Proactive Secret Sharing without a Trusted Party

A (t + 1, n) proactive secret sharing is to protect a secret in long-lived system by distributing it to a group of n participants and refreshing their shares periodically in this fixed group, while any t + 1 and more than t + 1 shares can reconstruct the secret. In this paper, we propose a proactive secret sharing scheme without a trusted party, who generates and distributes shares among the participants. Our scheme is uniformly efficient and tolerates t Byzantine faults in any single time interval, where the number of participants n>=3t + 1. We also prove that the proposed scheme is secure under the discrete logarithm intractability assumption.