AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
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Given any linear secret sharing scheme with a multiplication protocol, we show that a given set of players holding shares of two values $a, b \in {\mathbb Z}_{p}$ for some prime p, it is possible to compute a sharing of ρ such that ρ = (a b) with only eight rounds and 29驴 + 36log2(驴) invocations of the multiplication protocol, where 驴 = log(p). The protocol is unconditionally secure against active/adaptive adversaries when the underlying secret sharing scheme has these properties. The proposed protocol is an improvement in the sense that it requires fewer rounds and less invocations of the multiplication protocol than previous solutions.Further, most of the work required is independent of a and b and may be performed in advance in a pre-processing phase before the inputs become available, this is important for practical implementations of multiparty computations, where one can have a set-up phase. Ignoring pre-processing in the analysis, only two rounds and 4驴 invocations of the multiplication protocol are required.