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import warnings
import pytest
from sympy import FF, symbols
from pyecsca.ec.mod import (
Mod,
gcd,
extgcd,
Undefined,
miller_rabin,
has_gmp,
RawMod,
SymbolicMod,
jacobi,
)
from pyecsca.ec.error import (
NonInvertibleError,
NonResidueError,
NonInvertibleWarning,
NonResidueWarning,
)
from pyecsca.misc.cfg import getconfig, TemporaryConfig
def test_gcd():
assert gcd(15, 20) == 5
assert extgcd(15, 0) == (1, 0, 15)
assert extgcd(15, 20) == (-1, 1, 5)
def test_jacobi():
assert jacobi(5, 1153486465415345646578465454655646543248656451) == 1
assert jacobi(564786456646845, 46874698564153465453246546545456849797895547657) == -1
assert jacobi(564786456646845, 46874698564153465453246546545456849797895) == 0
def test_miller_rabin():
assert miller_rabin(2)
assert miller_rabin(3)
assert miller_rabin(5)
assert not miller_rabin(8)
assert miller_rabin(0xE807561107CCF8FA82AF74FD492543A918CA2E9C13750233A9)
assert not miller_rabin(0x6F6889DEB08DA211927370810F026EB4C17B17755F72EA005)
def test_inverse():
p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF
assert Mod(
0x702BDAFD3C1C837B23A1CB196ED7F9FADB333C5CFE4A462BE32ADCD67BFB6AC1, p
).inverse() == Mod(0x1CB2E5274BBA085C4CA88EEDE75AE77949E7A410C80368376E97AB22EB590F9D, p)
with pytest.raises(NonInvertibleError):
Mod(0, p).inverse()
with pytest.raises(NonInvertibleError):
Mod(5, 10).inverse()
getconfig().ec.no_inverse_action = "warning"
with warnings.catch_warnings(record=True) as w:
Mod(0, p).inverse()
assert issubclass(w[0].category, NonInvertibleWarning)
with warnings.catch_warnings(record=True) as w:
Mod(5, 10).inverse()
assert issubclass(w[0].category, NonInvertibleWarning)
getconfig().ec.no_inverse_action = "ignore"
Mod(0, p).inverse()
Mod(5, 10).inverse()
getconfig().ec.no_inverse_action = "error"
def test_is_residue():
assert Mod(4, 11).is_residue()
assert not Mod(11, 31).is_residue()
assert Mod(0, 7).is_residue()
assert Mod(1, 2).is_residue()
def test_bit_length():
x = Mod(3, 5)
assert x.bit_length() == 2
def test_sqrt():
p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF
assert Mod(
0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC, p
).sqrt() in (
0x9ADD512515B70D9EC471151C1DEC46625CD18B37BDE7CA7FB2C8B31D7033599D,
0x6522AED9EA48F2623B8EEAE3E213B99DA32E74C9421835804D374CE28FCCA662,
)
with pytest.raises(NonResidueError):
Mod(
0x702BDAFD3C1C837B23A1CB196ED7F9FADB333C5CFE4A462BE32ADCD67BFB6AC1, p
).sqrt()
getconfig().ec.non_residue_action = "warning"
with warnings.catch_warnings(record=True) as w:
Mod(
0x702BDAFD3C1C837B23A1CB196ED7F9FADB333C5CFE4A462BE32ADCD67BFB6AC1, p
).sqrt()
assert issubclass(w[0].category, NonResidueWarning)
getconfig().ec.non_residue_action = "ignore"
Mod(
0x702BDAFD3C1C837B23A1CB196ED7F9FADB333C5CFE4A462BE32ADCD67BFB6AC1, p
).sqrt()
with TemporaryConfig() as cfg:
cfg.ec.non_residue_action = "warning"
with warnings.catch_warnings(record=True) as w:
Mod(
0x702BDAFD3C1C837B23A1CB196ED7F9FADB333C5CFE4A462BE32ADCD67BFB6AC1,
p,
).sqrt()
assert issubclass(w[0].category, NonResidueWarning)
assert Mod(0, p).sqrt() == Mod(0, p)
q = 0x75D44FEE9A71841AE8403C0C251FBAD
assert Mod(0x591E0DB18CF1BD81A11B2985A821EB3, q).sqrt() in \
(0x113B41A1A2B73F636E73BE3F9A3716E, 0x64990E4CF7BA44B779CC7DCC8AE8A3F)
getconfig().ec.non_residue_action = "error"
def test_eq():
assert Mod(1, 7) == 1
assert Mod(1, 7) != "1"
assert Mod(1, 7) == Mod(1, 7)
assert Mod(1, 7) != Mod(5, 7)
assert Mod(1, 7) != Mod(1, 5)
def test_pow():
a = Mod(5, 7)
assert a ** (-1) == a.inverse()
assert a ** 0 == Mod(1, 7)
assert a ** (-2) == a.inverse() ** 2
def test_wrong_mod():
a = Mod(5, 7)
b = Mod(4, 11)
with pytest.raises(ValueError):
a + b
def test_wrong_pow():
a = Mod(5, 7)
c = Mod(4, 11)
with pytest.raises(TypeError):
a ** c
def test_other():
a = Mod(5, 7)
b = Mod(3, 7)
assert int(-a) == 2
assert str(a) == "5"
assert 6 - a == Mod(1, 7)
assert a != b
assert a / b == Mod(4, 7)
assert a // b == Mod(4, 7)
assert 5 / b == Mod(4, 7)
assert 5 // b == Mod(4, 7)
assert a / 3 == Mod(4, 7)
assert a // 3 == Mod(4, 7)
assert divmod(a, b) == (Mod(1, 7), Mod(2, 7))
assert a + b == Mod(1, 7)
assert 5 + b == Mod(1, 7)
assert a + 3 == Mod(1, 7)
assert a != 6
assert hash(a) is not None
def test_undefined():
u = Undefined()
for k, meth in u.__class__.__dict__.items():
if k in (
"__module__",
"__new__",
"__init__",
"__doc__",
"__hash__",
"__abstractmethods__",
"_abc_impl",
"__slots__",
"x",
"n"
):
continue
args = [5 for _ in range(meth.__code__.co_argcount - 1)]
if k == "__repr__":
assert meth(u) == "Undefined"
elif k in ("__eq__", "__ne__"):
assert not meth(u, *args)
else:
try:
res = meth(u, *args)
assert res == NotImplemented
except NotImplementedError:
pass
def test_implementation():
if not has_gmp:
pytest.skip("Only makes sense if more Mod implementations are available.")
with TemporaryConfig() as cfg:
cfg.ec.mod_implementation = "python"
assert isinstance(Mod(5, 7), RawMod)
def test_symbolic():
x = symbols("x")
p = 13
k = FF(p)
sx = SymbolicMod(x, p)
a = k(3)
b = k(5)
r = sx * a + b
assert isinstance(r, SymbolicMod)
assert r.n == p
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