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import pickle
from contextlib import nullcontext as does_not_raise
import pytest
from pyecsca.ec.coordinates import AffineCoordinateModel
from pyecsca.ec.mod import mod
from pyecsca.ec.model import ShortWeierstrassModel, MontgomeryModel
from pyecsca.ec.params import get_params
from pyecsca.ec.point import Point, InfinityPoint
from pyecsca.ec.error import UnsatisfiedAssumptionError
@pytest.fixture()
def secp128r1_coords(secp128r1):
return secp128r1.curve.coordinate_model
@pytest.fixture()
def affine_model():
return AffineCoordinateModel(ShortWeierstrassModel())
def test_construction(secp128r1_coords):
with pytest.raises(ValueError):
Point(secp128r1_coords)
with pytest.raises(ValueError):
Point(secp128r1_coords, X=mod(1, 3), Y=mod(2, 7), Z=mod(1, 3))
def test_to_affine(secp128r1, secp128r1_coords, affine_model):
pt = Point(
secp128r1_coords,
X=mod(0x161FF7528B899B2D0C28607CA52C5B86, secp128r1.curve.prime),
Y=mod(0xCF5AC8395BAFEB13C02DA292DDED7A83, secp128r1.curve.prime),
Z=mod(1, secp128r1.curve.prime),
)
affine = pt.to_affine()
assert isinstance(affine.coordinate_model, AffineCoordinateModel)
assert set(affine.coords.keys()) == set(affine_model.variables)
assert affine.coords["x"] == pt.coords["X"]
assert affine.coords["y"] == pt.coords["Y"]
assert affine.to_affine() == affine
affine = InfinityPoint(secp128r1_coords).to_affine()
assert isinstance(affine, InfinityPoint)
secp128r1_xz = get_params("secg", "secp128r1", "xz")
with pytest.raises(NotImplementedError):
secp128r1_xz.generator.to_affine()
secp128r1_modified = get_params("secg", "secp128r1", "modified")
modified = secp128r1_modified.generator.to_affine()
assert modified is not None
def test_to_model(secp128r1, secp128r1_coords, affine_model):
affine = Point(
affine_model,
x=mod(0xABCD, secp128r1.curve.prime),
y=mod(0xEF, secp128r1.curve.prime),
)
other = affine.to_model(secp128r1_coords, secp128r1.curve)
assert other.coordinate_model == secp128r1_coords
assert set(other.coords.keys()) == set(secp128r1_coords.variables)
assert other.coords["X"] == affine.coords["x"]
assert other.coords["Y"] == affine.coords["y"]
assert other.coords["Z"] == mod(1, secp128r1.curve.prime)
infty = InfinityPoint(AffineCoordinateModel(secp128r1.curve.model))
other_infty = infty.to_model(secp128r1_coords, secp128r1.curve)
assert isinstance(other_infty, InfinityPoint)
with pytest.raises(ValueError):
secp128r1.generator.to_model(secp128r1_coords, secp128r1.curve)
@pytest.mark.parametrize("category,curve,coords,raises", [
("secg", "secp128r1", "projective", does_not_raise()),
("secg", "secp128r1", "jacobian", does_not_raise()),
("secg", "secp128r1", "modified", does_not_raise()),
("secg", "secp128r1", "xyzz", does_not_raise()),
("secg", "secp128r1", "xz", pytest.raises(NotImplementedError)), # Not really possible
("other", "Curve25519", "xz", pytest.raises(NotImplementedError)), # Not really possible
("other", "E-222", "inverted", does_not_raise()),
("other", "E-222", "projective", does_not_raise()),
# ("other", "E-222", "yz", does_not_raise()), # No STD curve satisfies this formula assumption
# ("other", "E-222", "yzsquared", does_not_raise()), # No STD curve satisfies this formula assumption
("other", "Ed25519", "extended", does_not_raise()),
("other", "Ed25519", "inverted", does_not_raise()),
("other", "Ed25519", "projective", does_not_raise()),
])
def test_to_from_affine(category, curve, coords, raises):
params = get_params(category, curve, coords)
with raises:
other = params.generator.to_affine().to_model(params.curve.coordinate_model, params.curve)
assert params.generator == other
