pyecsca.ec.formula.base module

Provides an abstract base class of a formula.

class pyecsca.ec.formula.base.OpResult(name, value, op, *parents)

Bases: object

Result of an operation.

parents: Tuple

name: str

value: Mod

op: OpType

class pyecsca.ec.formula.base.FormulaAction(formula, *points, **inputs)

Bases: ResultAction

Execution of a formula, on some input points and parameters, with some outputs.

formula: Formula

The formula that was executed.

inputs: MutableMapping[str, Mod]

The input variables (point coordinates and parameters).

intermediates: MutableMapping[str, List[OpResult]]

Intermediates computed during execution.

op_results: List[OpResult]

The intermediates but ordered as they were computed.

outputs: MutableMapping[str, OpResult]

The output variables.

input_points: List[Any]

The input points.

output_points: List[Any]

The output points.

add_operation(op, value)

add_result(point, **outputs)

exit(result)

property result: Any

inside: bool

class pyecsca.ec.formula.base.Formula

Bases: ABC

Formula operating on points.

name: str

Name of the formula.

shortname: ClassVar[str]

A shortname for the type 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.

num_inputs: ClassVar[int]

Number of inputs (points) of the formula.

num_outputs: ClassVar[int]

Number of outputs (points) of the formula.

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 output_index

Return the starting index where this formula stores its outputs.

property inputs

Return the input variables of the formula.

property outputs

Return the output variables of the formula.

property num_operations: int

Return the number of operations.

property num_multiplications: int

Return the number of multiplications.

property num_divisions: int

Return the number of divisions.

property num_inversions: int

Return the number of inversions.

property num_powers: int

Return the number of powers.

property num_squarings: int

Return the number of squarings.

property num_addsubs: int

Return the number of additions and subtractions.

class pyecsca.ec.formula.base.AdditionFormula

Bases: Formula, ABC

Formula that adds two points.

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.

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.

shortname: ClassVar[str] = 'add'

A shortname for the type of the formula.

num_inputs: ClassVar[int] = 2

Number of inputs (points) of the formula.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

class pyecsca.ec.formula.base.DoublingFormula

Bases: Formula, ABC

Formula that doubles a point.

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.

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.

shortname: ClassVar[str] = 'dbl'

A shortname for the type of the formula.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

class pyecsca.ec.formula.base.TriplingFormula

Bases: Formula, ABC

Formula that triples a point.

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.

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.

shortname: ClassVar[str] = 'tpl'

A shortname for the type of the formula.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

class pyecsca.ec.formula.base.NegationFormula

Bases: Formula, ABC

Formula that negates a point.

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.

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.

shortname: ClassVar[str] = 'neg'

A shortname for the type of the formula.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

class pyecsca.ec.formula.base.ScalingFormula

Bases: Formula, ABC

Formula that somehow scales the point (to a given representative of a projective class).

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.

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.

shortname: ClassVar[str] = 'scl'

A shortname for the type of the formula.

num_inputs: ClassVar[int] = 1

Number of inputs (points) of the formula.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

class pyecsca.ec.formula.base.DifferentialAdditionFormula

Bases: Formula, ABC

Differential addition formula that adds two points with a known difference.

The first input point is the difference of the third input and the second input (P[0] = P[2] - P[1]).

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.

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.

shortname: ClassVar[str] = 'dadd'

A shortname for the type of the formula.

num_inputs: ClassVar[int] = 3

Number of inputs (points) of the formula.

num_outputs: ClassVar[int] = 1

Number of outputs (points) of the formula.

class pyecsca.ec.formula.base.LadderFormula

Bases: Formula, ABC

Ladder formula for simultaneous addition of two points and doubling of the one of them, with a known difference.

The first input point is the difference of the third input and the second input (P[0] = P[2] - P[1]). The first output point is the doubling of the second input point (O[0] = 2 * P[1]). The second output point is the addition of the second and third input points (O[1] = P[1] + P[2]).

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.

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.

shortname: ClassVar[str] = 'ladd'

A shortname for the type of the formula.

num_inputs: ClassVar[int] = 3

Number of inputs (points) of the formula.

num_outputs: ClassVar[int] = 2

Number of outputs (points) of the formula.