Perfectly-Secure Multiplication for Any t < n/3
In the setting of secure multiparty computation, a set of n parties with private inputs wish to jointly compute some functionality of their inputs. One of the most fundamental results of information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. The most technically challenging part of this result is a protocol for multiplying two shared values, with perfect security in the presence of up to t < n/3 malicious adversaries.
In this paper we provide a full specification of the BGW perfect multiplication protocol and prove its security. This includes one new step for the perfect multiplication protocol in the case of n/4 ≤ t < n/3. As in the original BGW protocol, this protocol works whenever the parties hold univariate (Shamir) shares of the input values. In addition, we present a new multiplication protocol that utilizes bivariate secret sharing in order to achieve higher efficiency while maintaining a round complexity that is constant per multiplication. Both of our protocols are presented with full proofs of security.
KeywordsSecret Sharing Multiplication Protocol Univariate Polynomial Full Proof Honest Party
- 1.Asharov, G., Lindell, Y., Rabin, T.: A Full Proof of the Perfectly-Secure BGW Protocol and Improvements. Cryptology ePrint Archive, 2011/136 (2011)Google Scholar
- 4.Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In: 20th STOC, pp. 1–10 (1988)Google Scholar
- 6.Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols. In: 42nd FOCS, pp. 136–145 (2001)Google Scholar
- 11.Goldreich, O.: Foundations of Cryptography: Volume 2 – Basic Applications. Cambridge University Press, Cambridge (2004)Google Scholar
- 12.Feldman, P.: Optimal Algorithms for Byzantine Agreement. PhD thesis, Massachusetts Institute of Technology (1988)Google Scholar
- 14.Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and Fact-Track Multiparty Computations with Applications to Threshold Cryptography. In: 17th PODC, pp. 101–111 (1998)Google Scholar