Universal Encryption of Individual Sequences Under Maximal Leakage

2025-04-30

AI Summary

This paper investigates universal, model-free encryption of individual sequences under the maximal information leakage metric, focusing on the fundamental limits of finite-state encryptors. We propose a fully data-driven, assumption-free construction: cascading Lempel–Ziv adaptive compression with a one-time pad (OTP). For individual sequences, we derive the first tight upper and lower bounds on the maximal leakage rate and rigorously prove that our scheme asymptotically achieves the optimal leakage performance. Our key contributions are threefold: (1) establishing the minimum achievable maximal leakage rate for universal encryption; (2) providing the first explicit, implementable model-free construction attaining this fundamental limit; and (3) unifying individual-sequence information theory, finite-state machine modeling, and adaptive compression theory to establish a novel paradigm for secure encryption without statistical assumptions.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Study encryption of individual sequences under maximal leakage
• Derive bounds on leakage for finite-state encrypters
• Prove Lempel-Ziv plus one-time pad minimizes leakage asymptotically

Innovation

• Lempel-Ziv compression for data reduction
• One-time pad encryption for security
• Maximal leakage metric for evaluation