A Graph–Theoretic Approach to Steganography

  • Stefan Hetzl
  • Petra Mutzel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3677)


We suggest a graph-theoretic approach to steganography based on the idea of exchanging rather than overwriting pixels. We construct a graph from the cover data and the secret message. Pixels that need to be modified are represented as vertices and possible partners of an exchange are connected by edges. An embedding is constructed by solving the combinatorial problem of calculating a maximum cardinality matching. The secret message is then embedded by exchanging those samples given by the matched edges. This embedding preserves first-order statistics. Additionally, the visual changes can be minimized by introducing edge weights.

We have implemented an algorithm based on this approach with support for several types of image and audio files and we have conducted computational studies to evaluate the performance of the algorithm.


Steganography graph theory information hiding 


  1. 1.
    Anderson, R.J.: Stretching the Limits of Steganography. In: Anderson, R. (ed.) IH 1996. LNCS, vol. 1174, pp. 39–48. Springer, Heidelberg (1996)CrossRefGoogle 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.
    Franz, E.: Steganography Preserving Statistical Properties. In: Petitcolas, F.A.P. (ed.) IH 2002. LNCS, vol. 2578, pp. 278–294. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Fridrich, J., Goljan, M., Soukal, D.: Higher–order statistical steganalysis of palette images. In: Proceedings of the Electronic Imaging SPIE Santa Clara, CA, January 2003, pp. 178–190 (2003)Google Scholar
  5. 5.
    Fridrich, J.J.: Feature-based Steganalysis for JPEG images and Its Implications for Future Design of Steganographic Schemes. In: Fridrich, J. (ed.) IH 2004. LNCS, vol. 3200, pp. 67–81. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Fridrich, J.J., Goljan, M., Hogea, D., Soukal, D.: Quantitative steganalysis of digital images: estimating the secret message length. Multimedia Systems 9(3), 288–302 (2003)CrossRefGoogle Scholar
  7. 7.
    Hetzl, S.: Steghide,
  8. 8.
    Micali, S., Vazirani, V.V.: An \( {O}(\sqrt{|V|}{|E|}) \) Algorithm for Finding Maximum Matching in General Graphs. In: 21st Annual Symposium on Foundations of Computer Science, Syracuse, New York, October 1980, pp. 17–27. IEEE, Los Alamitos (1980)Google Scholar
  9. 9.
    Möhring, R., Müller-Hannemann, M.: Cardinality Matching: Heuristic Search for Augmenting Paths. Technical Report 439, Fachbereich Mathematik, Technische Universität Berlin (1995)Google Scholar
  10. 10.
    Provos, N.: Defending Against Statistical Steganalysis. In: 10th USENIX Security Symposium, Proceedings (2001)Google Scholar
  11. 11.
    Sallee, P.: Model-based Steganography. In: Kalker, T., Cox, I., Ro, Y.M. (eds.) IWDW 2003. LNCS, vol. 2939, pp. 154–167. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Westfeld, A.: F5–A Steganographic Algorithm: High Capacity Despite Better Steganalysis. In: Moskowitz, I.S. (ed.) IH 2001. LNCS, vol. 2137, pp. 289–302. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Westfeld, A.: Detecting Low Embedding Rates. In: Petitcolas, F.A.P. (ed.) IH 2002. LNCS, vol. 2578, pp. 324–339. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Westfeld, A., Pfitzmann, A.: Attacks on Steganographic Systems. In: Pfitzmann, A. (ed.) IH 1999. LNCS, vol. 1768, pp. 61–76. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2005

Authors and Affiliations

  • Stefan Hetzl
    • 1
  • Petra Mutzel
    • 2
  1. 1.Institute of Computer Languages (E185)Vienna University of TechnologyViennaAustria
  2. 2.Institute of Algorithm Engineering, LS11University of DortmundDortmundGermany

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