def test_random(self):
# Randomized tests
for _ in range(0, 10):
alpha = [FQ.random() for _ in range(0, 4)]
points = [(FQ(i), shamirs_poly(FQ(i), alpha))
for i in range(0, len(alpha))]
assert alpha[0] == lagrange(points, 0)
assert alpha[0] != lagrange(points[1:], 0)
assert alpha[0] != lagrange(points[2:], 0)
def test_random_small(self):
q = 100003
for _ in range(0, 10):
alpha = [FQ.random(q) for _ in range(0, 4)]
points = [(FQ(i, q), shamirs_poly(FQ(i, q), alpha))
for i in range(0, len(alpha))]
assert alpha[0] == lagrange(points, 0)
assert alpha[0] != lagrange(points[1:], 0)
assert alpha[0] != lagrange(points[2:], 0)
# XXX: scipy's lagrange has floating point precision for large numbers
points_x, points_y = unzip(points)
interpolation = scipy_lagrange([_.n for _ in points_x], [_.n for _ in points_y])
assert int(interpolation.c[-1]) == alpha[0]
def test_static(self):
# Verify against static test vectors
alpha = [
6808181831819141657160280673506432691407806061837762993142662373500430825792,
4138536697521448323155976179625860582331141320072618244300034508091478437877,
20259243729221075783953642258755031830946498253783650311586175820530608751936,
11227115470523445882235139084890542822660569362938710556861479160600812964997
]
points = [(i, shamirs_poly(i, alpha)) for i in range(0, len(alpha))]
test_points = [
(0,
6808181831819141657160280673506432691407806061837762993142662373500430825792
),
(1,
20544834857245836424258632451520592838797650598216707762192147676147522484985
),
(2,
10833210933219706719196668784844423052753721417299010433393634464005858464330
),
(3,
1259517139202877390892412692306630092142705895884865660519589327528699562575
)
]
assert points == test_points
assert alpha[0] == lagrange(points, 0)