# Information Security and Cryptography Research Group

## Broadcast (and Round) Efficient Verifiable Secret Sharing

### Juan Garay, Clint Givens, Rafail Ostrovsky, and Pavel Raykov

The 7th International Conference on Information Theoretic Security — ICITS 2013, Lecture Notes in Computer Science, Springer, vol. 8317, pp. 200–219, Nov 2013.

Verifiable secret sharing (VSS) is a fundamental cryptographic primitive, lying at the core of secure multi-party computation (MPC) and, as the distributed analogue of a commitment functionality, used in numerous applications. In this paper we focus on unconditionally secure VSS protocols with honest majority.

In this setting it is typically assumed that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast” channel. Because broadcast cannot be simulated on a point-to-point network when a third or more of the parties are corrupt, it is impossible to construct VSS (and more generally, MPC) protocols in this setting without using a broadcast channel (or some equivalent addition to the model).

A great deal of research has focused on increasing the efficiency of VSS, primarily in terms of round complexity. In this work we consider a refinement of the round complexity of VSS, by adding a measure we term broadcast complexity. We view the broadcast channel as an expensive resource and seek to minimize the number of rounds in which it is invoked as well.

We construct a (linear) VSS protocol which uses the broadcast channel only twice in the sharing phase, while running in an overall constant number of rounds.

## BibTeX Citation

@inproceedings{GGOR13,
author       = {Juan Garay and Clint Givens and Rafail Ostrovsky and Pavel Raykov},
title        = {Broadcast (and Round) Efficient Verifiable Secret Sharing},