## Cryptology ePrint Archive: Report 2015/304

Communication-Optimal Proactive Secret Sharing for Dynamic Groups

Joshua Baron and Karim El Defrawy and Joshua Lampkins and Rafail Ostrovsky

Abstract: Proactive secret sharing (PSS) schemes are designed for settings where long-term confidentiality of secrets has to be guaranteed, specifically, when all participating parties may eventually be corrupted. PSS schemes periodically refresh secrets and reset corrupted parties to an uncorrupted state; in PSS the corruption threshold $t$ is replaced with a corruption rate which cannot be violated. In dynamic proactive secret sharing (DPSS) the number of parties can vary during the course of execution. DPSS is ideal when the set of participating parties changes over the lifetime of the secret or where removal of parties is necessary if they become severely corrupted. This paper presents the first DPSS schemes with optimal amortized, $O(1)$, per-secret communication compared to $O(n^4)$ or $\exp(n)$ in number of parties, $n$, required by existing schemes. We present perfectly and statistically secure schemes with near-optimal threshold in each case. We also describe how to construct a communication-efficient dynamic proactively-secure multiparty computation (DPMPC) protocol which achieves the same thresholds.

Category / Keywords: cryptographic protocols / Proactive Security, Secret Sharing, Mobile Secret Sharing, Dynamic Groups, Secure Multiparty Computation