Abstract
An obfuscator \(\mathcal O\) is Virtual Grey Box (VGB) for a class \(\mathcal C\) of circuits if, for any \(C\in{\mathcal C}\) and any predicate π, deducing π(C) given \(\mathcal O(C)\) is tantamount to deducing π(C) given unbounded computational resources and polynomially many oracle queries to C. VGB obfuscation is often significantly more meaningful than indistinguishability obfuscation (IO). In fact, for some circuit families of interest VGB is equivalent to full-fledged Virtual Black Box obfuscation.
We investigate the feasibility of obtaining VGB obfuscation for general circuits. We first formulate a natural strengthening of IO, called strong IO (SIO). Essentially, \(\mathcal O\) is SIO for class \(\mathcal C\) if \({\mathcal O}(C)\approx{\mathcal O}(C')\) whenever the pair (C,C′) is taken from a distribution over \(\mathcal C\) where, for all x, C(x) ≠ C′(x) only with negligible probability.
We then show that an obfuscator is VGB for a class \(\mathcal C\) if and only if it is SIO for \(\mathcal C\). This result is unconditional and holds for any \(\mathcal C\). We also show that for some circuit collections, SIO implies virtual black-box obfuscation.
Finally, we formulate a slightly stronger variant of the semantic security property of graded encoding schemes [Pass-Seth-Telang Crypto 14], and show that existing obfuscators such as the obfuscator of Barak et. al [Eurocrypt 14] are SIO for all circuits in NC1, assuming that the underlying graded encoding scheme satisfies our variant of semantic security.
Put together, we obtain VGB obfuscation for all NC1 circuits under assumptions that are almost the same as those used by Pass et. al to obtain IO for NC1 circuits. We also show that semantic security is in essence necessary for showing VGB obfuscation.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Barak, B., Bitansky, N., Canetti, R., Kalai, Y.T., Paneth, O., Sahai, A.: Obfuscation for evasive functions. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 26–51. Springer, Heidelberg (2014)
Bitansky, N., Canetti, R.: On strong simulation and composable point obfuscation. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 520–537. Springer, Heidelberg (2010)
Bitansky, N., Canetti, R., Cohn, H., Goldwasser, S., Kalai, Y.T., Paneth, O., Rosen, A.: The impossibility of obfuscation with auxiliary input or a universal simulator. CoRR, abs/1401.0348 (2014)
Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001)
Barak, B., Garg, S., Kalai, Y.T., Paneth, O., Sahai, A.: Protecting obfuscation against algebraic attacks. Cryptology ePrint Archive, Report 2013/631 (2013), http://eprint.iacr.org/
Brakerski, Z., Rothblum, G.N.: Virtual black-box obfuscation for all circuits via generic graded encoding. Cryptology ePrint Archive, Report 2013/563 (2013), http://eprint.iacr.org/
Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013)
Canetti, R., Vaikuntanathan, V.: Obfuscating branching programs using black-box pseudo-free groups. Cryptology ePrint Archive, Report 2013/500 (2013), http://eprint.iacr.org/
Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013)
Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS (2013)
Goldwasser, S., Kalai, Y.T.: On the impossibility of obfuscation with auxiliary input. In: FOCS, pp. 553–562 (2005)
Gentry, C., Lewko, A., Sahai, A., Waters, B.: Indistinguishability obfuscation from the multilinear subgroup elimination assumption. Cryptology ePrint Archive, Report 2014/309 (2014), http://eprint.iacr.org/
Hada, S.: Zero-knowledge and code obfuscation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 443–457. Springer, Heidelberg (2000)
Pass, R., Telang, S., Seth, K.: Obfuscation from semantically-secure multi-linear encodings. Cryptology ePrint Archive, Report 2013/781 (2013), http://eprint.iacr.org/
Sahai, A., Waters, B.: How to use indistinguishability obfuscation: Deniable encryption, and more. IACR Cryptology ePrint Archive 2013, 454 (2013)
Wee, H.: On obfuscating point functions. IACR Cryptology ePrint Archive 2005, 1 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 International Association for Cryptologic Research
About this paper
Cite this paper
Bitansky, N., Canetti, R., Kalai, Y.T., Paneth, O. (2014). On Virtual Grey Box Obfuscation for General Circuits. In: Garay, J.A., Gennaro, R. (eds) Advances in Cryptology – CRYPTO 2014. CRYPTO 2014. Lecture Notes in Computer Science, vol 8617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44381-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-44381-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44380-4
Online ISBN: 978-3-662-44381-1
eBook Packages: Computer ScienceComputer Science (R0)