Brief Announcement

Abstract

In a secret sharing scheme a dealer shares a secret s among n parties such that an adversary corrupting up to t parties does not learn s, while any t+1 parties can efficiently recover s. Over a long period of time all parties may be corrupted thus violating the threshold, which is accounted for in Proactive Secret Sharing (PSS). PSS schemes periodically rerandomize (refresh) the shares of the secret and invalidate old ones. PSS retains confidentiality even when all parties are corrupted over the lifetime of the secret, but no more than t during a certain window of time, called the refresh period. Existing PSS schemes only guarantee secrecy in the presence of an honest majority with less than n2 total corruptions during a refresh period; an adversary corrupting a single additional party, even if only passively, obtains the secret. This work is the first feasibility result demonstrating PSS tolerating a dishonest majority, it introduces the first PSS scheme secure against t