Unconditionally secure proactive verifiable secret sharing using new detection and recovery techniques

In this paper, a new proactive verifiable secret sharing (PVSS) scheme is proposed in an active mobile adversary setting. To the best of our knowledge, the only unconditionally secure PVSS is proposed in ASIACRYPT'02 by D'Arco and Stinson. In this protocol, the authors assume the existence of private channels as well as an authenticated broadcast channel. This scheme uses symmetric bivariate polynomials for secret sharing, i.e., each share is a polynomial over a finite field rather than a single field element, under the assumption that t <; n/4 where t is the threshold. We propose a new PVSS scheme with prominent properties using a simple detection method along with a novel recovery-and-renewal technique. First of all, we only consider private channels in our setting. In addition, our scheme can tolerate t <; n/3 corrupted players. Although we utilize a VSS scheme as a subprotocol in our scheme, shares of the secret are single field elements after the initialization by the dealer.