def test_value() -> None:
grp = ZqGroup(mpz(53))
assert grp(10) + grp(20) == grp(30)
assert 20 + grp(10) == grp(30)
assert grp(40) + grp(50) == grp(37)
assert grp(40) + 50 == grp(37)
assert ZqGroup(mpz(53))(20) != grp(20)
with pytest.raises(TypeError, match="Group mismatch"):
grp(10) + ZqGroup(mpz(53))(10)
with pytest.raises(TypeError):
grp(10) + cast(int, "twenty")
assert -grp(10) == grp(43)
assert grp(10) * grp(22) == grp(8)
assert 22 * grp(10) == grp(8)
with pytest.raises(TypeError, match="Group mismatch"):
grp(10) * ZqGroup(mpz(53))(10)
with pytest.raises(TypeError):
grp(10) * cast(int, "twentytwo")
# 1 = 16 * 10 - 3 * 53
assert 16 == grp(10).inv
assert repr(grp(10)) == "ZqGroup(53)(10)"
assert grp(10).asn1.dump() == b"\x02\x01\x0a"
def test_init() -> None:
with pytest.raises(ValueError, match="q is negative"):
ZqGroup(mpz(-13))
with pytest.raises(ValueError, match="q not prime"):
ZqGroup(mpz(12))
with pytest.raises(ValueError, match=r"2q \+ 1 not prime"):
ZqGroup(mpz(13))
def test_value_pow() -> None:
grp = QrGroup(mpz(23))
assert grp(13) ** -1 == grp(16)
assert grp(13) ** ZqGroup(mpz(11))(5) == grp(4)
assert ((grp(13) ** Fraction(3, 4)) ** Fraction(4, 1)) ** Fraction(1, 3) == grp(13)
with pytest.raises(TypeError, match="incompatible groups"):
grp(13) ** ZqGroup(mpz(29))(16)
with pytest.raises(Exception, match="Modulo not supported"):
pow(cast(int, grp(13)), -1, 123)
with pytest.raises(TypeError):
grp(13) ** cast(int, "two")
def test_call() -> None:
grp = ZqGroup(mpz(53))
assert grp(20) == 20
assert grp(200) == 41
assert grp(PreGroupValue(20)) == 20
with pytest.raises(ValueError, match="Not a valid group element"):
grp(PreGroupValue(200))
with pytest.raises(TypeError):
grp(cast(int, "twenty"))
def test_poly() -> None:
grp = ZqGroup(mpz(11))
# p(x) = 2 + 7x + 0x² + 1x³
p = Poly([grp(2), grp(7), grp(0), grp(1)], grp(0))
assert len(p) == 4
assert p[0] == grp(2)
assert p[2] == grp(0)
assert p(5) == grp(2 + 35 + 0 + 125)
assert repr(
p
) == "Poly([ZqGroup(11)(2), ZqGroup(11)(7), ZqGroup(11)(0), ZqGroup(11)(1)])"
def test_repr() -> None:
assert repr(ZqGroup(mpz(53))) == "ZqGroup(53)"
def test_rand_nonzero() -> None:
tmp = {int(ZqGroup(mpz(2)).rand_nonzero) for __ in range(100)}
assert tmp == {1}
def test_rand() -> None:
tmp = {int(ZqGroup(mpz(2)).rand) for __ in range(100)}
assert 0 <= min(tmp) <= max(tmp) <= 1
def test_len() -> None:
assert ZqGroup(mpz(53)).len == 53