Algorithmic Information Theory for Obfuscation Security

Rabih Mohsen, Alexandre Miranda Pinto

2015

Abstract

The main problem in designing effective code obfuscation is to guarantee security. State of the art obfuscation techniques rely on an unproven concept of security, and therefore are not regarded as provably secure. In this paper, we undertake a theoretical investigation of code obfuscation security based on Kolmogorov complexity and algorithmic mutual information. We introduce a new definition of code obfuscation that requires the algorithmic mutual information between a code and its obfuscated version to be minimal, allowing for controlled amount of information to be leaked to an adversary. We argue that our definition avoids the impossibility results of Barak et al. and is more advantageous then obfuscation indistinguishability definition in the sense it is more intuitive, and is algorithmic rather than probabilistic.

References

  1. Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., and Yang, K. (2012). On the (im)possibility of obfuscating programs. J. ACM, 59(2):6:1-6:48.
  2. Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S. P., and Yang, K. (2001). On the (im)possibility of obfuscating programs. IACR Cryptology ePrint Archive, 2001:69.
  3. Collberg, C., Thomborson, C., and Low, D. (1997). A Taxonomy of Obfuscating Transformations.
  4. Gács, P. (1974). On the symmetry of algorithmic information. Soviet Math. Dokl, 15:1477-1480.
  5. Garg, S., Raykova, M., Gentry, C., Sahai, A., Halevi, S., and Waters, B. (2013). Candidate indistinguishability obfuscation and functional encryption for all circuits. In In FOCS.
  6. Gauvrit, N., Zenil, H., and Delahaye, J. (2011). Assessing cognitive randomness: A kolmogorov complexity approach. CoRR, abs/1106.3059.
  7. Goldwasser, S. and Rothblum, G. N. (2007). On bestpossible obfuscation. In Proceedings of the 4th conference on Theory of cryptography, TCC'07, pages 194-213, Berlin, Heidelberg. Springer-Verlag.
  8. Jbara, A. and Feitelson, D. G. (2014). On the effect of code regularity on comprehension. In Proceedings of the 22Nd International Conference on Program Comprehension, ICPC 2014, pages 189-200, New York, NY, USA. ACM.
  9. Kieffer, J. C. and Yang, E. H. (1996). Sequential codes, lossless compression of individual sequences, and Kolmogorov complexity. IEEE Trans. on Information Theory, 42(1):29-39.
  10. Lathrop, J. I. (1997). Compression depth and the behavior of cellular automata. Complex Systems.
  11. Li, M. and Vitányi, P. M. (2008). An Introduction to Kolmogorov Complexity and Its Applications. Springer Publishing Company, Incorporated, 3 edition.
  12. McCabe, T. J. (1976). A complexity measure. IEEE Trans. Software Eng., 2(4):308-320.
  13. Shen, A. (1982). Axiomatic description of the entropy notion for finite objects. VIII All-USSR Conference (Logika i metodologija nauki),Vilnjus, pages 104 - 105. The paper in Russian.
  14. Shen, A., Uspensky, V., and Vereshchagin, N. (2014). Kolmogorov complexity and algorithmic randomness. MCCME Publishing house.
  15. Taveneaux, A. (2011). Towards an axiomatic system for kolmogorov complexity. Electronic Colloquium on Computational Complexity (ECCC), 18:14.
Download


Paper Citation


in Harvard Style

Mohsen R. and Miranda Pinto A. (2015). Algorithmic Information Theory for Obfuscation Security . In Proceedings of the 12th International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2015) ISBN 978-989-758-117-5, pages 76-87. DOI: 10.5220/0005548200760087


in Bibtex Style

@conference{secrypt15,
author={Rabih Mohsen and Alexandre Miranda Pinto},
title={Algorithmic Information Theory for Obfuscation Security},
booktitle={Proceedings of the 12th International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2015)},
year={2015},
pages={76-87},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005548200760087},
isbn={978-989-758-117-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2015)
TI - Algorithmic Information Theory for Obfuscation Security
SN - 978-989-758-117-5
AU - Mohsen R.
AU - Miranda Pinto A.
PY - 2015
SP - 76
EP - 87
DO - 10.5220/0005548200760087