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Algorithmic Learning for Steganography: Proper Learning of k-term DNF Formulas from Positive Samples

  • Matthias Ernst
  • Maciej Liśkiewicz
  • Rüdiger ReischukEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9472)

Abstract

Proper learning from positive samples is a basic ingredient for designing secure steganographic systems for unknown covertext channels. In addition, security requirements imply that the hypothesis should not contain false positives. We present such a learner for k-term DNF formulas for the uniform distribution and a generalization to q-bounded distributions. We briefly also describe how these results can be used to design a secure stegosystem.

References

  1. 1.
    Alekhnovich, M., Braverman, M., Feldman, V., Klivans, A.R., Pitassi, T.: The complexity of properly learning simple concept classes. J. Comput. Syst. Sci. 74(1), 16–34 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blumer, A., Ehrenfeucht, A., Haussler, D., Warmuth, M.K.: Learnability and the Vapnik-Chervonenkis dimension. J. ACM 36(4), 929–965 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    De, A., Diakonikolas, I., Servedio, R.A.: Learning from satisfying assignments. In: Indyk, P. (ed.) Proc. SODA, pp. 478–497. SIAM, Philadelphia (2015)Google Scholar
  4. 4.
    Dedić, N., Itkis, G., Reyzin, L., Russell, S.: Upper and lower bounds on black-box steganography. J. Cryptology 22(3), 365–394 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Flammini, M., Marchetti-Spaccamela, A., Kučera, L.: Learning DNF formulae under classes of probability distributions. In: Proc. COLT, pp. 85–92. ACM, New York (1992)Google Scholar
  6. 6.
    Fridrich, J.: Steganography in digital media: principles, algorithms, and applications. Cambridge University Press, New York (2009)CrossRefzbMATHGoogle Scholar
  7. 7.
    Hopper, N., von Ahn, L., Langford, J.: Provably secure steganography. IEEE T. Comput. 58(5), 662–676 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jerrum, M.R., Valiant, L.G., Vazirani, V.V.: Random generation of combinatorial structures from a uniform distribution. Theor. Comput. Sc. 43, 169–188 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ker, A.D., Bas, P., Böhme, R., Cogranne, R., Craver, S., Filler, T., Fridrich, J., Pevný, T.: Moving steganography and steganalysis from the laboratory into the real world. In: Proc. IH&MMSec, pp. 45–58. ACM, New York (2013)Google Scholar
  10. 10.
    Kodovsky, J., Fridrich, J., Holub, V.: Ensemble classifiers for steganalysis of digital media. IEEE T. Inform. Forensics and Sec. 7(2), 432–444 (2012)CrossRefGoogle Scholar
  11. 11.
    Kucera, L., Marchetti-Spaccamela, A., Protasi, M.: On learning monotone DNF formulae under uniform distributions. Inform. Comput. 110(1), 84–95 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Liśkiewicz, M., Reischuk, R., Wölfel, U.: Grey-box steganography. Theor. Comput. Sc. 505, 27–41 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Natarajan, B.K.: Probably approximate learning of sets and functions. SIAM J. Comput. 20(2), 328–351 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Pitt, L., Valiant, L.G.: Computational limitations on learning from examples. J. ACM 35(4), 965–984 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Sakai, Y., Maruoka, A.: Learning monotone log-term DNF formulas under the uniform distribution. Theory of Comput. Syst. 33(1), 17–33 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sakai, Y., Maruoka, A.: Learning \(k\)-term monotone boolean formulae. In: Doshita, S., Furukawa, K., Jantke, K.P., Nishida, T. (eds.) ALT 1992. LNCS, vol. 743, pp. 195–207. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  17. 17.
    Schaathun, H.G.: Machine Learning in Image Steganalysis. Wiley-IEEE Press, Chichester (2012)CrossRefGoogle Scholar
  18. 18.
    Valiant, L.G.: A theory of the learnable. CACM 27(11), 1134–1142 (1984)CrossRefzbMATHGoogle Scholar
  19. 19.
    Verbeurgt, K.: Learning DNF under the uniform distribution in quasi-polynomial time. In: Proc. COLT, pp. 314–326. Morgan Kaufmann Publishers Inc., San Francisco (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Matthias Ernst
    • 1
    • 2
  • Maciej Liśkiewicz
    • 1
  • Rüdiger Reischuk
    • 1
    Email author
  1. 1.Institut für Theoretische InformatikUniversität zu LübeckLübeckGermany
  2. 2.Graduate School for Computing in Medicine and Life SciencesUniversität zu LübeckLübeckGermany

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