pyecsca.ec.formula.code module

Provides a concrete class of a formula that has a constructor.

class pyecsca.ec.formula.code.CodeFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: Formula

A basic formula class that can be directly initialized with the code and other attributes.

name: str

Name of the formula.

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

unified: bool

Whether the formula specifies that it is unified.

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str]

A shortname for the type of the formula.

num_inputs: ClassVar[int]

Number of inputs (points) of the formula.

num_outputs: ClassVar[int]

Number of outputs (points) of the formula.

class pyecsca.ec.formula.code.CodeAdditionFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: AdditionFormula, CodeFormula

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

num_inputs: ClassVar[int] = 2

Number of inputs (points) of the formula.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str] = 'add'

A shortname for the type of the formula.

name: str

Name of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

unified: bool

Whether the formula specifies that it is unified.

class pyecsca.ec.formula.code.CodeDoublingFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: DoublingFormula, CodeFormula

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str] = 'dbl'

A shortname for the type of the formula.

name: str

Name of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

unified: bool

Whether the formula specifies that it is unified.

class pyecsca.ec.formula.code.CodeLadderFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: LadderFormula, CodeFormula

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

num_inputs: ClassVar[int] = 3

Number of inputs (points) of the formula.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

num_outputs: ClassVar[int] = 2

Number of outputs (points) of the formula.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str] = 'ladd'

A shortname for the type of the formula.

name: str

Name of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

unified: bool

Whether the formula specifies that it is unified.

class pyecsca.ec.formula.code.CodeTriplingFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: TriplingFormula, CodeFormula

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str] = 'tpl'

A shortname for the type of the formula.

name: str

Name of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

unified: bool

Whether the formula specifies that it is unified.

class pyecsca.ec.formula.code.CodeNegationFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: NegationFormula, CodeFormula

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str] = 'neg'

A shortname for the type of the formula.

name: str

Name of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

unified: bool

Whether the formula specifies that it is unified.

class pyecsca.ec.formula.code.CodeScalingFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: ScalingFormula, CodeFormula

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str] = 'scl'

A shortname for the type of the formula.

name: str

Name of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

unified: bool

Whether the formula specifies that it is unified.

class pyecsca.ec.formula.code.CodeDifferentialAdditionFormula(name, code, coordinate_model, parameters, assumptions, unified=False)

Bases: DifferentialAdditionFormula, CodeFormula

property assumptions_str

property input_index

Return the starting index where this formula reads its inputs.

property inputs

Return the input variables of the formula.

property num_addsubs: int

Return the number of additions and subtractions.

property num_divisions: int

Return the number of divisions.

num_inputs: ClassVar[int] = 3

Number of inputs (points) of the formula.

property num_inversions: int

Return the number of inversions.

property num_multiplications: int

Return the number of multiplications.

property num_operations: int

Return the number of operations.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property output_index

Return the starting index where this formula stores its outputs.

property outputs

Return the output variables of the formula.

shortname: ClassVar[str] = 'dadd'

A shortname for the type of the formula.

name: str

Name of the formula.

coordinate_model: Any

Coordinate model of the formula.

meta: MutableMapping[str, Any]

Meta information about the formula, such as its source.

parameters: List[str]

Formula parameters (i.e. new parameters introduced by the formula, like half = 1/2).

assumptions: List[Expression]

Assumptions of the formula (e.g. Z1 == 1 or 2*half == 1).

code: List[CodeOp]

The collection of ops that constitute the code of the formula.

unified: bool

Whether the formula specifies that it is unified.