Perfectly Secure Steganography Using Minimum Entropy Coupling
This work addresses the challenge of secure and efficient hidden communication for security and machine learning applications, offering a novel theoretical framework with practical implications.
The paper tackles the problem of achieving perfectly secure steganography for arbitrary covertext distributions by proving that perfect security is equivalent to using a coupling, and that maximum information throughput requires a minimum entropy coupling, leading to the first algorithms with such guarantees and demonstrating superior encoding efficiency compared to modern baselines in experiments with GPT-2, WaveRNN, and Image Transformer.
Steganography is the practice of encoding secret information into innocuous content in such a manner that an adversarial third party would not realize that there is hidden meaning. While this problem has classically been studied in security literature, recent advances in generative models have led to a shared interest among security and machine learning researchers in developing scalable steganography techniques. In this work, we show that a steganography procedure is perfectly secure under Cachin (1998)'s information-theoretic model of steganography if and only if it is induced by a coupling. Furthermore, we show that, among perfectly secure procedures, a procedure maximizes information throughput if and only if it is induced by a minimum entropy coupling. These insights yield what are, to the best of our knowledge, the first steganography algorithms to achieve perfect security guarantees for arbitrary covertext distributions. To provide empirical validation, we compare a minimum entropy coupling-based approach to three modern baselines -- arithmetic coding, Meteor, and adaptive dynamic grouping -- using GPT-2, WaveRNN, and Image Transformer as communication channels. We find that the minimum entropy coupling-based approach achieves superior encoding efficiency, despite its stronger security constraints. In aggregate, these results suggest that it may be natural to view information-theoretic steganography through the lens of minimum entropy coupling.