Efficient Secure Multiparty Computation Protocol in Asynchronous Network

Abstract

This paper proposes an efficient secure multiparty computation protocol among n players resilient to $t<\frac{n}{4}$ players in asynchronous model. We use Batch Secret Sharing [9] as building blocks. The construction of our protocol is along the line of [7]and [2] which work in synchronous model. The execution of our protocol can be divided into two phases: Pre-computation phase and the Circuit evaluation phase. The pre-computation phase needs to communicate $O( n^4 \lg |\mathcal{F}| + mn^2 \log |\mathcal{F}|)$ bits and Broadcast $O(n^2 \lg |\mathcal{F}|)$ bits, where m is the number of multiplication gates in the circuit and the circuit is over a finite field $\mathcal{F}$. The circuit evaluation phase needs to communicate $O(n^3 \lg |\mathcal{F}|+n^4 \lg n+mn^2 \lg |\mathcal{F}|)$ bits and Broadcast $O(n^2 \lg n)$ bits. Compared with the well-known secure multiparty computation protocol in asynchronous model [4] which needs to communicate $O(mn^4 \lg |\mathcal{F}|+mn^4 \lg n)$ bits and broadcast $O(mn^4 \lg n)$ bits, our protocol is quite efficient.