[Paper Review] Optimum Perfect Universal Steganography of Finite Memoryless Sources.

Félix Balado, David Haughton|arXiv (Cornell University)|Oct 10, 2014

Advanced Steganography and Watermarking Techniques3 citations

TL;DR

This paper proposes partitioned permutation coding as an optimal solution for perfect universal steganography in finite memoryless sources, achieving the maximum embedding rate under distortion constraints. It establishes a duality between steganography and lossless source coding by showing that adaptive arithmetic coding can implement optimal permutation coding, approaching the theoretical upper bound on the rate-distortion tradeoff.

ABSTRACT

Abstract—A theoretical analysis and a practical solution to the fundamental problem of optimum perfect universal steganog-raphy of finite memoryless sources with a passive warden are provided. The theoretical analysis rests on the fact that Slepian’s Variant I permutation coding implements first-order perfect universal steganography with maximum embedding rate. The practical solution underlines the duality between perfect steganography with optimum embedding rate and lossless source coding with optimum compression rate, since it is shown that permutation coding can be implemented by means of adaptive arithmetic coding. A distance constraint between host signal and information-carrying signal must be observed in universal steganography, and thus an optimum tradeoff between embed-ding rate and embedding distortion must be achieved. Partitioned permutation coding is shown to be the solution to this problem. A practical implementation of partitioned permutation coding is given that performs close to an unattainable upper bound on the rate-distortion function of the problem. Index Terms—Steganography, source coding, permutation cod-ing, arithmetic coding, rate-distortion. I.

Motivation & Objective

• To solve the fundamental problem of optimum perfect universal steganography for finite memoryless sources under a passive warden.
• To establish a theoretical foundation for maximum embedding rate in steganography using Slepian’s Variant I permutation coding.
• To bridge the gap between steganography and lossless source coding by demonstrating a duality between optimum embedding rate and optimum compression rate.
• To design a practical implementation that achieves near-optimal performance under distortion constraints.
• To derive and analyze the rate-distortion tradeoff in universal steganography, particularly under distance constraints between host and stego signals.

Proposed method

• Utilizes Slepian’s Variant I permutation coding as the theoretical basis for first-order perfect universal steganography with maximum embedding rate.
• Establishes a duality between perfect steganography with optimum embedding rate and lossless source coding with optimum compression rate.
• Employs adaptive arithmetic coding as a practical implementation mechanism for permutation coding, enabling efficient and universal steganographic encoding.
• Introduces partitioned permutation coding to manage the tradeoff between embedding rate and embedding distortion under a distance constraint.
• Analyzes the rate-distortion function of the steganographic system and derives an upper bound on performance.
• Demonstrates that the proposed practical implementation of partitioned permutation coding performs close to the unattainable theoretical upper bound.

Experimental results

Research questions

• RQ1 What is the maximum achievable embedding rate in perfect universal steganography for finite memoryless sources under a distortion constraint?
• RQ2 How can a duality between steganography and lossless source coding be formally established and exploited for optimal design?
• RQ3 Can permutation coding be practically implemented using adaptive arithmetic coding while preserving optimality?
• RQ4 What coding strategy achieves the optimal tradeoff between embedding rate and embedding distortion in universal steganography?
• RQ5 How close can a practical steganographic system come to the theoretical upper bound on the rate-distortion function?

Key findings

• Slepian’s Variant I permutation coding achieves first-order perfect universal steganography with the maximum possible embedding rate.
• A duality exists between optimum perfect steganography and optimum lossless source coding, enabling the use of adaptive arithmetic coding for practical implementation.
• Partitioned permutation coding is proven to be the optimal solution for balancing embedding rate and embedding distortion under distance constraints.
• The proposed practical implementation of partitioned permutation coding performs very close to the theoretical upper bound on the rate-distortion function.
• The rate-distortion function of the steganographic system is bounded, and the proposed method approaches this bound asymptotically.
• Adaptive arithmetic coding effectively realizes the theoretical performance of permutation coding in a universal and efficient manner.