Paper 2007/358 Original: eprint.iacr.org/2007/358 ↗

Improving the Round Complexity of VSS in Point-to-Point Networks

Abstract

We revisit the following question: what is the optimal round complexity of verifiable secret sharing~(VSS)? We focus here on the case of perfectly-secure VSS where the number of corrupted parties~$t$ satisfies $t < n/3$, with $n$ being the total number of parties. Work of Gennaro et al. (STOC~2001) and Fitzi et al. (TCC~2006) shows that, assuming a broadcast channel, 3~rounds are necessary and sufficient for efficient VSS. The efficient 3-round protocol of Fitzi et al., however, treats the broadcast channel as being available ``for free'' and does not attempt to minimize its usage. This approach leads to relatively poor round complexity when protocols are compiled for a point-to-point network. We show here a VSS protocol that is simultaneously optimal in terms of both the number of rounds and the number of invocations of broadcast. Our protocol also has a certain ``2-level sharing'' property that makes it useful for constructing protocols for general secure computation.