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Title:
Improving the Round Complexity of VSS in Point-to-Point Networks
Authors: Jonathan Katz, Chiu-Yuen Koo, Ranjit Kumaresan
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.
ePrint: https://eprint.iacr.org/2007/358
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