Abstract
In the random oracle model, parties are given oracle access to a random function (i.e., a uniformly chosen function from the set of all functions), and are assumed to have unbounded computational power (though they can only make a bounded number of oracle queries). This model provides powerful properties that allow proving the security of many protocols, even such that cannot be proved secure in the standard model (under any hardness assumptions). The random oracle model is also used for showing that a given cryptographic primitive cannot be used in a black-box way to construct another primitive; in their seminal work, ImpagliazzoRu89 [STOC ’89] showed that no key-agreement protocol exists in the random oracle model, yielding that key-agreement cannot be black-box reduced to one-way functions. Their work has a long line of followup works (Simon [EC ’98], Gertner et al. [STOC ’00] and Gennaro et al. [SICOMP ’05], to name a few), showing that given oracle access to a certain type of function family (e.g., the family that “implements” public-key encryption) is not sufficient for building a given cryptographic primitive (e.g., oblivious transfer). Yet, the following question remained open:
What is the exact power of the random oracle model?
We make progress towards answering this question, showing that essentially, any no private input, semi-honest two-party functionality that can be securely implemented in the random oracle model, can be securely implemented information theoretically (where parties are assumed to be all powerful, and no oracle is given). We further generalize the above result to function families that provide some natural combinatorial property.
Our result immediately yields that essentially the only no-input functionalities that can be securely realized in the random oracle model (in the sense of secure function evaluation), are the trivial ones (ones that can be securely realized information theoretically). In addition, we use the recent information theoretic impossibility result of McGregor et al. [FOCS ’10], to show the existence of functionalities (e.g., inner product) that cannot be computed both accurately and in a differentially private manner in the random oracle model; yielding that protocols for computing these functionalities cannot be black-box reduced to one-way functions.
Chapter PDF
References
Barak, B., Mahmoody-Ghidary, M.: Merkle Puzzles Are Optimal — An O(n2)-Query Attack on Any Key Exchange from a Random Oracle. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 374–390. Springer, Heidelberg (2009)
Beimel, A., Nissim, K., Omri, E.: Distributed private data analysis: On simultaneously solving how and what. CoRR, abs/1103.2626 (2011)
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)
Chang, Y.-C., Hsiao, C.-Y., Lu, C.-J.: On the Impossibilities of Basing One-Way Permutations on Central Cryptographic Primitives. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 110–124. Springer, Heidelberg (2002)
Dachman-Soled, D., Lindell, Y., Mahmoody, M., Malkin, T.: On the Black-Box Complexity of Optimally-Fair Coin Tossing. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 450–467. Springer, Heidelberg (2011)
Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Gennaro, R., Trevisan, L.: Lower bounds on the efficiency of generic cryptographic constructions. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp. 305–313 (2000)
Gennaro, R., Gertner, Y., Katz, J., Trevisan, L.: Bounds on the efficiency of generic cryptographic constructions. SIAM Journal on Computing 35(1), 217–246 (2005)
Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The relationship between public key encryption and oblivious transfer. In: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC (2000)
Goldwasser, S., Tauman-Kalai, Y.: On the (in)security of the fiat-shamir paradigm. In: Proceedings of the 44th Annual Symposium on Foundations of Computer Science, FOCS (2003)
Haitner, I., Hoch, J.J., Reingold, O., Segev, G.: Finding collisions in interactive protocols – A tight lower bound on the round complexity of statistically-hiding commitments. In: Proceedings of the 48th Annual Symposium on Foundations of Computer Science, FOCS (2007)
Haitner, I., Omri, E., Zarosim, H.: Limits on the usefulness of random oracles. Technical Report 2012/573, Cryptology ePrint Archive (2012), http://eprint.iacr.org/2012/573
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 (STOC), pp. 44–61. ACM Press (1989)
Kahn, J., Saks, M., Smyth, C.: A dual version of reimer’s inequality and a proof of rudich’s conjecture. In: Proceedings of the 15th Annual IEEE Conference on Computational Complexity, 2000, pp. 98–103 (2000)
Kim, J.H., Simon, D., Tetali, P.: Limits on the efficiency of one-way permutation-based hash functions. In: 40th Annual Symposium on Foundations of Computer Science, 1999, pp. 535–542 (1999)
Mahmoody, M., Maji, H.K., Prabhakaran, M.: Limits of random oracles in secure computation. Technical Report, arXiv:1205.3554v1 (2012)
McGregor, A., Mironov, I., Pitassi, T., Reingold, O., Talwar, K., Vadhan, S.P.: The limits of two-party differential privacy. In: Electronic Colloquium on Computational Complexity (ECCC), p. 106 (2011); Preliminary version in FOCS 2010 (2010)
Merkle, R.C.: Secure communications over insecure channels. In: SIMMONS: Secure Communications and Asymmetric Cryptosystems (1982)
Mironov, I., Pandey, O., Reingold, O., Vadhan, S.: Computational Differential Privacy. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 126–142. Springer, Heidelberg (2009)
Pointcheval, D., Stern, J.: Security Proofs for Signature Schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387–398. Springer, Heidelberg (1996)
Rudich, S.: The Use of Interaction in Public Cryptosystems. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 242–251. Springer, Heidelberg (1992)
Simon, D.R.: Findings Collisions on a One-Way Street: Can Secure Hash Functions Be Based on General Assumptions? In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 334–345. Springer, Heidelberg (1998)
Wee, H.: One-Way Permutations, Interactive Hashing and Statistically Hiding Commitments. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 419–433. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 International Association for Cryptologic Research
About this paper
Cite this paper
Haitner, I., Omri, E., Zarosim, H. (2013). Limits on the Usefulness of Random Oracles. In: Sahai, A. (eds) Theory of Cryptography. TCC 2013. Lecture Notes in Computer Science, vol 7785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36594-2_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-36594-2_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36593-5
Online ISBN: 978-3-642-36594-2
eBook Packages: Computer ScienceComputer Science (R0)