def decode_point(bs, T):
"""
Decode a string encoded version of a Point into a Point.
"""
if not bs:
raise error("can't decode a blank Point")
if bord(bs[0]) == 0:
return INFINITY
elif bord(bs[0]) == 4: # uncompressed point
if len(bs) % 2 == 0: # should be two even strings, plus 1 byte
raise error('wrong length for uncompressed point')
length = (len(bs) - 1) // 2 + 1
x = number.bytes_to_long(bs[1:length])
y = number.bytes_to_long(bs[length:])
else:
x = number.bytes_to_long(bs[1:])
y_prime = (bord(bs[0]) == 3)
alpha = (x ** 3 + T.a * x + T.b) % T.p
beta = number.sqrt(alpha, T.p)
if beta % 2 == y_prime:
y = beta
else:
y = T.p - beta
p = Point(x, y, T)
if not p.verify():
raise error("decoded an invalid point")
return p
def test_sqrt(self):
self.assertEqual(number.sqrt(83, 673), 140)