Entropically secure encryption with faster key expansion

TL;DR

This paper introduces a faster key expansion method for entropically secure encryption that maintains security, especially benefiting scenarios with large message sizes and quantum state randomization.

Contribution

A novel, faster key expansion technique for entropically secure encryption that preserves security guarantees in classical and quantum contexts.

Findings

Achieves the same security as existing methods

Doubles the speed of key expansion in certain cases

Improves approximate quantum state randomization efficiency

Abstract

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.