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A game-theoretic method for designing distortion function in spatial steganography

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Abstract

Most modern secure image steganographic schemes define distortion functions for constraining the embedding changes to those parts of the image that are difficult to model such as textured or noisy regions. However, thus arguments disregard Kerckhoffs’ principle: the warden also knows the adaptivity criterion as well and may be able reproduce or estimate it. This paper proposes a new idea that the embedding distortion is designed based on game theory. We present a two-player zero-sum game between steganographer and attacker related to the security of practical steganography, and there exists a unique mixed strategy Nash equilibrium. The distortion function is first achieved from the original method S-UNIWARD (Spatial-UNIversal Wavelet Relative Distortion), and then we readjust the distortion function according to the above Nash equilibrium. The new distortion not only ensures the embedding changes focus on textured region but also correlates to the Kerckhoffs’ principle. Experiment results show that the statistical security of the proposed method is improved by approximately 6.2 % with the features of modern rich models.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 61379152, No. 61402162), Hunan Provincial Natural Science Foundation of China (Grant No. 14JJ7024), and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130161120004).

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Authors and Affiliations

  1. Key Laboratory of Cryptography & Information Security under the Chinese People’s Armed Police Force, Electronic Department, Engineering University of the Chinese People’s Armed Police Force, Xi’an, 710086, China

    Jun Li, Xiaoyuan Yang & Minqing Zhang

  2. College of Computer Science and Electronic Engineering, Hunan University, Changsha, 410082, China

    Xin Liao

  3. Institution of Network & Information Security under Engineering University of the Chinese People’s Armed Police Force, Xi’an, 710086, China

    Jun Li & Feng Pan

  4. Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Xin Liao

Authors
  1. Jun Li
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  2. Xiaoyuan Yang
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  3. Xin Liao
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  4. Feng Pan
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  5. Minqing Zhang
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Correspondence to Jun Li or Xin Liao.

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Li, J., Yang, X., Liao, X. et al. A game-theoretic method for designing distortion function in spatial steganography. Multimed Tools Appl 76, 12417–12431 (2017). https://doi.org/10.1007/s11042-016-3632-7

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  • DOI: https://doi.org/10.1007/s11042-016-3632-7

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