Maximal correlation secrecy

This paper shows that the maximal correlation between the message and the ciphertext provides good secrecy guarantees for ciphers with short keys. We show that a small maximal correlation ρ can be achieved via a randomly generated cipher with key length ≈ 2 log(1/ρ), independent of the message length, and by a stream cipher with key length ≈ 2 log(1/ρ)+log n for a message of length n. We provide a converse result showing that these ciphers are close to optimal. We then show that any cipher with a small maximal correlation achieves a variant of semantic security with computationally unbounded adversary, similar to entropic security proposed by Russell and Wang. Finally, we show that a small maximal correlation implies secrecy with respect to several mutual information based criteria but is not necessarily implied by them.