task.py

from secrets import SECRET, PRIVATE, FLAG
import hashlib
import SocketServer

PORT = 1337

G = 0xe6a5905121b0fd7661e2eb06db9a4d96799165478a0b2baf09836c59ccf4f086bc2a55191ee4bf8b2324f6f53294da244342aba000f7b915861ba2167d09c5569910ae80990c3c79040879d8e16e48219127718d9ff05f71a905041564e9bcb55417b39cdb0b7afc6863ccd10b90ee42f856840e0dd5f8602e49592b58a22d39
P = 0xf2a4ca87978e05b112ef4a16b547c5036cd51fadac0cf967c152e56378c792a45e76e0ebfd62b2b23e94ca3727fbe1ebb308211cf8938c8a735db2de4cd26f0beb53b51fc2a5474bd0d466fc54fce13a4ec2b9840800ecdf337c55105c9b7d702b7f2d20bb3cba16a5948a208f8886ab2eddd1284a5b8ec457bf696be4bbb51b
Q = 0x9821a36da85bf3bcfb379d7cc39f5b6db7a553d5
PUBLIC = 0x5596b39949bab7979f8a679c11daad86ed59394ff4956769ec036d579ae6f80cd99bd12c442e10ee6aceed275739cb07417842d28d45f82b7a64d506c6f50f95622491a07c834260d64eb75bdaccdfdcf8ca4584f0c300403a4bed1ca515854b97732c8638118f71720c054f15d441f784a8c7b0c1a41dd07eb9acaaa7a7126e

def h(x):
  return int(hashlib.md5(x).hexdigest(), 16)

def egcd(a, b):
  if a == 0:
    return (b, 0, 1)
  else:
    g, y, x = egcd(b % a, a)
    return (g, x - (b // a) * y, y)

def modinv(a, m):
  g, x, y = egcd(a, m)
  if g != 1:
    raise Exception('modular inverse does not exist')
  else:
    return x % m

def makeMsg(name, n):
  return 'MSG = {n: ' + n + ', name: ' + name + '}'

def makeK(name, n):
  return 'K = {n: ' + n + ', name: ' + name + ', secret: ' + SECRET + '}'

def sign(name, n):
  k = h(makeK(name, n))
  print k
  r = pow(G, k, P) % Q
  s = (modinv(k, Q) * (h(makeMsg(name, n)) + PRIVATE * r)) % Q
  return (r*Q + s)

def verify(name, n, sig):
  r = sig / Q
  s = sig % Q
  if r < 0 or s < 0 or r > Q:
    return False
  w = modinv(s, Q)
  u1 = (h(makeMsg(name, n)) * w) % Q
  u2 = (r * w) % Q
  v = ((pow(G, u1, P) * pow(PUBLIC, u2, P)) % P) % Q
  return r == v

def register(name, n):
  if name == 'admin':
    return 'admin name not allowed'
  if len(name) > 5:
    return 'name too long'
  return str(pow(sign(name, n), 65537, int(n.encode('hex'), 16)))

def login(name, n, sig):
  if not verify(name, n, int(sig.encode('hex'), 16)):
    return 'failed to verify'
  if name == 'admin':
    return FLAG
  else:
    return 'Hello ' + name

def process(data):
  [fun, params] = data.split(':')
  if fun == 'register':
    [name, n] = [x.decode('base64') for x in params.split(',')]
    return register(name, n)
  elif fun == 'login':
    [name, n, sig] = [x.decode('base64') for x in params.split(',')]
    return login(name, n, sig)
  else:
    return 'bad function'

class ThreadedTCPRequestHandler(SocketServer.BaseRequestHandler):
  def handle(self):
    data = self.request.recv(1024)
    try:
      ret = process(data)
    except:
      ret = 'Error'
    self.request.sendall(ret + '\n') 

class ThreadedTCPServer(SocketServer.ThreadingMixIn, SocketServer.TCPServer):
  pass

if __name__ == '__main__':
  server = ThreadedTCPServer(('0.0.0.0', PORT), ThreadedTCPRequestHandler)
  server.allow_reuse_address = True
  server.serve_forever()