Efficient Statistical Asynchronous Verifiable Secret Sharing and Multiparty Computation with Optimal Resilience

Veriflable Secret Sharing (VSS) is a fundamental primitive used as a building block in many distributed cryptographic tasks, such as Secure Multiparty Computation (MPC) and Byzantine Agreement (BA). An important variant of VSS is Asynchronous VSS (AVSS) which is designed to work over asynchronous networks. AVSS is a two phase (Sharing, Reconstruction) protocol carried out among n parties in the presence of a computationally unbounded active adversary, who can corrupt up to t parties. We assume that every two parties in the network are directly connected by a pairwise secure channel. In this paper, we present a new statistical AVSS protocol with optimal resilience; i.e. with n = 3t + 1. Our protocol privately communicates 5 O((‘n 3 + n 4 log 1 )log 1 † ) bits and A-casts 6 O(n 3 log(n)) bits to simultaneously share ‘ ‚ 1 elements from a flnite fleld F, where † is the error parameter of our protocol.

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