klefki.algebra.concrete.EllipticCurveGroupSecp256r1(*args)

Bases: klefki.algebra.groups.EllipticCurveGroup

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

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