  This paper shows that the Hirschfeld-Gebelein-R\'enyi maximal correlation
between the message and the ciphertext provides good secrecy guarantees for
cryptosystems that use short keys. We first establish a bound on the
eavesdropper's advantage in guessing functions of the message in terms of
maximal correlation and the R\'enyi entropy of the message. This result implies
that maximal correlation is stronger than the notion of entropic security
introduced by Russell and Wang. We then show that a small maximal correlation
$\rho$ can be achieved via a randomly generated cipher with key length
$\approx2\log(1/\rho)$, independent of the message length, and by a stream
cipher with key length $2\log(1/\rho)+\log n+2$ for a message of length $n$. We
establish a converse showing that these ciphers are close to optimal. This is
in contrast to entropic security for which there is a gap between the lower and
upper bounds. 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. Hence, maximal correlation is a stronger and more
practically relevant measure of secrecy than mutual information.
