Communication-optimal proactive secret sharing for dynamic groups

Abstract

Proactive secret sharing (PSS) schemes are designed for settings where long-term confidentiality of secrets is required, 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 of parties is replaced with a corruption rate which cannot be violated. In dynamic proactive secret sharing (DPSS) the group of participating parties can vary during the course of execution. Accordingly, 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 scheme with optimal amortized per-secret communication in the number of parties, n: This paper requires O(1) communication, as compared to O(n4) or exp(n) in previous work. 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.