def random_polynomial(degree):
"""
Returns a random polynomial of a prescribed degree which is NOT the zero polynomial.
"""
leading = FieldElement.random_element(
exclude_elements=[FieldElement.zero()])
p = [FieldElement.random_element() for i in range(degree)] + [leading]
return Polynomial(p)
def test_compose():
for _ in range(10):
outer_poly = random_polynomial(randint(0, 1024))
inner_poly = random_polynomial(randint(0, 16))
# Validate the evaluation of the composition poly outer_poly(inner_poly) on a random point.
point_to_eval = FieldElement.random_element()
assert ((outer_poly.compose(inner_poly)
).eval(point_to_eval) == outer_poly.eval(
inner_poly.eval(point_to_eval)))
def test_poly_interpolation():
for _ in range(10):
# Generate a random polynomial.
degree = randint(0, 100)
p = random_polynomial(degree)
# Evaluate it on a number of points that is at least its degree.
x_vals = set()
while len(x_vals) < degree + 1:
x_vals.add(FieldElement.random_element())
x_vals = list(x_vals)
y_vals = [p.eval(x) for x in x_vals]
# Obtain a polynomial from the evaluation.
interpolated_p = interpolate_poly(x_vals, y_vals)
# Check equality.
assert p == interpolated_p
def test_merkle_get_authentication_path():
for _ in range(10):
data_length = randint(0, 2000)
data = [FieldElement.random_element() for _ in range(data_length)]
m = MerkleTree(data)
leaf_id = randint(0, data_length - 1)
decommitment = m.get_authentication_path(leaf_id)
# Check a correct decommitment.
content = data[leaf_id]
assert verify_decommitment(leaf_id, content, decommitment, m.root)
# Check that altering the decommitment causes verification to fail.
altered = decommitment[:]
random_index = randint(0, len(altered) - 1)
altered[random_index] = sha256(
altered[random_index].encode()).hexdigest()
assert not verify_decommitment(leaf_id, content, altered, m.root)
# Check that altering the content causes verification to fail.
other_content = data[randint(0, data_length - 1)]
assert not verify_decommitment(leaf_id, other_content, decommitment,
m.root) or other_content == content
def test_field_div():
for _ in range(100):
t = FieldElement.random_element(exclude_elements=[FieldElement.zero()])
t_inv = FieldElement.one() / t
assert t_inv == t.inverse()
assert t_inv * t == FieldElement.one()
