Abstract
We consider the problem of extending oblivious transfers: Given a small number of oblivious transfers “for free,” can one implement a large number of oblivious transfers? Beaver has shown how to extend oblivious transfers given a one-way function. However, this protocol is inefficient in practice, in part due to its non-black-box use of the underlying one-way function.
We give efficient protocols for extending oblivious transfers in the random oracle model. We also put forward a new cryptographic primitive which can be used to instantiate the random oracle in our constructions. Our methods suggest particularly fast heuristics for oblivious transfer that may be useful in a wide range of applications.
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References
Beaver, D.: Correlated Pseudorandomness and the Complexity of Private Computations. In: STOC, pp. 479–488 (1996)
Bellare, M., Boldyreva, A., Palacio, A.: A Separation between the Random- Oracle Model and the Standard Model for a Hybrid Encryption Problem, Electronic Colloquium on Computational Complexity. In: ECCC (2003)
Bellare, M., Rogaway, P.: Random Oracles are Practical: a Paradigm for Designing Efficient Protocols. In: Proc. of the 1st ACM Conference on Computer and Communications Security, pp. 62–73. ACM press, New York (1993)
Bellare, M., Kilian, J., Rogaway, P.: The security of cipher block chaining. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 341–358. Springer, Heidelberg (1994)
Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 91–111. Springer, Heidelberg (1994)
Brassard, G., Crépeau, C., Robert, J.-M.: All-or-nothing disclosure of secrets. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 234–238. Springer, Heidelberg (1987)
Canetti, R.: Security and composition of multiparty cryptographic protocols. J. of Cryptology 13(1) (2000)
Canetti, R., Goldreich, G., Halevi, S.: The Random Oracle Methodology, Revisited (preliminary version), STOC: ACM Symposium on Theory of Computing (1998)
Crépeau, C.: Equivalence between two flavors of oblivious transfers. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 350–354. Springer, Heidelberg (1988)
Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. C. ACM 28, 637–647 (1985)
Even, S., Mansour, Y.: A construction of a cipher from a single pseudorandom permutation. Journal of Cryptology 10(3), 151–162 (Summer 1997); Earlier version in Matsumoto, T., Imai, H., Rivest, R.L. (eds.): ASIACRYPT 1991. LNCS, vol. 739, pp. 210–224. Springer, Heidelberg (1993)
Feigenbaum, J., Ishai, Y., Malkin, T., Nissim, K., Strauss, M., Wright, R.N.: Secure multiparty computation of approximations. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 927–938. Springer, Heidelberg (2001)
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: IEEE Symposium on Foundations of Computer Science, pp. 305–313 (2000)
Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The Relationship between Public Key Encryption and Oblivious Transfer. In: Proc. of the 41st Annual Symposium on Foundations of Computer Science, FOCS 2000 (2000)
Gertner, Y., Malkin, T., Reingold, O.: On the Impossibility of Basing Trapdoor Functions on Trapdoor Predicates. In: Proc. of the 42st Annual Symposium on Foundations of Computer Science, FOCS 2001 (2001)
Gilboa, N.: Two Party RSA Key Generation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 116–129. Springer, Heidelberg (1999)
Goldreich, O.: Secure multi-party computation (February 1999), Available at http://philby.ucsb.edu/cryptolib/BOOKS
Goldreich, O., Micali, S., Wigderson, A.: Proofs that Yield Nothing but Their Validity and a Methodology of Cryptographic Protocol Design. In: Proc. of the 27th FOCS, pp. 174–187 (1986)
Goldreich, O., Vainish, R.: How to Solve Any Protocol problem – an Efficiency Improvement. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 73–86. Springer, Heidelberg (1988)
Goldwasser, S., Tauman, Y.: On the (In)security of the Fiat-Shamir Paradigm. In: Electronic Colloquium on Computational Complexity, ECCC (2003)
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proceedings of 21st Annual ACM Symposium on the Theory of Computing, pp. 44–61 (1989)
Kilian, J.: Founding Cryptography on Oblivious Transfer. In: Proc of the 20th STOC, pp. 20–29. ACM, New York (1988)
Kilian, J., Rogaway, P.: How to protect DES against exhaustive key search. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 252–267. Springer, Heidelberg (1996)
Kim, J.H., Simon, D.R., Tetali, P.: Limits on the efficiency of one-way permutations- based hash functions. In: Proceedings of the 40th IEEE Symposium on Foundations of Computer Science, pp. 535–542 (1999)
Lindell, Y., Pinkas, B.: Privacy Preserving Data Mining. Journal of Cryptology 15(3), 177–206 (2002)
Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: STOC 2001, pp. 590–599 (2001)
Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: SODA 2001 (2001)
Naor, M., Pinkas, B.: Oblivious Transfer and Polynomial Evaluation. In: STOC: ACM Symposium on Theory of Computing, STOC (1999)
Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: ACM Conference on Electronic Commerce, pp. 129–139 (1999)
Nielsen, J.: Separating random oracle proofs from complexity theoretic proofs: The non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002)
Rabin, M.O.: How to exchange secrets by oblivious transfer. Technical Report TR-81, Harvard Aiken Computation Laboratory (1981)
Shoup, V.: OAEP reconsidered. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 239–259. Springer, Heidelberg (2001)
Simon, D.: Finding 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)
Petrank, E., Rackoff, C.: Message Authentication of Unknown Variable Length Data. Journal of Cryptology 13(3), 315–338 (2000)
Yao, A.: Protocols for Secure Computations (Extended Abstract). In: Proc. of FOCS 1982, pp. 160–164 (1982)
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Ishai, Y., Kilian, J., Nissim, K., Petrank, E. (2003). Extending Oblivious Transfers Efficiently. In: Boneh, D. (eds) Advances in Cryptology - CRYPTO 2003. CRYPTO 2003. Lecture Notes in Computer Science, vol 2729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45146-4_9
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