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_fromdocs2(self):
p = 100003
k = 4
a = [randn(p) for _ in range(0, k)] # [6257, 85026, 44499, 14701]
F = lambda i, x: a[i] * (x**i)
X = lambda x: a[0] + F(1, x) + F(2, x) + F(3, x)
# Create the shares
Sx = range(1, 5)
Sy = [X(_) for _ in Sx]
for x, y in zip(Sx, Sy):
z = shamirs_poly_n(x, a, p)
assert z == y % p
# Then recover secret
assert a[0] == int(scipy_lagrange(Sx, Sy).c[-1])
def test_fromdocs2(self):
p = 100003
k = 4
a = [FQ.random(p) for _ in range(0, k)] # [6257, 85026, 44499, 14701]
F = lambda i, x: a[i] * (x**i)
X = lambda x: a[0] + F(1, x) + F(2, x) + F(3, x)
# Create the shares
Sx = range(1, 5)
Sy = [X(_) for _ in Sx]
for x, y in zip(Sx, Sy):
z = shamirs_poly(FQ(x, p), a)
assert z == y
# Then recover secret
result = int(scipy_lagrange(Sx, [_.n for _ in Sy]).c[-1]) % p
assert a[0] == result