We introduce CHURP (CHUrn-Robust Proactive secret sharing). CHURP enables secure secret-sharing in dynamic settings, where the committee of nodes storing a secret changes over time. Designed for blockchains, CHURP has lower communication complexity than previous schemes: O(n) on-chain and O(n2) off-chain in the optimistic case of no node failures.

CHURP includes several technical innovations: An efficient new proactivization scheme of independent interest, a technique (using asymmetric bivariate polynomials) for efficiently changing secret-sharing thresholds, and a hedge against setup failures in an efficient polynomial commitment scheme. We also introduce a general new technique for inexpensive off-chain communication across the peer- to-peer networks of permissionless blockchains.

We formally prove the security of CHURP, report on an implementation, and present performance measurements.

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