Fisher Information Determines Capacity of ε-Secure Steganography

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.

[1]  J. Doob.  Stochastic processes , 1953 .

[2]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[3]  Christian Cachin,et al.  An information-theoretic model for steganography , 1998, Inf. Comput..

[4]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[5]  Jessica J. Fridrich,et al.  Digital image steganography using stochastic modulation , 2003, IS&T/SPIE Electronic Imaging.

[6]  Maxim Sidorov,et al.  Hidden Markov models and steganalysis , 2004, MM&Sec '04.

[7]  B. S. Manjunath,et al.  Steganalysis for Markov cover data with applications to images , 2006, IEEE Transactions on Information Forensics and Security.

[8]  Jessica J. Fridrich,et al.  New blind steganalysis and its implications , 2006, Electronic Imaging.

[9]  Pedro Comesaña Alfaro,et al.  On the capacity of stegosystems , 2007, MM&Sec.

[10]  Andrew D. Ker.  The ultimate steganalysis benchmark? , 2007, MM&Sec.

[11]  Andrew D. Ker.  A Capacity Result for Batch Steganography , 2007, IEEE Signal Processing Letters.

[12]  Tomás Pevný,et al.  Statistically undetectable jpeg steganography: dead ends challenges, and opportunities , 2007, MM&Sec.

[13]  Ying Wang,et al.  Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions , 2007, IEEE Transactions on Information Theory.

[14]  Tomás Pevný,et al.  The square root law of steganographic capacity , 2008, MM&Sec '08.

[15]  W. Pearlman,et al.  Capacity of Steganographic Channels , 2009, IEEE Trans. Inf. Theory.

[16]  Andrew D. Ker.  Estimating Steganographic Fisher Information in Real Images , 2009, Information Hiding.

[17]  Jessica J. Fridrich,et al.  The square root law of steganographic capacity for Markov covers , 2009, Electronic Imaging.

[18]  Jessica J. Fridrich,et al.  Complete characterization of perfectly secure stego-systems with mutually independent embedding operation , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.