In Paillier cryptoststem many ciphertexts can correspond to the same plaintext. How can I modify the scheme so to make the correspondence between ciphertexts and plaintexts a one to one correspondece? I've already eliminated the randomness from the scheme (i.e. all encryptions are done with the same $r$).
My reason for this is that I want to compute the arithmetic mean of two encrypted numbers by repeatedly subtracting 2 (which I can do no-problem) until I hit 0 which I then need to detect.