Abstract
In symmetric secure function evaluation (SSFE), Alice has an input x, Bob has an input y, and both parties wish to securely compute f(x,y). We show several new results classifying the feasibility of securely implementing these functions in several security settings. Namely, we give new alternate characterizations of the functions that have (statistically) secure protocols against passive and active (standalone), computationally unbounded adversaries. We also show a strict, infinite hierarchy of complexity for SSFE functions with respect to universally composable security against unbounded adversaries. That is, there exists a sequence of functions f 1, f 2, ... such that there exists a UC-secure protocol for f i in the f j -hybrid world if and only if i ≤ j.
The main new technical tool that unifies our unrealizability results is a powerful protocol simulation theorem, which may be of independent interest. Essentially, in any adversarial setting (UC, standalone, or passive), f is securely realizable if and only if a very simple (deterministic) “canonical” protocol for f achieves the desired security. Thus, to show that f is unrealizable, one need simply demonstrate a single attack on a single simple protocol.
The original version of the book was revised: The copyright line was incorrect. The Erratum to the book is available at DOI: 10.1007/978-3-642-00457-5_36
Partially supported by NSF grants CNS 07-47027 and CNS 07-16626.
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References
Backes, M., Müller-Quade, J., Unruh, D.: On the necessity of rewinding in secure multiparty computation. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 157–173. Springer, Heidelberg (2007)
Beaver, D.: Perfect privacy for two-party protocols. In: Feigenbaum, J., Merritt, M. (eds.) Proceedings of DIMACS Workshop on Distributed Computing and Cryptography, vol. 2, pp. 65–77. American Mathematical Society (1989)
Beimel, A., Malkin, T., Micali, S.: The all-or-nothing nature of two-party secure computation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 80–97. Springer, Heidelberg (1999)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. Electronic Colloquium on Computational Complexity (ECCC) TR01-016 (2001); Extended abstract in FOCS 2001
Canetti, R., Kushilevitz, E., Lindell, Y.: On the limitations of universally composable two-party computation without set-up assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656. Springer, Heidelberg (2003)
Chor, B., Kushilevitz, E.: A zero-one law for boolean privacy (extended abstract). In: STOC, pp. 62–72. ACM, New York (1989)
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(3), 691–729 (1991); Preliminary version in FOCS 1986
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: STOC, pp. 44–61. ACM Press, New York (1989)
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)
Kilian, J.: Founding cryptography on oblivious transfer. In: STOC, pp. 20–31. ACM, New York (1988)
Kilian, J.: Uses of Randomness in Algorithms and Protocols. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (1989)
Kilian, J.: A general completeness theorem for two-party games. In: STOC, pp. 553–560. ACM, New York (1991)
Kilian, J.: More general completeness theorems for secure two-party computation. In: Proc. 32nd STOC, pp. 316–324. ACM, New York (2000)
Kilian, J., Kushilevitz, E., Micali, S., Ostrovsky, R.: Reducibility and completeness in private computations. SIAM J. Comput. 29(4), 1189–1208 (2000)
Kraschewski, D., Müller-Quade, J.: Completeness theorems with constructive proofs for symmetric, asymmetric and general 2-party-functions (unpublished manuscript, 2008)
Künzler, R., Müller-Quade, J., Raub, D.: Secure computability of functions in the it setting with dishonest majority and applications to long-term security (in these proceedings)
Kushilevitz, E.: Privacy and communication complexity. In: FOCS, pp. 416–421. IEEE, Los Alamitos (1989)
Lindell, Y.: Lower bounds for concurrent self composition. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 203–222. Springer, Heidelberg (2004)
Maji, H., Prabhakaran, M., Rosulek, M.: Complexity of multiparty computation problems: The case of 2-party symmetric secure function evaluation. Cryptology ePrint Archive, Report 2008/454 (2008), http://eprint.iacr.org/
Prabhakaran, M., Rosulek, M.: Cryptographic complexity of multi-party computation problems: Classifications and separations. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 262–279. Springer, Heidelberg (2008)
Yao, A.C.: Protocols for secure computation. In: Proc. 23rd FOCS, pp. 160–164. IEEE, Los Alamitos (1982)
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Maji, H.K., Prabhakaran, M., Rosulek, M. (2009). Complexity of Multi-party Computation Problems: The Case of 2-Party Symmetric Secure Function Evaluation. In: Reingold, O. (eds) Theory of Cryptography. TCC 2009. Lecture Notes in Computer Science, vol 5444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00457-5_16
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