random_affine = params.curve.affine_random()
assert random_affine.to_model(params.curve.coordinate_model, params.curve).to_affine() == random_affine
def test_equals(secp128r1, secp128r1_coords):
pt = Point(
secp128r1_coords,
X=mod(0x4, secp128r1.curve.prime),
Y=mod(0x6, secp128r1.curve.prime),
Z=mod(2, secp128r1.curve.prime),
)
other = Point(
secp128r1_coords,
X=mod(0x2, secp128r1.curve.prime),
Y=mod(0x3, secp128r1.curve.prime),
Z=mod(1, secp128r1.curve.prime),
)
third = Point(
secp128r1_coords,
X=mod(0x5, secp128r1.curve.prime),
Y=mod(0x3, secp128r1.curve.prime),
Z=mod(1, secp128r1.curve.prime),
)
assert pt.equals(other)
assert pt != other
assert not pt.equals(2) # type: ignore
assert pt != 2
assert not pt.equals(third)
assert pt != third
assert pt.equals_scaled(other)
assert pt.equals_affine(other)
assert not pt.equals_scaled(third)
assert pt.equals_homog(pt)
assert pt.equals_homog(other)
assert other.equals_homog(pt)
assert not pt.equals_homog(third)
assert not third.equals_homog(pt)
infty_one = InfinityPoint(secp128r1_coords)
infty_other = InfinityPoint(secp128r1_coords)
assert infty_one.equals(infty_other)
assert infty_one.equals_affine(infty_other)
assert infty_one.equals_scaled(infty_other)
assert infty_one.equals_homog(infty_other)
assert infty_one == infty_other
assert not pt.equals(infty_one)
assert not pt.equals_affine(infty_one)
assert not pt.equals_scaled(infty_one)
assert not pt.equals_homog(infty_one)
mont = MontgomeryModel()
different = Point(
mont.coordinates["xz"],
X=mod(
0x64DACCD2656420216545E5F65221EB,
0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA,
),
Z=mod(1, 0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA),
)
assert not pt.equals(different)
assert pt != different
def test_homog():
model = ShortWeierstrassModel()
for coords_name, coords in model.coordinates.items():
try:
params = get_params("secg", "secp128r1", coords_name, infty=False)
except UnsatisfiedAssumptionError:
continue
infty = params.curve.neutral
rand_aff = params.curve.affine_random()
one1 = rand_aff.to_model(coords, params.curve)
one2 = rand_aff.to_model(coords, params.curve, randomized=True)
one3 = rand_aff.to_model(coords, params.curve, randomized=True)
assert one1.equals_homog(one2)
assert one1.equals_homog(one3)
assert one2.equals_homog(one3)
assert not one1.equals_homog(infty)
assert infty.equals_homog(infty)
while True:
other_aff = params.curve.affine_random()
if other_aff != rand_aff:
break
other = other_aff.to_model(coords, params.curve)
assert not one1.equals_homog(other)
assert not one2.equals_homog(other)
assert not one3.equals_homog(other)
def test_bytes(secp128r1, secp128r1_coords):
pt = Point(
secp128r1_coords,
X=mod(0x4, secp128r1.curve.prime),
Y=mod(0x6, secp128r1.curve.prime),
Z=mod(2, secp128r1.curve.prime),
)
assert bytes(pt) == \
b"\x04\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x06\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x02"
assert bytes(InfinityPoint(secp128r1_coords)) == b"\x00"
def test_iter(secp128r1, secp128r1_coords):
pt = Point(
secp128r1_coords,
X=mod(0x4, secp128r1.curve.prime),
Y=mod(0x6, secp128r1.curve.prime),
Z=mod(2, secp128r1.curve.prime),
)
t = tuple(pt)
assert len(t) == 3
assert len(pt) == 3
assert len(InfinityPoint(secp128r1_coords)) == 0
assert len(tuple(InfinityPoint(secp128r1_coords))) == 0
def test_pickle(secp128r1, secp128r1_coords):
pt = Point(
secp128r1_coords,
X=mod(0x4, secp128r1.curve.prime),
Y=mod(0x6, secp128r1.curve.prime),
Z=mod(2, secp128r1.curve.prime),
)
pickle.dumps(secp128r1_coords)
assert pt == pickle.loads(pickle.dumps(pt))
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