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.
M. Ernst—This work was supported by the Graduate School for Computing in Medicine and Life Sciences funded by Germany’s Excellence Initiative [DFG GSC 235/2].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
Blumer, A., Ehrenfeucht, A., Haussler, D., Warmuth, M.K.: Learnability and the Vapnik-Chervonenkis dimension. J. ACM 36(4), 929–965 (1989)
De, A., Diakonikolas, I., Servedio, R.A.: Learning from satisfying assignments. In: Indyk, P. (ed.) Proc. SODA, pp. 478–497. SIAM, Philadelphia (2015)
Dedić, N., Itkis, G., Reyzin, L., Russell, S.: Upper and lower bounds on black-box steganography. J. Cryptology 22(3), 365–394 (2009)
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)
Fridrich, J.: Steganography in digital media: principles, algorithms, and applications. Cambridge University Press, New York (2009)
Hopper, N., von Ahn, L., Langford, J.: Provably secure steganography. IEEE T. Comput. 58(5), 662–676 (2009)
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)
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)
Kodovsky, J., Fridrich, J., Holub, V.: Ensemble classifiers for steganalysis of digital media. IEEE T. Inform. Forensics and Sec. 7(2), 432–444 (2012)
Kucera, L., Marchetti-Spaccamela, A., Protasi, M.: On learning monotone DNF formulae under uniform distributions. Inform. Comput. 110(1), 84–95 (1994)
Liśkiewicz, M., Reischuk, R., Wölfel, U.: Grey-box steganography. Theor. Comput. Sc. 505, 27–41 (2013)
Natarajan, B.K.: Probably approximate learning of sets and functions. SIAM J. Comput. 20(2), 328–351 (1991)
Pitt, L., Valiant, L.G.: Computational limitations on learning from examples. J. ACM 35(4), 965–984 (1988)
Sakai, Y., Maruoka, A.: Learning monotone log-term DNF formulas under the uniform distribution. Theory of Comput. Syst. 33(1), 17–33 (2000)
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)
Schaathun, H.G.: Machine Learning in Image Steganalysis. Wiley-IEEE Press, Chichester (2012)
Valiant, L.G.: A theory of the learnable. CACM 27(11), 1134–1142 (1984)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ernst, M., Liśkiewicz, M., Reischuk, R. (2015). Algorithmic Learning for Steganography: Proper Learning of k-term DNF Formulas from Positive Samples. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-662-48971-0_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48970-3
Online ISBN: 978-3-662-48971-0
eBook Packages: Computer ScienceComputer Science (R0)