Applying Trapdoor Function directly to plaintext Suppose we have a secure trapdoor function defined on (G, F, F^-1) where G is a randomized algorithm outputs a key pair (pk, sk). Why would this trapdoor function become insecure if we apply F directly to plaintext message?
E(pk,m) = c = F(pk, m)
An eavesdropper could easily test any candidate message to determine

whether or that candidate message was the plaintext message.

def test_candidate_message_(pk,c,candidate):
 if c == F(pk,candidate):
  return True
 else:
  return False