pyecsca.ec.model module

Provides curve model classes for the supported curve models.

class CurveModel

Bases: object

Model(form) of an elliptic curve.

name: str

shortname: str

coordinates: MutableMapping[str, CoordinateModel]

parameter_names: List[str]

coordinate_names: List[str]

equation: Expression

ysquared: Expression

base_addition: List[Module]

base_doubling: List[Module]

base_negation: List[Module]

base_neutral: List[Module]

full_weierstrass: List[Module]

to_weierstrass: List[Module]

from_weierstrass: List[Module]

class ShortWeierstrassModel

Bases: EFDCurveModel

Short-Weierstrass curve model.

\[y^2 = x^3 + a x + b\]

name: str

shortname: str

coordinates: MutableMapping[str, CoordinateModel]

parameter_names: List[str]

coordinate_names: List[str]

equation: Expression

ysquared: Expression

base_addition: List[Module]

base_doubling: List[Module]

base_negation: List[Module]

base_neutral: List[Module]

full_weierstrass: List[Module]

to_weierstrass: List[Module]

from_weierstrass: List[Module]

class MontgomeryModel

Bases: EFDCurveModel

Montgomery curve model.

\[B y^2 = x^3 + A x^2 + x\]

name: str

shortname: str

coordinates: MutableMapping[str, CoordinateModel]

parameter_names: List[str]

coordinate_names: List[str]

equation: Expression

ysquared: Expression

base_addition: List[Module]

base_doubling: List[Module]

base_negation: List[Module]

base_neutral: List[Module]

full_weierstrass: List[Module]

to_weierstrass: List[Module]

from_weierstrass: List[Module]

class EdwardsModel

Bases: EFDCurveModel

Edwards curve model.

\[x^2 + y^2 = c^2 (1 + d x^2 y^2)\]

name: str

shortname: str

coordinates: MutableMapping[str, CoordinateModel]

parameter_names: List[str]

coordinate_names: List[str]

equation: Expression

ysquared: Expression

base_addition: List[Module]

base_doubling: List[Module]

base_negation: List[Module]

base_neutral: List[Module]

full_weierstrass: List[Module]

to_weierstrass: List[Module]

from_weierstrass: List[Module]

class TwistedEdwardsModel

Bases: EFDCurveModel

Twisted-Edwards curve model.

\[a x^2 + y^2 = 1 + d x^2 y^2\]

name: str

shortname: str

coordinates: MutableMapping[str, CoordinateModel]

parameter_names: List[str]

coordinate_names: List[str]

equation: Expression

ysquared: Expression

base_addition: List[Module]

base_doubling: List[Module]

base_negation: List[Module]

base_neutral: List[Module]

full_weierstrass: List[Module]

to_weierstrass: List[Module]

from_weierstrass: List[Module]