Abstract
In response to various cryptanalysis results on white-box cryptography, Bringer et al. presented a novel white-box strategy. They propose to extend the round computations of a block cipher with a set of random equations and perturbations, and complicate the analysis by implementing each such round as one system that is obfuscated with annihilating linear input and output encodings. The improved version presented by Bringer et al. implements the AEw/oS, which is an AES version with key-dependent S-boxes (the S-boxes are in fact the secret key). In this paper we present an algebraic analysis to recover equivalent keys from the implementation. We show how the perturbations and system of random equations can be distinguished from the implementation, and how the linear input and output encodings can be eliminated. The result is that we have decomposed the white-box implementation into a much more simple, functionally equivalent implementation and retrieved a set of keys that are equivalent to the original key. Our cryptanalysis has a worst time complexity of 217 and a negligible space complexity.
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References
Billet, O., Gilbert, H.: A Traceable Block Cipher. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 331–346. Springer, Heidelberg (2003)
Billet, O., Gilbert, H., Ech-Chatbi, C.: Cryptanalysis of a White Box AES Implementation. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 227–240. Springer, Heidelberg (2004)
Bringer, J., Chabanne, H., Dottax, E.: Perturbing and Protecting a Traceable Block Cipher. In: Leitold, H., Markatos, E.P. (eds.) CMS 2006. LNCS, vol. 4237, pp. 109–119. Springer, Heidelberg (2006)
Bringer, J., Chabanne, H., Dottax, E.: White box cryptography: Another attempt. Cryptology ePrint Archive, Report 2006/468 (2006), http://eprint.iacr.org/
Chow, S., Eisen, P.A., Johnson, H., van Oorschot, P.C.: White-Box Cryptography and an AES Implementation. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 250–270. Springer, Heidelberg (2003)
Chow, S., Eisen, P.A., Johnson, H., van Oorschot, P.C.: A white-box DES implementation for DRM applications. In: Feigenbaum, J. (ed.) DRM 2002. LNCS, vol. 2696, pp. 1–15. Springer, Heidelberg (2003)
Ding, J.: A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 305–318. Springer, Heidelberg (2004)
Faugère, J.-C., Perret, L.: Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 30–47. Springer, Heidelberg (2006)
Goubin, L., Masereel, J.-M., Quisquater, M.: Cryptanalysis of White Box DES Implementations. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 278–295. Springer, Heidelberg (2007)
Jacob, M., Boneh, D., Felten, E.W.: Attacking an Obfuscated Cipher by Injecting Faults. In: Feigenbaum, J. (ed.) DRM 2002. LNCS, vol. 2696, pp. 16–31. Springer, Heidelberg (2003)
Link, H.E., Neumann, W.D.: Clarifying Obfuscation: Improving the Security of White-Box DES. In: Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC 2005), Washington, DC, USA, vol. 1, pp. 679–684. IEEE Computer Society, Los Alamitos (2005)
Michiels, W., Gorissen, P., Hollmann, H.D.L.: Cryptanalysis of a Generic Class of White-Box Implementations. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 414–428. Springer, Heidelberg (2009)
National Institute of Standards and Technology. Advanced encryption standard. FIPS publication 197 (2001), http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf
Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996)
Wyseur, B.: White-Box Cryptography. PhD thesis, Katholieke Universiteit Leuven (2009)
Wyseur, B., Michiels, W., Gorissen, P., Preneel, B.: Cryptanalysis of White-Box DES Implementations with Arbitrary External Encodings. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 264–277. Springer, Heidelberg (2007)
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De Mulder, Y., Wyseur, B., Preneel, B. (2010). Cryptanalysis of a Perturbated White-Box AES Implementation. In: Gong, G., Gupta, K.C. (eds) Progress in Cryptology - INDOCRYPT 2010. INDOCRYPT 2010. Lecture Notes in Computer Science, vol 6498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17401-8_21
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DOI: https://doi.org/10.1007/978-3-642-17401-8_21
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