On the Statistical Properties of Syndrome Trellis Coding

  • Olaf Markus KöhlerEmail author
  • Cecilia Pasquini
  • Rainer Böhme
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10431)


Steganographic systems use Syndrome Trellis Coding (STC) to control the selection of embedding positions in a cover, subject to a set of stochastic constraints. This paper reports observations from a series of experiments on the ability of Syndrome Trellis Coding to approximate independent Bernoulli random variables. We find that approximation errors are generally small except for some outliers at boundary positions. Bivariate dependencies between embedding changes do reveal the use of the code and its parameters. While risky outliers can be hidden by permuting the cover before coding, or avoided by using the proposed “outlier corrected” variant OC-STC, the aggregate bivariate statistics are invariant to permutations and therefore constitute a potential security risk in the presence of powerful attackers.



Alexander Schlögl helped us with implementing STC on the HPC. Pascal Schöttle and the anonymous reviewers of IWDW provided us with very valuable comments. The computational results presented have been achieved using the HPC infrastructure “LEO” of the University of Innsbruck. This research was supported by Archimedes Privatstiftung, Innsbruck, and by Deutsche Forschungsgemeinschaft (DFG) under the grant “Informationstheoretische Schranken digitaler Bildforensik”.


  1. 1.
    Bas, P., Filler, T., Pevný, T.: “Break our steganographic system”: the Ins and Outs of organizing BOSS. In: Filler, T., Pevný, T., Craver, S., Ker, A. (eds.) IH 2011. LNCS, vol. 6958, pp. 59–70. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-24178-9_5 CrossRefGoogle Scholar
  2. 2.
    Carnein, M., Schöttle, P., Böhme, R.: Predictable rain? Steganalysis of public-key steganography using wet paper codes. In: ACM Information Hiding and Multimedia Security Workshop, pp. 97–108, Salzburg, Austria (2014)Google Scholar
  3. 3.
    Filler, T., Fridrich, J., Judas, J.: Syndrome Trellis Coding, Binghamton reference implementation. Accessed June 2017
  4. 4.
    Filler, T., Fridrich, J.: Gibbs construction in steganography. IEEE Trans. Inf. Forensics Secur. 5(4), 705–720 (2010)CrossRefGoogle Scholar
  5. 5.
    Filler, T., Fridrich, J.: Minimizing additive distortion functions with non-binary embedding operation in steganography. In: IEEE International Workshop on Information Forensics and Security (WIFS), pp. 1–6, Tenerife, Spain (2010)Google Scholar
  6. 6.
    Filler, T., Judas, J., Fridrich, J.: Minimizing embedding impact in steganography using trellis-coded quantization. In: Proceedings of SPIE-IS&T Electronic Imaging: Security, Forensics, Steganography and Watermarking of Multimedia Contents X, p. 754105, San Jose, CA (2010)Google Scholar
  7. 7.
    Filler, T., Judas, J., Fridrich, J.: Minimizing additive distortion in steganography using syndrome-trellis codes. IEEE Trans. Inf. Forensics Secur. 6(3), 920–935 (2011)CrossRefGoogle Scholar
  8. 8.
    Fridrich, J.: Minimizing the embedding impact in steganography. In: ACM Multimedia and Security Workshop, pp. 2–10, Geneva, Switzerland (2006)Google Scholar
  9. 9.
    Fridrich, J.: Steganography in Digital Media: Principles, Algorithms, and Applications. Cambridge University Press, Cambridge (2009)CrossRefzbMATHGoogle Scholar
  10. 10.
    Holub, V., Fridrich, J.: Designing steganographic distortion using directional filters. In: IEEE International Workshop on Information Forensics and Security (WIFS), pp. 234–239, Tenerife, Spain (2012)Google Scholar
  11. 11.
    Ker, A.D.: Locating steganographic payload via WS residuals. In: ACM Multimedia and Security Workshop, pp. 27–32, Oxford, UK (2008)Google Scholar
  12. 12.
    Li, B., Wang, M., Huang, J., Li, X.: A new cost function for spatial image steganography. In: IEEE International Conference on Image Processing (ICIP), pp. 4206–4210, Paris, France (2014)Google Scholar
  13. 13.
    Pevnỳ, T., Ker, A.D.: Steganographic key leakage through payload metadata. In: ACM Information Hiding and Multimedia Security Workshop, pp. 109–114, Salzburg, Austria (2014)Google Scholar
  14. 14.
    Reed, I.S., Chen, X.: Error-Control Coding for Data Networks. Springer, New York (2012)Google Scholar
  15. 15.
    Sedighi, V., Cogranne, R., Fridrich, J.: Content-adaptive steganography by minimizing statistical detectability. IEEE Trans. Inf. Forensics Secur. 11(2), 221–234 (2016)CrossRefGoogle Scholar
  16. 16.
    University of Innsbruck: Supercomputer LEO3E. Accessed June 2017
  17. 17.
    Wang, Y.H.: On the number of successes in independent trials. Statistica Sinica 3(2), 295–312 (1993)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Olaf Markus Köhler
    • 1
    Email author
  • Cecilia Pasquini
    • 1
    • 2
  • Rainer Böhme
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversität InnsbruckInnsbruckAustria
  2. 2.Department of Information SystemsUniversität MünsterMünsterGermany

Personalised recommendations