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Publication

Permutation Codes and Steganography

2013-05-26, Balado, Félix, Haughton, David

We show that Slepian’s Variant I permutation codes implement first-order perfect steganography (i.e., histogram-preserving steganography). We give theoretical expressions for the embedding distortion, embedding rate and embedding efficiency of permutation codes in steganography, which demonstrate that these codes conform to prior analyses of the properties of capacity-achieving perfect stegosystems with a passive warden. We also propose a modification of adaptive arithmetic coding that near optimally implements permutation coding with a low complexity, confirming all our theoretical predictions. Finally we discuss how to control the embedding distortion. Permutation coding turns out to be akin to Sallee’s model-based steganography, and to supersede both this method and LSB matching.

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Publication

Asymptotically Optimum Perfect Universal Steganography of Finite Memoryless Sources

2018-02, Balado, Félix, Haughton, David

A solution to the problem of asymptotically optimum perfect universal steganography of finite memoryless sources with a passive warden is provided, which is then extended to contemplate a distortion constraint. The solution rests on the fact that Slepian’s Variant I permutation coding implements firstorder perfect universal steganography of finite host signals with optimum embedding rate. The duality between perfect universal steganography with asymptotically optimum embedding rate and lossless universal source coding with asymptotically optimum compression rate is evinced in practice by showing that permutation coding can be implemented by means of adaptive arithmetic coding. Next, a distortion constraint between the host signal and the information-carrying signal is considered. Such a constraint is essential whenever real-world host signals with memory (e.g., images, audio, or video) are decorrelated to conform to the memoryless assumption. The constrained version of the problem requires trading off embedding rate and distortion. Partitioned permutation coding is shown to be a practical way to implement this trade-off, performing close to an unattainable upper bound on the rate-distortion function of the problem.