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from copy import copy
from typing import Mapping, Any
from public import public
from .coordinates import CoordinateModel, AffineCoordinateModel
from .mod import Mod, Undefined
from .op import CodeOp
@public
class Point(object):
"""A point with coordinates in a coordinate model."""
coordinate_model: CoordinateModel
coords: Mapping[str, Mod]
def __init__(self, model: CoordinateModel, **coords: Mod):
if not set(model.variables) == set(coords.keys()):
raise ValueError
self.coordinate_model = model
self.coords = coords
def __getattribute__(self, name):
if "coords" in super().__getattribute__("__dict__"):
coords = super().__getattribute__("coords")
if name in coords:
return coords[name]
return super().__getattribute__(name)
def to_affine(self) -> "Point":
"""Convert this point into the affine coordinate model, if possible."""
if isinstance(self.coordinate_model, AffineCoordinateModel):
return copy(self)
ops = set()
for s in self.coordinate_model.satisfying:
try:
ops.add(CodeOp(s))
except:
pass
affine_model = AffineCoordinateModel(self.coordinate_model.curve_model)
result_variables = set(map(lambda x: x.result, ops))
if not result_variables.issuperset(affine_model.variables):
raise NotImplementedError
result = {}
for op in ops:
if op.result not in affine_model.variables:
continue
result[op.result] = op(**self.coords)
return Point(affine_model, **result)
@staticmethod
def from_affine(coordinate_model: CoordinateModel, affine_point: "Point") -> "Point":
"""Convert an affine point into a given coordinate model, if possible."""
if not isinstance(affine_point.coordinate_model, AffineCoordinateModel):
raise ValueError
result = {}
n = affine_point.coords["x"].n
for var in coordinate_model.variables: # XXX: This just works for the stuff currently in EFD.
if var == "X":
result[var] = affine_point.coords["x"]
elif var == "Y":
result[var] = affine_point.coords["y"]
elif var.startswith("Z"):
result[var] = Mod(1, n)
elif var == "T":
result[var] = Mod(affine_point.coords["x"] * affine_point.coords["y"], n)
else:
raise NotImplementedError
return Point(coordinate_model, **result)
def equals(self, other: Any) -> bool:
"""Test whether this point is equal to `other` irrespective of the coordinate model (in the affine sense)."""
if not isinstance(other, Point):
return False
if self.coordinate_model.curve_model != other.coordinate_model.curve_model:
return False
return self.to_affine() == other.to_affine()
def __eq__(self, other):
if not isinstance(other, Point):
return False
if self.coordinate_model != other.coordinate_model:
return False
return self.coords == other.coords
def __str__(self):
args = ", ".join([f"{key}={val}" for key, val in self.coords.items()])
return f"[{args}]"
def __repr__(self):
return f"Point([{str(self)}] in {self.coordinate_model})"
@public
class InfinityPoint(Point):
"""A point at infinity."""
def __init__(self, model: CoordinateModel):
coords = {key: Undefined() for key in model.variables}
super().__init__(model, **coords)
def to_affine(self) -> "InfinityPoint":
return InfinityPoint(AffineCoordinateModel(self.coordinate_model.curve_model))
@staticmethod
def from_affine(coordinate_model: CoordinateModel, affine_point: "Point") -> "InfinityPoint":
raise NotImplementedError
def equals(self, other) -> bool:
return self == other
def __eq__(self, other):
if type(other) is not InfinityPoint:
return False
else:
return self.coordinate_model == other.coordinate_model
def __str__(self):
return "Infinity"
def __repr__(self):
return f"InfinityPoint({self.coordinate_model})"
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