Abstract
Most practical stegosystems for digital media work by applying a mutually independent embedding operation to each element of the cover. For such stegosystems, the Fisher information w.r.t. the change rate is a perfect security descriptor equivalent to KL divergence between cover and stego images. Under the assumption of Markov covers, we derive a closed-form expression for the Fisher information and show how it can be used for comparing stegosystems and optimizing their performance. In particular, using an analytic cover model fit to experimental data obtained from a large number of natural images, we prove that the ±1 embedding operation is asymptotically optimal among all mutually independent embedding operations that modify cover elements by at most 1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wang, Y., Moulin, P.: Perfectly secure steganography: Capacity, error exponents, and code constructions. IEEE Transactions on Information Theory, Special Issue on Security (June 2008)
Comesana, P., Pérez-Gonzáles, F.: On the capacity of stegosystems. In: Dittmann, J., Fridrich, J. (eds.) Proceedings of the 9th ACM Multimedia & Security Workshop, Dallas, TX, September 20-21, pp. 3–14 (2007)
Harmsen, J.J., Pearlman, W.A.: Capacity of steganographic channels. Submitted to IEEE Transactions on Information Theory (2008), http://arxiv.org/abs/0810.4171
Filler, T., Fridrich, J., Ker, A.D.: The square root law of steganographic capacity for Markov covers. In: Delp, E.J., Wong, P.W., Memon, N., Dittmann, J. (eds.) Proceedings SPIE, Electronic Imaging, Security and Forensics of Multimedia XI, San Jose, CA, January 18-21 (2009)
Ker, A.D., Pevný, T., Kodovský, J., Fridrich, J.: The square root law of steganographic capacity. In: Ker, A., Dittmann, J., Fridrich, J. (eds.) Proceedings of the 10th ACM Multimedia & Security Workshop, Oxford, UK, September 22-23, pp. 107–116 (2008)
Ker, A.D.: A capacity result for batch steganography. IEEE Signal Processing Letters 14(8), 525–528 (2007)
Filler, T., Fridrich, J.: Complete characterization of perfectly secure stego-systems with mutually independent embedding operation. In: Proceedings IEEE, International Conference on Acoustics, Speech, and Signal Processing, Taipei, Taiwan, April 19-24 (2009)
Ker, A.D.: Estimating steganographic Fisher information in real images. In: Katzenbeisser, S., Sadeghi, A.-R. (eds.) IH 2009. LNCS, vol. 5806, pp. 73–88. Springer, Heidelberg (2009)
Kodovský, J., Fridrich, J., Pevný, T.: Statistically undetectable JPEG steganography: Dead ends, challenges, and opportunities. In: Dittmann, J., Fridrich, J. (eds.) Proceedings of the 9th ACM Multimedia & Security Workshop, Dallas, TX, September 20-21, pp. 3–14 (2007)
Doob, J.L.: Stochastic processes, 1st edn. Wiley, New York (1953)
Sullivan, K., Madhow, U., Manjunath, B., Chandrasekaran, S.: Steganalysis for Markov cover data with applications to images. IEEE Transactions on Information Forensics and Security 1(2), 275–287 (2006)
Sidorov, M.: Hidden Markov models and steganalysis. In: Dittmann, J., Fridrich, J. (eds.) Proceedings of the 6th ACM Multimedia & Security Workshop, Magdeburg, Germany, September 20-21, pp. 63–67 (2004)
Cachin, C.: An information-theoretic model for steganography. In: Aucsmith, D. (ed.) IH 1998. LNCS, vol. 1525, pp. 306–318. Springer, Heidelberg (1998)
Ker, A.D.: The ultimate steganalysis benchmark? In: Dittmann, J., Fridrich, J. (eds.) Proceedings of the 9th ACM Multimedia & Security Workshop, Dallas, TX, September 20-21, pp. 141–148 (2007)
Kay, S.M.: Fundamentals of Statistical Signal Processing, Detection Theory, vol. II. Prentice-Hall, Englewood Cliffs (1998)
Filler, T.: Important properties of normalized KL-divergence under HMC model. Technical report, DDE Lab, SUNY Binghamton (2008), http://dde.binghamton.edu/filler/kl-divergence-hmc.pdf
Fridrich, J., Goljan, M.: Digital image steganography using stochastic modulation. In: Delp, E.J., Wong, P.W. (eds.) Proceedings SPIE, Electronic Imaging, Security, Steganography, and Watermarking of Multimedia Contents V, Santa Clara, CA, January 21-24, vol. 5020, pp. 191–202 (2003)
Goljan, M., Fridrich, J., Holotyak, T.: New blind steganalysis and its implications. In: Delp, E.J., Wong, P.W. (eds.) Proceedings SPIE, Electronic Imaging, Security, Steganography, and Watermarking of Multimedia Contents VIII, San Jose, CA, January 16-19, vol. 6072, pp. 1–13 (2006)
Filler, T.: Fisher information determines capacity of ε-secure steganography - proofs. Technical report, SUNY Binghamton (2009), http://dde.binghamton.edu/filler/pdf/Fill09ihwproofs.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Filler, T., Fridrich, J. (2009). Fisher Information Determines Capacity of ε-Secure Steganography. In: Katzenbeisser, S., Sadeghi, AR. (eds) Information Hiding. IH 2009. Lecture Notes in Computer Science, vol 5806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04431-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-04431-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04430-4
Online ISBN: 978-3-642-04431-1
eBook Packages: Computer ScienceComputer Science (R0)