Abstract
Secure computation (i.e., performing computation while keeping privacy of the inputs) is a fundamental research area in cryptography and a fundamental capability in the theory of computing. Deterministic automata evaluation is a fundamental computation problem, with numerous application areas, including regular expressions, string matching, constant-space computations.
In this paper, we investigate the complexity of achieving secure 2-party deterministic automata evaluation protocols. We show black-box reductions between this problem and the problem of constructing secure 2-party information retrieval protocols, and viceversa. Using previous results, this implies various interesting consequences: completeness of secure deterministic automata evaluation in the class of problems having 2-party and multi-party secure function evaluation protocols (previously, only 2 less natural problems were showed to be complete, or non-constructive characterizations of complete problems were given), and, under standard cryptographic assumptions, a communication-efficient secure protocol for automata evaluation (no such problem was given in the literature) and a time-efficient secure protocol faster than applying Yao’s benchmark general solution.
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References
Aiello, B., Ishai, Y., Reingold, O.: Priced oblivious transfer: how to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_8
Bogetoft, P., et al.: Secure multiparty computation goes live. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 325–343. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03549-4_20
Di Crescenzo, G., Cook, D.L., McIntosh, A., Panagos, E.: Practical and privacy-preserving information retrieval from a database table. J. Comput. Secur. 24(4), 479–506 (2016)
Di Crescenzo, G., Malkin, T., Ostrovsky, R.: Single database private information retrieval implies oblivious transfer. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 122–138. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6_10
Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)
Freedman, M.J., Ishai, Y., Pinkas, B., Reingold, O.: Keyword search and oblivious pseudorandom functions. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 303–324. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_17
Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38(1), 691–729 (1991)
Goldreich, O.: The Foundations of Cryptography: Volume 2, Basic Applications. Cambridge University Press, Cambridge (2004)
Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)
Harnik, D., Naor, M., Reingold, O., Rosen, A.: Completeness in two-party secure computation: a computational view. J. Cryptol. 19(4), 521–552 (2006)
Huang, Y., Evans, D., Katz, J., Malka, L.: Faster secure two-party computation using garbled circuits. In: Proceedings of the 20th USENIX Security Symposium, San Francisco, CA, USA, 8–12 August 2011 (2011)
Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_31
Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_32
Kilian, J.: A note on efficient proofs and arguments. In: Proceedings of ACM STOC 1992 (1992)
Kilian, J.: Founding cryptography on oblivious transfer. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, USA, 2–4 May 1988, pp. 20–31 (1988)
Kilian, J., Kushilevitz, E., Micali, S., Ostrovsky, R.: Reducibility and completeness in private computations. SIAM J. Comput. 29(4), 1189–1208 (2000)
Kushilevitz, E., Ostrovsky, R.: Replication is NOT needed: SINGLE database, computationally-private information retrieval. In: 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, Miami Beach, Florida, USA, 19–22 October 1997, pp. 364–373 (1997)
Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - secure two-party computation system. In: Proceedings of the 13th USENIX Security Symposium, San Diego, CA, USA, 9–13 August 2004, pp. 287–302 (2004)
Mohassel, P., Niksefat, S., Sadeghian, S., Sadeghiyan, B.: An efficient protocol for oblivious DFA evaluation and applications. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 398–415. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27954-6_25
Rabin, M.O.: How to exchange secrets with oblivious transfer. IACR Cryptology ePrint Archive 2005:187 (2005)
Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167 (1986)
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This work was supported by the Defense Advanced Research Projects Agency (DARPA) via Air Force Research Laboratory (AFRL), contract number FA8750-14-C-0057. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation hereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA, AFRL or the U.S. Government.
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Di Crescenzo, G., Coan, B., Kirsch, J. (2020). Secure Deterministic Automata Evaluation: Completeness and Efficient 2-party Protocols. In: Simion, E., Géraud-Stewart, R. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2019. Lecture Notes in Computer Science(), vol 12001. Springer, Cham. https://doi.org/10.1007/978-3-030-41025-4_4
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