def test_paper_check(self):
t12_11_3 = ClassGroup(12, 11, 3)
t93_109_32 = ClassGroup(93, 109, 32)
self.assertEqual(t12_11_3.discriminant(), -23)
self.assertEqual(t93_109_32.discriminant(), -23)
t = t12_11_3 * t93_109_32
self.assertEqual(t, ClassGroup(1, -15, 62))
self.assertEqual(t.discriminant(), -23)
t1 = t93_109_32 * t12_11_3
self.assertEqual(t, t1)
# the normalize and reduce example from the paper
f = ClassGroup(195751, 1212121, 1876411)
self.assertEqual(f.normalized(), (195751, 37615, 1807))
self.assertEqual(f.reduced(), (1, 1, 1))
def compute_order(g: ClassGroup) -> int:
d = g.discriminant()
quadRoot = int((-d)**0.25)
size = quadRoot
order = 0
while order == 0:
babylist = list(
accumulate(repeat(g, quadRoot - 1), ClassGroup.multiply))
babyset = set(babylist)
gSqrt = (g**quadRoot).normalized()
bigStep = gSqrt
result = next(
filter(
lambda giant: giant[1] in babyset,
accumulate(repeat((1, bigStep), size), lambda old, new:
(old[0] + new[0], old[1] * new[1]))), None)
if result is not None:
order = (result[0] * quadRoot - babylist.index(result[1]) - 1)
return order
size *= 2
def judge_entry(mystr):
assert len(mystr) < 100000
lines = mystr.strip().split(b'\n')
assert len(lines) == 3
ds = set()
for line in lines:
# File format:
# challenge(in hex) length a b c order
vals = [x.strip() for x in line.strip().split(b' ')]
assert len(vals) == 6
length = int(vals[1])
assert length < 5000
assert all(len(x) < length for x in vals[2:])
assert len(vals[0]) <= 32
d = create_discriminant(a2b_hex(vals[0]), length)
g = ClassGroup(int(vals[2]), int(vals[3]), int(vals[4]))
assert g.discriminant() == d
assert g != g.identity()
order = int(vals[5])
assert order > 1
assert g**order == g.identity()
assert d not in ds
ds.add(d)
return -max(ds)
def test_bad_multiply(self):
n1 = ClassGroup(2243390248, -565721959, 35664920)
n2 = ClassGroup(2, 1, 370)
n = n1 * n2
self.assertEqual(n.discriminant(), n1.discriminant())
self.assertEqual(n.discriminant(), n2.discriminant())