## CryptoDB

### Paper: Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Authors: Serge Fehr Chen Yuan DOI: 10.1007/978-3-030-17659-4_16 Search ePrint Search Google Robust secret sharing enables the reconstruction of a secret-shared message in the presence of up to t (out of n) incorrect shares. The most challenging case is when $n = 2t+1$, which is the largest t for which the task is still possible, up to a small error probability $2^{-\kappa }$ and with some overhead in the share size.Recently, Bishop, Pastro, Rajaraman and Wichs [3] proposed a scheme with an (almost) optimal overhead of $\widetilde{O}(\kappa )$. This seems to answer the open question posed by Cevallos et al. [6] who proposed a scheme with overhead of $\widetilde{O}(n+\kappa )$ and asked whether the linear dependency on n was necessary or not. However, a subtle issue with Bishop et al.’s solution is that it (implicitly) assumes a non-rushing adversary, and thus it satisfies a weaker notion of security compared to the scheme by Cevallos et al. [6], or to the classical scheme by Rabin and BenOr [13].In this work, we almost close this gap. We propose a new robust secret sharing scheme that offers full security against a rushing adversary, and that has an overhead of $O(\kappa n^\varepsilon )$, where $\varepsilon > 0$ is arbitrary but fixed. This $n^\varepsilon$-factor is obviously worse than the $\mathrm {polylog}(n)$-factor hidden in the $\widetilde{O}$ notation of the scheme of Bishop et al. [3], but it greatly improves on the linear dependency on n of the best known scheme that features security against a rushing adversary (when $\kappa$ is substantially smaller than n).A small variation of our scheme has the same $\widetilde{O}(\kappa )$ overhead as the scheme of Bishop et al. and achieves security against a rushing adversary, but suffers from a (slightly) superpolynomial reconstruction complexity.
##### BibTeX
@article{eurocrypt-2019-29394,
title={Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary},
booktitle={Advances in Cryptology – EUROCRYPT 2019},
series={Advances in Cryptology – EUROCRYPT 2019},
publisher={Springer},
volume={11478},
pages={472-499},
doi={10.1007/978-3-030-17659-4_16},
author={Serge Fehr and Chen Yuan},
year=2019
}