An Efficient Protocol for Secure Two-Party Computation in the Presence of Malicious Adversaries
We show an efficient secure two-party protocol, based on Yao’s construction, which provides security against malicious adversaries. Yao’s original protocol is only secure in the presence of semi-honest adversaries. Security against malicious adversaries can be obtained by applying the compiler of Goldreich, Micali and Wigderson (the “GMW compiler”). However, this approach does not seem to be very practical as it requires using generic zero-knowledge proofs.
Our construction is based on applying cut-and-choose techniques to the original circuit and inputs. Security is proved according to the ideal/real simulation paradigm, and the proof is in the standard model (with no random oracle model or common reference string assumptions). The resulting protocol is computationally efficient: the only usage of asymmetric cryptography is for running O(1) oblivious transfers for each input bit (or for each bit of a statistical security parameter, whichever is larger). Our protocol combines techniques from folklore (like cut-and-choose) along with new techniques for efficiently proving consistency of inputs. We remark that a naive implementation of the cut-and-choose technique with Yao’s protocol does not yield a secure protocol. This is the first paper to show how to properly implement these techniques, and to provide a full proof of security.
Our protocol can also be interpreted as a constant-round black-box reduction of secure two-party computation to oblivious transfer and perfectly-hiding commitments, or a black-box reduction of secure two-party computation to oblivious transfer alone, with a number of rounds which is linear in a statistical security parameter. These two reductions are comparable to Kilian’s reduction, which uses OT alone but incurs a number of rounds which is linear in the depth of the circuit .
KeywordsSecure Protocol Commitment Scheme Oblivious Transfer Honest Party Malicious Adversary
- 4.Beaver, D.: Foundations of Secure Interactive Computing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 377–391. Springer, Heidelberg (1992)Google Scholar
- 6.Cramer, R.J.F., Damgård, I.B., Schoenmakers, B.: Proof of Partial Knowledge and Simplified Design of Witness Hiding Protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)Google Scholar
- 9.Goldreich, O.: Foundations of Cryptography: Volume 2 – Basic Applications. Cambridge University Press, Cambridge (2004)Google Scholar
- 11.Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game – A Completeness Theorem for Protocols with Honest Majority. In: 19th STOC, pp. 218–229 (1987), For details see: Goldreich, O.: Foundations of Cryptography: Volume 2 – Basic Applications. Cambridge University Press, Cambridge (2004)Google Scholar
- 12.Goldwasser, S., Levin, L.: Fair Computation of General Functions in Presence of Immoral Majority. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 77–93. Springer, Heidelberg (1991)Google Scholar
- 14.Halevi, S., Micali, S.: Practical and Provably-Secure Commitment Schemes from Collision-Free Hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 201–215. Springer, Heidelberg (1996)Google Scholar
- 15.Jarecki, S., Shmatikov, V.: Efficient Two-Party Secure Computation on Committed Inputs. Eurocrypt 2007, in these proceedings (2007)Google Scholar
- 18.Kilian, J.: Founding Cryptography on Oblivious Transfer. In: 20th STOC, pp. 20–31 (1988)Google Scholar
- 19.Kiraz, M., Schoenmakers, B.: A Protocol Issue for the Malicious Case of Yao’s Garbled Circuit Construction. In: Proceedings of 27th Symposium on Information Theory in the Benelux, pp. 283–290 (2006)Google Scholar
- 20.Lindell, Y., Pinkas, B.: A Proof of Yao’s Protocol for Secure Two-Party Computation. To appear in the Journal of Cryptology, Also appeared as Cryptology ePrint Archive, Report 2004/175 (2004)Google Scholar
- 21.Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay – A Secure Two-Party Computation System. In: 13th USENIX Security Symposium, pp. 287–302 (2004)Google Scholar
- 22.Micali, S., Rogaway, P.: Secure Computation. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 392–404. Springer, Heidelberg (1992)Google Scholar
- 25.Naor, M., Pinkas, B.: Efficient Oblivious Transfer Protocols. In: 12th SODA, pp. 448–457 (2001)Google Scholar
- 26.Pedersen, T.P.: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)Google Scholar
- 27.Rabin, M.: How to Exchange Secrets by Oblivious Transfer. Tech. Memo TR-81, Aiken Computation Laboratory, Harvard U. (1981)Google Scholar
- 28.Woodruff, D.: Revisiting the Efficiency of Malicious Two-Party Computation. Eurocrypt ’2007, in these proceedings (2007)Google Scholar
- 29.Yao, A.: How to Generate and Exchange Secrets. In: 27th FOCS, pp. 162–167 (1986)Google Scholar