Minimizing Additive Distortion in Steganography Using Syndrome-Trellis Codes

This paper proposes a complete practical methodology for minimizing additive distortion in steganography with general (nonbinary) embedding operation. Let every possible value of every stego element be assigned a scalar expressing the distortion of an embedding change done by replacing the cover element by this value. The total distortion is assumed to be a sum of per-element distortions. Both the payload-limited sender (minimizing the total distortion while embedding a fixed payload) and the distortion-limited sender (maximizing the payload while introducing a fixed total distortion) are considered. Without any loss of performance, the nonbinary case is decomposed into several binary cases by replacing individual bits in cover elements. The binary case is approached using a novel syndrome-coding scheme based on dual convolutional codes equipped with the Viterbi algorithm. This fast and very versatile solution achieves state-of-the-art results in steganographic applications while having linear time and space complexity w.r.t. the number of cover elements. We report extensive experimental results for a large set of relative payloads and for different distortion profiles, including the wet paper channel. Practical merit of this approach is validated by constructing and testing adaptive embedding schemes for digital images in raster and transform domains. Most current coding schemes used in steganography (matrix embedding, wet paper codes, etc.) and many new ones can be implemented using this framework.

[1]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.

[2]  Marten van Dijk,et al.  Embedding Information in Grayscale Images , 2001 .

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

[4]  Tomás Pevný,et al.  Steganalysis by Subtractive Pixel Adjacency Matrix , 2009, IEEE Transactions on Information Forensics and Security.

[5]  Aaron D. Wyner,et al.  Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959. , 1993 .

[6]  Hyoung Joong Kim,et al.  Less detectable JPEG steganography method based on heuristic optimization and BCH syndrome coding , 2009, MM&Sec '09.

[7]  Jessica J. Fridrich,et al.  Writing on wet paper , 2005, IEEE Transactions on Signal Processing.

[8]  Dana S. Richards,et al.  Modified Matrix Encoding Technique for Minimal Distortion Steganography , 2006, Information Hiding.

[9]  Weiming Zhang,et al.  Generalization of the ZZW Embedding Construction for Steganography , 2009, IEEE Transactions on Information Forensics and Security.

[10]  Jessica J. Fridrich,et al.  Minimizing embedding impact in steganography using trellis-coded quantization , 2010, Electronic Imaging.

[11]  Jessica J. Fridrich,et al.  Wet ZZW construction for steganography , 2009, 2009 First IEEE International Workshop on Information Forensics and Security (WIFS).

[12]  Jessica J. Fridrich,et al.  Minimizing additive distortion functions with non-binary embedding operation in steganography , 2010, 2010 IEEE International Workshop on Information Forensics and Security.

[13]  Andrew J. Viterbi,et al.  Trellis Encoding of memoryless discrete-time sources with a fidelity criterion , 1974, IEEE Trans. Inf. Theory.

[14]  Jessica J. Fridrich,et al.  Constructing Good Covering Codes for Applications in Steganography , 2008, Trans. Data Hiding Multim. Secur..

[15]  Jessica J. Fridrich,et al.  Practical methods for minimizing embedding impact in steganography , 2007, Electronic Imaging.

[16]  Jessica J. Fridrich,et al.  On completeness of feature spaces in blind steganalysis , 2008, MM&Sec '08.

[17]  Weiming Zhang,et al.  Improving the Embedding Efficiency of Wet Paper Codes by Paper Folding , 2009, IEEE Signal Processing Letters.

[18]  Rainer Böhme,et al.  Improved statistical steganalysis using models of heterogeneous cover signals , 2009 .

[19]  Weiming Zhang,et al.  Maximizing Steganographic Embedding Efficiency by Combining Hamming Codes and Wet Paper Codes , 2008, Information Hiding.

[20]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

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

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

[23]  Antje Winkler,et al.  Embedding with syndrome coding based on BCH codes: The corrected version of this paper is now available as full text. To view the original document as presented in the printed proceedings (with its errors), download the supplemental file , 2006, MM&Sec '06.

[24]  Vladimir Sidorenko,et al.  Decoding of convolutional codes using a syndrome trellis , 1994, IEEE Trans. Inf. Theory.

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

[26]  A. Robert Calderbank,et al.  Covering properties of convolutional codes and associated lattices , 1995, IEEE Trans. Inf. Theory.

[27]  Pierre Moulin,et al.  Data-Hiding Codes , 2005, Proceedings of the IEEE.

[28]  Weiming Zhang,et al.  Improving Embedding Efficiency of Covering Codes for Applications in Steganography , 2007, IEEE Communications Letters.

[29]  Hyoung-Joong Kim,et al.  Fast BCH Syndrome Coding for Steganography , 2009, Information Hiding.

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

[31]  Ingemar J. Cox,et al.  Trellis coded modulation to improve dirty paper trellis watermarking , 2007, Electronic Imaging.

[32]  Yuhong Yang,et al.  Information Theory, Inference, and Learning Algorithms , 2005 .

[33]  Jessica J. Fridrich,et al.  Calibration revisited , 2009, MM&Sec '09.

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

[35]  Jessica J. Fridrich,et al.  Asymptotic Behavior of the ZZW Embedding Construction , 2009, IEEE Transactions on Information Forensics and Security.

[36]  Xinpeng Zhang,et al.  Efficient double-layered steganographic embedding , 2007 .

[37]  R. Crandall,et al.  Some Notes on Steganography , 1999 .

[38]  Tomás Pevný,et al.  Modern steganalysis can detect YASS , 2010, Electronic Imaging.

[39]  Tomás Pevný,et al.  Using High-Dimensional Image Models to Perform Highly Undetectable Steganography , 2010, Information Hiding.

[40]  Jessica J. Fridrich,et al.  Perturbed quantization steganography , 2005, Multimedia Systems.

[41]  Neri Merhav,et al.  On the error exponent of trellis source coding , 2005, IEEE Transactions on Information Theory.

[42]  Kannan Ramchandran,et al.  Distributed source coding using syndromes (DISCUS): design and construction , 2003, IEEE Trans. Inf. Theory.

[43]  Jessica J. Fridrich,et al.  Gibbs Construction in Steganography , 2010, IEEE Transactions on Information Forensics and Security.

[44]  Rüdiger L. Urbanke,et al.  Polar Codes are Optimal for Lossy Source Coding , 2009, IEEE Transactions on Information Theory.

[45]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .