def differential(P, Q):
"""Polynomial differential operator
Parameters
----------
P : Poly
Polynomial to be differentiated.
Q : Poly
Polynomial to differentiate by. Must be decomposed. If
polynomial array, the output is the Jacobian matrix.
"""
P, Q = Poly(P), Poly(Q)
if not is_decomposed(Q):
differential(decompose(Q)).sum(0)
if Q.shape:
return Poly([differential(P, q) for q in Q])
if Q.dim > P.dim:
P = setdim(P, Q.dim)
else:
Q = setdim(Q, P.dim)
qkey = Q.keys[0]
A = {}
for key in P.keys:
newkey = np.array(key) - np.array(qkey)
if np.any(newkey < 0):
continue
A[tuple(newkey)] = P.A[key]*np.prod([fac(key[i], \
exact=True)/fac(newkey[i], exact=True) \
for i in xrange(P.dim)])
return Poly(A, P.dim, None)
def differential(P, Q):
"""Polynomial differential operator
Parameters
----------
P : Poly
Polynomial to be differentiated.
Q : Poly
Polynomial to differentiate by. Must be decomposed. If
polynomial array, the output is the Jacobian matrix.
"""
P, Q = Poly(P), Poly(Q)
if not is_decomposed(Q):
differential(decompose(Q)).sum(0)
if Q.shape:
return Poly([differential(P, q) for q in Q])
if Q.dim > P.dim:
P = setdim(P, Q.dim)
else:
Q = setdim(Q, P.dim)
qkey = Q.keys[0]
A = {}
for key in P.keys:
newkey = np.array(key) - np.array(qkey)
if np.any(newkey < 0):
continue
A[tuple(newkey)] = P.A[key] * np.prod(
[fac(key[i], exact=True) / fac(newkey[i], exact=True) for i in xrange(P.dim)]
)
return Poly(A, P.dim, None)
server = WLSK_S.init()
with socket.socket() as sock:
sock.bind((my_addr, SERVER_PORT))
sock.listen(1)
print('Listening on \x1b[1m{}\x1b[0m:{} as a {}'.format(my_addr, SERVER_PORT, SERVER))
while True:
print('\nAwaiting connection...')
conn, addr = sock.accept()
print('Received connection from {0[0]}:{0[1]}'.format(addr))
data = conn.recv(BUFFER_SIZE)
(idA_, idB_, iv2, e_, m_) = base.decompose(data)
delay()
print('Received secrets from {}'.format(RESPONDER))
debug("idA' = {}\nidB' = {}\ne' = {}\nm' = {}".format(idA_, idB_, iv2, e_, m_))
(_, iv3, e__, m__) = server(idA_, idB_, iv2, e_, m_)
delay()
print('Sending secrets...')
debug("e'' = {}\nm'' = {}".format(e__, m__))
conn.send(base.compose([iv3, e__, m__]))
conn.close()
delay()
print('\x1b[32mSession finished\x1b[0m')
print('Received connection from {0[0]}:{0[1]}'.format(addr))
idA = conn.recv(BUFFER_SIZE)
print("{}'s identity is {}".format(INITIATOR, idA))
delay()
print('Generating nonce...')
delay()
(b4, n) = responder(idA)
debug('n = {}'.format(n))
conn.send(n)
data = conn.recv(BUFFER_SIZE)
conn.close()
(iv1, e, m) = base.decompose(data)
print('Received secrets from {}'.format(INITIATOR))
debug('e = {}\nm = {}'.format(e, m))
(b6, idA_, idB_, iv2, e_, m_) = b4(iv1, e, m)
print('Connecting to the {}...'.format(SERVER))
delay()
with socket.create_connection((server_addr, SERVER_PORT)) as ssock:
print('Sending encrypted data...')
debug("idA' = {}\nidB' = {}\ne' = {}\nm' = {}".format(idA_, idB_, iv2, e_, m_))
delay()
ssock.send(base.compose([idA_, idB_, iv2, e_, m_]))
data = ssock.recv(BUFFER_SIZE)