Bitspotting: Detecting Optimal Adaptive Steganography

  • Benjamin Johnson
  • Pascal Schöttle
  • Aron Laszka
  • Jens Grossklags
  • Rainer Böhme
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8389)


We analyze a two-player zero-sum game between a steganographer, Alice, and a steganalyst, Eve. In this game, Alice wants to hide a secret message of length \(k\) in a binary sequence, and Eve wants to detect whether a secret message is present. The individual positions of all binary sequences are independently distributed, but have different levels of predictability. Using knowledge of this distribution, Alice randomizes over all possible size-\(k\) subsets of embedding positions. Eve uses an optimal (possibly randomized) decision rule that considers all positions, and incorporates knowledge of both the sequence distribution and Alice’s embedding strategy.

Our model extends prior work by removing restrictions on Eve’s detection power. The earlier work determined where Alice should hide the bits when Eve can only look in one position. Here, we expand Eve’s capacity to spot these bits by allowing her to consider all positions. We give defining formulas for each player’s best response strategy and minimax strategy; and we present additional structural constraints on the game’s equilibria. For the special case of length-two binary sequences, we compute explicit equilibria and provide numerical illustrations.


Game theory Content-adaptive steganography Security 


  1. 1.
    Böhme, R.: Advanced Statistical Steganalysis. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  2. 2.
    Böhme, R., Westfeld, A.: Exploiting preserved statistics for steganalysis. In: Fridrich, J. (ed.) IH 2004. LNCS, vol. 3200, pp. 82–96. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  3. 3.
    Ettinger, J.M.: Steganalysis and game equilibria. In: Aucsmith, D. (ed.) IH 1998. LNCS, vol. 1525, pp. 319–328. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  4. 4.
    Franz, E.: Steganography preserving statistical properties. In: Petitcolas, Fabien A.P. (ed.) IH 2002. LNCS, vol. 2578, pp. 278–294. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  5. 5.
    Fridrich, J.: Steganography in Digital Media: Principles, Algorithms, and Applications, 1st edn. Cambridge University Press, New York (2009)CrossRefGoogle Scholar
  6. 6.
    Fridrich, J., Goljan, M.: On estimation of secret message length in LSB steganography in spatial domain. In: SPIE, vol. 5306, pp. 23–34 (2004)Google Scholar
  7. 7.
    Fridrich, J., Kodovskỳ, J.: Multivariate Gaussian model for designing additive distortion for steganography. In: ICASSP. IEEE (2013)Google Scholar
  8. 8.
    Johnson, B., Schöttle, P., Böhme, R.: Where to hide the bits ? In: Grossklags, J., Walrand, J. (eds.) GameSec 2012. LNCS, vol. 7638, pp. 1–17. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  9. 9.
    Ker, A.D.: Batch steganography and the threshold game. In: SPIE, vol. 6505, pp. 650–504 (2007)Google Scholar
  10. 10.
    Nash, J.: Non-cooperative games. The Annals Math. 54(2), 286–295 (1951)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Pevný, T., Filler, T., Bas, P.: Using high-dimensional image models to perform highly undetectable steganography. In: Böhme, R., Fong, P.W.L., Safavi-Naini, R. (eds.) IH 2010. LNCS, vol. 6387, pp. 161–177. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  12. 12.
    Pfitzmann, A., Köhntopp, M.: Anonymity, unobservability, and pseudonymity - a proposal for terminology. In: Federrath, H. (ed.) Designing Privacy Enhancing Technologies. LNCS, vol. 2009, pp. 1–9. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  13. 13.
    Schöttle, P., Böhme, R.: A game-theoretic approach to content-adaptive steganography. In: Kirchner, M., Ghosal, D. (eds.) IH 2012. LNCS, vol. 7692, pp. 125–141. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  14. 14.
    Schöttle, P., Laszka, A., Johnson, B., Grossklags, J., Böhme, R.: A game-theoretic analysis of content-adaptive steganography with independent embedding. In: EUSIPCO. IEEE (2013)Google Scholar
  15. 15.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Benjamin Johnson
    • 1
  • Pascal Schöttle
    • 2
  • Aron Laszka
    • 3
  • Jens Grossklags
    • 4
  • Rainer Böhme
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Information SystemsUniversity of MünsterMünsterGermany
  3. 3.Department of Networked Systems and ServicesBudapest University of Technology and EconomicsBudapestHungary
  4. 4.College of Information Sciences and TechnologyPennsylvania State UniversityState CollegeUSA

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