diff options
Diffstat (limited to 'pyecsca/ec/point.py')
| -rw-r--r-- | pyecsca/ec/point.py | 71 |
1 files changed, 66 insertions, 5 deletions
diff --git a/pyecsca/ec/point.py b/pyecsca/ec/point.py index 162b9aa..1833f46 100644 --- a/pyecsca/ec/point.py +++ b/pyecsca/ec/point.py @@ -1,13 +1,15 @@ """Provides a :py:class:`.Point` class and a special :py:class:`.InfinityPoint` class for the point at infinity.""" from copy import copy -from typing import Mapping, TYPE_CHECKING +from operator import itemgetter +from typing import Mapping, Set, TYPE_CHECKING from public import public from pyecsca.ec.context import ResultAction from pyecsca.ec.coordinates import AffineCoordinateModel, CoordinateModel -from pyecsca.ec.mod import Mod, Undefined, mod +from pyecsca.ec.mod import Mod, Undefined, mod, square_roots, cube_roots +from pyecsca.ec.error import NonResidueError from pyecsca.ec.op import CodeOp @@ -141,11 +143,13 @@ class Point: if randomized: lmbd = Mod.random(curve.prime) for var, value in result.items(): - result[var] = value * (lmbd ** coordinate_model.homogweights[var]) + weight = coordinate_model.homogweights[var] + lpow = lmbd ** weight + result[var] = value * lpow return action.exit(Point(coordinate_model, **result)) def equals_affine(self, other: "Point") -> bool: - """Test whether this point is equal to :paramref:`~.equals_affine.other` irrespective of the coordinate model (in the affine sense).""" + """Test whether this point is equal to :paramref:`~.equals_affine.other` in the affine sense.""" if not isinstance(other, Point) or isinstance(other, InfinityPoint): return False if self.coordinate_model.curve_model != other.coordinate_model.curve_model: @@ -158,7 +162,7 @@ class Point: The "z" scaling formula maps the projective class to a single representative. - :param other: The point to compare + :param other: The point to compare. :raises ValueError: If the "z" formula is not available for the coordinate system. :return: Whether the points are equal. """ @@ -174,6 +178,60 @@ class Point: else: raise ValueError("No scaling formula available.") + def equals_homog(self, other: "Point") -> bool: + """ + Test whether this point is equal to :paramref:`~.equals_homog.other` in the coordinate system. + + :param other: The point to compare. + :return: Whether the points are equal. + """ + if not isinstance(other, Point) or isinstance(other, InfinityPoint): + return False + if self.coordinate_model.curve_model != other.coordinate_model.curve_model: + return False + weights = sorted(self.coordinate_model.homogweights.items(), key=itemgetter(1)) + lambdas: Set[Mod] = set() + for var, weight in weights: + var1 = self.coords[var] + var2 = other.coords[var] + if var1 == 0 and var2 == 0: + continue + if var1 == 0 or var2 == 0: + return False + val = var2 / var1 + if not lambdas: + if weight == 1: + lambdas.add(val) + elif weight == 2: + if not val.is_residue(): + return False + lambdas.update(square_roots(val)) + elif weight == 3: + if not val.is_cubic_residue(): + return False + lambdas.update(cube_roots(val)) + elif weight == 4: + if not val.is_residue(): + return False + first = val.sqrt() + try: + lambdas.update(square_roots(first)) + except NonResidueError: + pass + try: + lambdas.update(square_roots(-first)) + except NonResidueError: + pass + else: + raise NotImplementedError( + f"Equality checking does not support {weight} weight." + ) + else: + lambdas = set(filter(lambda candidate: candidate ** weight == val, lambdas)) + if not lambdas: + return False + return True + def equals(self, other: "Point") -> bool: """Test whether this point is equal to `other` irrespective of the coordinate model (in the affine sense).""" return self.equals_affine(other) @@ -240,6 +298,9 @@ class InfinityPoint(Point): def equals_scaled(self, other: "Point") -> bool: return self == other + def equals_homog(self, other: "Point") -> bool: + return self == other + def equals(self, other: "Point") -> bool: return self == other |