def server(ID, Y, SS, U, V):
P = H(ID)
y = big.from_bytes(Y)
Q = ecp2.generator()
P = y * P
sQ = ECp2()
if not sQ.fromBytes(SS):
return (False, Fp12(), Fp12())
TU = ECp()
if not TU.fromBytes(U):
return (False, bytearray(0), bytearray(0))
TV = ECp()
if not TV.fromBytes(V):
return (False, bytearray(0), bytearray(0))
TU.add(P)
# TU.affine()
r = pair.double_ate(Q, TV, sQ, TU)
r = pair.fexp(r)
if r.isone():
return (True, bytearray(0), bytearray(0))
# failed - diagnose it
E = r.toBytes()
r = pair.e(Q, TU)
F = r.toBytes()
return (False, E, F)
def extract_pin(ID, PIN, SK):
P = H(ID)
P = -(PIN * P)
S = ECp()
if not S.fromBytes(SK):
return bytearray(0)
S.add(P)
# S.affine()
return S.toBytes(False)
def add_G1(A, B):
""" Add two points in G1: C = A + B """
A1 = ECp()
B1 = ECp()
if not A1.fromBytes(A):
return None
if not B1.fromBytes(B):
return None
A1.add(B1)
return A1.toBytes(False)
def client_2(X, Y, ID, PIN, TK):
P = H(ID)
S = ECp()
if not S.fromBytes(TK):
return bytearray(0)
x = big.from_bytes(X)
y = big.from_bytes(Y)
x = (x + y) % curve.r
x = curve.r - x
S.add(PIN * P)
S = x * S
return S.toBytes(False)