Active Security in Multiparty Computation over Black-Box Groups
Most previous work on unconditionally secure multiparty computation has focused on computing over a finite field (or ring). Multiparty computation over other algebraic structures has not received much attention, but is an interesting topic whose study may provide new and improved tools for certain applications. At CRYPTO 2007, Desmedt et al introduced a construction for a passive-secure multiparty multiplication protocol for black-box groups, reducing it to a certain graph coloring problem, leaving as an open problem to achieve security against active attacks.
We present the first n-party protocol for unconditionally secure multiparty computation over a black-box group which is secure under an active attack model, tolerating any adversary structure Δ satisfying the Q 3 property (in which no union of three subsets from Δ covers the whole player set), which is known to be necessary for achieving security in the active setting. Our protocol uses Maurer’s Verifiable Secret Sharing (VSS) but preserves the essential simplicity of the graph-based approach of Desmedt et al, which avoids each shareholder having to rerun the full VSS protocol after each local computation. A corollary of our result is a new active-secure protocol for general multiparty computation of an arbitrary Boolean circuit.
KeywordsMulti-Party Computation General Adversary Structures Non-Abelian Group Black-Box Graph Colouring Active Security
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- 1.Barrington, D.A.: Bounded-Width Polynomial-Size Branching Programs Recognize Exactly Those Languages in NC 1. In: STOC 1986, pp. 1–5 (1986)Google Scholar
- 3.Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In: STOC 1988, pp. 1–10 (1988)Google Scholar
- 4.Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: STOC 1988, pp. 11–19 (1988)Google Scholar
- 8.Desmedt, Y., Pieprzyk, J., Steinfeld, R., Sun, X., Tartary, C., Wang, H., Yao, A.C.-C.: Graph coloring applied to secure computation in non-abelian groups. J. Cryptology (to appear, 2011)Google Scholar
- 10.Fitzi, M., Hirt, M., Maurer, U.M.: Trading Correctness for Privacy in Unconditional Multi-party Computation. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 121–136. Springer, Heidelberg (1998)Google Scholar
- 13.Goldreich, O.: Foundations of Cryptography: vol. II - Basic Applications. Cambridge University Press (2004)Google Scholar
- 14.Goldreich, O., Micali, S., Wigderson, A.: How to Play Any Mental Game. In: STOC 1987, pp. 218–229 (1987)Google Scholar
- 15.Hirt, M., Maurer, U.: Complete Characterization of Adversaries Tolerable in Secure Multi-Party Computation. In: PODC 1997, pp. 25–34 (1997)Google Scholar