Universal Encryption of Individual Sequences Under Maximal Leakage

TL;DR

This paper studies secure encryption of deterministic, individual sequences under the maximal leakage metric. It derives a converse bound (Theorem 1) tying the per-symbol leakage to the LZ78 complexity of the plaintext and the finite-state encrypter’s key-rate, and shows that the bound is asymptotically tight via an achievability scheme based on LZ78 compression followed by one-time pad encryption, culminating in Theorem 2 which yields a universal encrypter with near-optimal leakage performance. The results collectively demonstrate that, in the single-sequence setting, compress-then-OTP encryption using LZ complexity is asymptotically optimal for minimizing information leakage, extending prior work on perfect secrecy and finite-state encryptability. The work provides a rigorous connection between empirical compression complexity and secure encryption in a worst-case, distribution-free framework, with potential extensions to lossy, side-information, and broader FSM models.

Abstract

We consider the Shannon cipher system in the framework of individual sequences and finite-state encrypters under the metric of maximal leakage of information. A lower bound and an asymptotically matching upper bound on the leakage are derived, which lead to the conclusion that asymptotically minimum leakage can be attained by Lempel-Ziv compression followed by one-time pad encryption of the compressed bit-stream.