Abstract
It is well known that the random-oracle (RO) model is not sound in the sense that there are schemes that are secure in the RO model but are insecure when instantiated by any family of hash functions. However, existing separation results do not hold for all cryptographic schemes in the RO model (e.g., bit encryption), leaving open the possibility that such schemes can be soundly instantiated.
In this work we refute this possibility, assuming the existence of indistinguishability obfuscation. First, we present a separation for bit encryption; namely, we show that there exists a bit-encryption protocol secure in the RO model but is insecure when the random oracle is instantiated by any concrete function. Second, we show how to adapt this separation to work for most natural simulation-based and game-based definitions. Our techniques can easily be adapted to other idealized models, and thus we present a unified approach to showing separations for many protocols of interest in various idealized models.
Full version available at http://eprint.iacr.org/2014/863.
M.D. Green—Work supported in part by the Defense Advanced Research Projects Agency (DARPA) and the Air Force Research Laboratory (AFRL) under contract FA8750-11-2-0211 and the Office of Naval Research under contract N00014-14-1-0333.
J. Katz—Work supported in part by NSF award #1223623.
A.J. Malozemoff—Work supported in part by NSF award #1223623 and with Government support through the National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFG 168a, awarded by DoD, Air Force Office of Scientific Research.
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- 1.
Note that using \(i\mathcal O \) for circuit obfuscation only gives a separation for hash functions of a priori fixed length.
- 2.
Recall that \(\mathsf {Eval}\) is the algorithm such that \({\mathsf {Eval}} (s,x) = f_s(x)\) for all \(s\in {{\{0,1\}}^{}} ^n \) and \(x\in {{\{0,1\}}^{*}} \).
- 3.
\(\mathcal {F}_\mathbf {\textsf {RO}}\) is defined in Fig. 1.
- 4.
This is without loss of generality because \(M_{i,j}^k\) can always be the empty message.
- 5.
Note that we only need \({\mathcal {O}} _{\textsf {enc}} \) to prove our separations results.
- 6.
\(\mathcal F _{\textsf {GG}}\) is defined in Fig. 2.
References
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)
Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (Im)possibility of obfuscating programs. J. ACM 59(2), 6 (2012)
Bellare, M., Boldyreva, A., Palacio, A.: An uninstantiable random-oracle-model scheme for a hybrid-encryption problem. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 171–188. Springer, Heidelberg (2004)
Bellare, M., Hoang, V.T., Keelveedhi, S.: Instantiating random oracles via UCEs. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 398–415. Springer, Heidelberg (2013)
Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62–73. ACM Press (1993)
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. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 71–89. Springer, Heidelberg (2014)
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)
Brzuska, C., Farshim, P., Mittelbach, A.: Random-oracle uninstantiability from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 428–455. Springer, Heidelberg (2015)
Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press (2001)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004)
Canetti, R., Goldreich, O., Halevi, S.: On the random-oracle methodology as applied to length-restricted signature schemes. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 40–57. Springer, Heidelberg (2004)
Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: 34th STOC, pp. 494–503. ACM Press (2002)
Coron, J.-S., Naccache, D., Tibouchi, M.: Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 446–464. Springer, Heidelberg (2012)
De Caro, A., Iovino, V., Jain, A., O’Neill, A., Paneth, O., Persiano, G.: On the achievability of simulation-based security for functional encryption. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 519–535. Springer, Heidelberg (2013)
Dent, A.W.: Adapting the weaknesses of the random oracle model to the generic group model. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 100–109. Springer, Heidelberg (2002)
Dent, A.W.: Fundamental problems in provable security and cryptography. Philos. Trans. R. So. A 364, 3215–3230 (2006)
Dodis, Y., Oliveira, R., Pietrzak, K.: On the generic insecurity of the full domain hash. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 449–466. Springer, Heidelberg (2005)
Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS (2013)
Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2008)
Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: 44th FOCS, pp. 102–115. IEEE Computer Society Press (2003)
Hofheinz, D., Jager, T., Khurana, D., Sahai, A., Waters, B., Zhandry, M.: How to generate and use universal samplers. Cryptology ePrint Archive, Report 2014/507 (2014). http://eprint.iacr.org/2014/507
Hofheinz, D., Kamath, A., Koppula, V., Waters, B.: Adaptively secure constrained pseudorandom functions. Cryptology ePrint Archive, Report 2014/720 (2014). http://eprint.iacr.org/2014/720
Hofheinz, D., Müller-Quade, J.: Universally composable commitments using random oracles. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 58–76. Springer, Heidelberg (2004)
Kiltz, E., Pietrzak, K.: On the security of padding-based encryption schemes – or – why we cannot prove OAEP secure in the standard model. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 389–406. Springer, Heidelberg (2009)
Leurent, G., Nguyen, P.Q.: How risky is the random-oracle model? In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 445–464. Springer, Heidelberg (2009)
Maurer, U.M., Renner, R.S., Holenstein, C.: Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004)
Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: the non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, p. 111. Springer, Heidelberg (2002)
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)
Acknowledgments
The authors would like to thank Brent Waters and Susan Hohenberger for helpful conversations during the course of this work.
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Green, M.D., Katz, J., Malozemoff, A.J., Zhou, HS. (2016). A Unified Approach to Idealized Model Separations via Indistinguishability Obfuscation. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_31
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