The square root law of steganographic capacity

There are a number of recent information theoretic results demonstrating (under certain conditions) a sublinear relationship between the number of cover objects and their total steganographic capacity. In this paper we explain how these results may be adapted to the steganographic capacity of a single cover object, which under the right conditions should be proportional to the square root of the cover size. Then we perform some experiments using three genuine steganography methods in digital images, covering both spatial and DCT domains. Measuring detectability under four different steganalysis methods, for a variety of payload and cover sizes, we observe close accordance with a square root law.

[1]  Bernhard Schölkopf,et al.  A Kernel Method for the Two-Sample-Problem , 2006, NIPS.

[2]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

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

[4]  Tomás Pevný,et al.  Benchmarking for Steganography , 2008, Information Hiding.

[5]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

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

[7]  Rainer Böhme,et al.  Assessment of Steganalytic Methods Using Multiple Regression Models , 2005, Information Hiding.

[8]  Ingo Steinwart,et al.  On the Influence of the Kernel on the Consistency of Support Vector Machines , 2002, J. Mach. Learn. Res..

[9]  Andrew D. Ker.  Batch Steganography and Pooled Steganalysis , 2006, Information Hiding.

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

[11]  Ross J. Anderson.  Stretching the Limits of Steganography , 1996, Information Hiding.

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

[13]  Andrew D. Ker.  Steganalysis of LSB matching in grayscale images , 2005, IEEE Signal Processing Letters.

[14]  Andreas Westfeld,et al.  F5-A Steganographic Algorithm , 2001, Information Hiding.

[15]  Jessica J. Fridrich,et al.  Matrix embedding for large payloads , 2006, IEEE Transactions on Information Forensics and Security.

[16]  Rainer Böhme,et al.  Revisiting weighted stego-image steganalysis , 2008, Electronic Imaging.

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

[18]  Tomás Pevný,et al.  Merging Markov and DCT features for multi-class JPEG steganalysis , 2007, Electronic Imaging.

[19]  Andreas Westfeld,et al.  F5—A Steganographic Algorithm High Capacity Despite Better Steganalysis , 2001 .

[20]  Rainer Böhme,et al.  A two-factor error model for quantitative steganalysis , 2006, Electronic Imaging.

[21]  Andrew D. Ker.  A General Framework for Structural Steganalysis of LSB Replacement , 2005, Information Hiding.

[22]  Andrew D. Ker.  Steganographic strategies for a square distortion function , 2008, Electronic Imaging.

[23]  Andrew D. Ker.  Improved Detection of LSB Steganography in Grayscale Images , 2004, Information Hiding.

[24]  Jessica J. Fridrich,et al.  Wet paper codes with improved embedding efficiency , 2006, IEEE Transactions on Information Forensics and Security.