Publicly Auditable Secure Multi-Party Computation
In the last few years the efficiency of secure multi-party computation (MPC) increased in several orders of magnitudes. However, this alone might not be enough if we want MPC protocols to be used in practice. A crucial property that is needed in many applications is that everyone can check that a given (secure) computation was performed correctly – even in the extreme case where all the parties involved in the computation are corrupted, and even if the party who wants to verify the result was not participating. This is especially relevant in the clients-servers setting, where many clients provide input to a secure computation performed by a few servers. An obvious example of this is electronic voting, but also in many types of auctions one may want independent verification of the result. Traditionally, this is achieved by using non-interactive zero-knowledge proofs during the computation.
A recent trend in MPC protocols is to have a more expensive preprocessing phase followed by a very efficient online phase, e.g., the recent so-called SPDZ protocol by Damgård et al. Applications such as voting and some auctions are perfect use-case for these protocols, as the parties usually know well in advance when the computation will take place, and using those protocols allows us to use only cheap information-theoretic primitives in the actual computation. Unfortunately no protocol of the SPDZ type supports an audit phase.
In this paper, we show how to achieve efficient MPC with a public audit. We formalize the concept of publicly auditable secure computation and provide an enhanced version of the SPDZ protocol where, even if all the servers are corrupted, anyone with access to the transcript of the protocol can check that the output is indeed correct. Most importantly, we do so without significantly compromising the performance of SPDZ i.e. our online phase has complexity approximately twice that of SPDZ.
KeywordsEfficient Multi-Party Computation Public Verifiability Electronic Voting
Unable to display preview. Download preview PDF.
- 1.Helios, B.A.: Web-based open-audit voting. In: USENIX Security Symposium, vol. 17, pp. 335–348 (2008)Google Scholar
- 2.Ajtai, M., Komlós, J., Szemerédi, E.: An o(n log n) sorting network. In: STOC, pp. 1–9 (1983)Google Scholar
- 4.Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992)Google Scholar
- 8.Chaum, D., Ryan, P.Y.A., Schneider, S.: A practical voter-verifiable election scheme. In: De Capitani di Vimercati, S., Syverson, P., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 118–139. Springer, Heidelberg (2005)Google Scholar
- 10.Cohen, J.D., Fischer, M.J.: A robust and verifiable cryptographically secure election scheme. In: FOCS, vol. 85, pp. 372–382 (1985)Google Scholar
- 15.Jacobus, S., de Hoogh, A.: Design of Large Scale Applications of Secure Multiparty Computation: Secure Linear Programming. PhD thesis, Technische Universiteit Eindhoven (2012)Google Scholar
- 16.Fiore, D., Gennaro, R.: Publicly verifiable delegation of large polynomials and matrix computations, with applications. In: ACM Conference on Computer and Communications Security, pp. 501–512 (2012)Google Scholar
- 19.Huang, Y., Evans, D., Katz, J.: Private set intersection: Are garbled circuits better than custom protocols? In: NDSS (2012)Google Scholar
- 21.Lim, C.H., Lee, P.J.: More flexible exponentiation with precomputation. In: Desmedt, Y.G. (ed.) Advances in Cryptology - CRYPT0 1994. LNCS, vol. 839, pp. 95–107. Springer, Heidelberg (1994)Google Scholar
- 23.Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: Proceedings of the 1st ACM Conference on Electronic Commerce, pp. 129–139. ACM (1999)Google Scholar
- 25.Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) Advances in Cryptology - CRYPT0 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)Google Scholar
- 27.Sako, K., Kilian, J.: Receipt-free mix-type voting scheme. In: Guillou, L.C., Quisquater, J.-J. (eds.) Advances in Cryptology - EUROCRYPT 1995. LNCS, vol. 921, pp. 393–403. Springer, Heidelberg (1995)Google Scholar
- 29.Stadler, M.A.: Publicly verifiable secret sharing. In: Maurer, U.M. (ed.) Advances in Cryptology - EUROCRYPT 1996. LNCS, vol. 1070, pp. 190–199. Springer, Heidelberg (1996)Google Scholar
- 30.Truderung, T., Vogt, A., Küsters, R.: Accountability: definition and relationship to verifiability. In: Proceedings of the 17th ACM Conference on Computer and Communications Security, pp. 526–535. ACM (2010)Google Scholar