  Entropically secure encryption is a way to encrypt a large plaintext with a
small key and still have information-theoretic security, thus in a certain
sense circumventing Shannon's result that perfect encryption requires the key
to be at least as long as the entropy of the plaintext. Entropically secure
encryption is not perfect, and it works only if a lower bound is known on the
entropy of the plaintext. The typical implementation is to expand the short key
to the size of the plaintext, e.g. by multiplication with a public random
string, and then use one-time pad encryption. This works in the classical as
well as the quantum setting. In this paper, we introduce a new key expansion
method that is faster than existing ones. We prove that it achieves the same
security. The speed gain is most notable when the key length is a sizeable
fraction of the message length. In particular, a factor of 2 is gained in the
case of approximate randomization of quantum states.
