Abstract
Assuming trapdoor permutations, we show that there exist function families that cannot be VBB-obfuscated even if both the obfuscator and the obfuscated program have access to a random oracle. Specifically, these families are the robust unobfuscatable families of [Bitansky-Paneth, STOC 13].
Our result stands in contrast to the general VBB obfuscation algorithms in more structured idealized models where the oracle preserves certain algebraic homomorphisms [Canetti-Vaikuntanathan, ePrint 13; Brakerski-Rothblum, TCC 14; Barak et al., Eurocrypt 14].
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
Bitansky, N., Canetti, R., Goldwasser, S., Halevi, S., Kalai, Y.T., Rothblum, G.N.: Program obfuscation with leaky hardware. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 722–739. Springer, Heidelberg (2011)
Bitansky, N., Canetti, R., Kalai, Y.T., Paneth, O.: On virtual grey box obfuscation for general circuits. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 108–125. Springer, Heidelberg (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. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 221–238. Springer, Heidelberg (2014)
Bitansky, N., Paneth, O.: On the impossibility of approximate obfuscation and applications to resettable cryptography. In: STOC, pp. 241–250 (2013)
Brakerski, Z., Rothblum, G.N.: Virtual black-box obfuscation for all circuits via generic graded encoding. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 1–25. Springer, Heidelberg (2014)
Babai, L., Szemerédi, E.: On the complexity of matrix group problems I. In: 25th Annual Symposium on Foundations of Computer Science, West Palm Beach, Florida, USA, October 24-26, pp. 229–240 (1984)
Canetti, R.: Towards realizing random oracles: Hash functions that hide all partial information. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 455–469. Springer, Heidelberg (1997)
Canetti, R., Vaikuntanathan, V.: Obfuscating branching programs using black-box pseudo-free groups. IACR Cryptology ePrint Archive, 2013:500 (2013)
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)
Goyal, V., Ishai, Y., Sahai, A., Venkatesan, R., Wadia, A.: Founding cryptography on tamper-proof hardware tokens. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 308–326. Springer, Heidelberg (2010)
Goldwasser, S., Rothblum, G.N.: On best-possible obfuscation. J. Cryptology 27(3), 480–505 (2014)
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing, Seattle, Washigton, USA, May 14-17, pp. 44–61 (1989)
Lynn, B., Prabhakaran, M., Sahai, A.: Positive results and techniques for obfuscation. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 20–39. Springer, Heidelberg (2004)
Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)
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
© 2015 International Association for Cryptologic Research
About this paper
Cite this paper
Canetti, R., Kalai, Y.T., Paneth, O. (2015). On Obfuscation with Random Oracles. In: Dodis, Y., Nielsen, J.B. (eds) Theory of Cryptography. TCC 2015. Lecture Notes in Computer Science, vol 9015. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46497-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-662-46497-7_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-46496-0
Online ISBN: 978-3-662-46497-7
eBook Packages: Computer ScienceComputer Science (R0)