Churp

Abstract

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(n 2 ) 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 secretsharing 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 peerto-peer networks of permissionless blockchains.We formally prove the security of CHURP, report on an implementation, and present performance measurements.

A Dynamic Proactive Secret Sharing Scheme for Quadratic Functions

“…Any mobile and active PPT adversary A that controls ≤ t parties from C and ≤ t parties from C learns no information about the secret vector s or the N evaluation results {F k (s)} N k=1 . Remark 1: Similar to [18], the integrity and secrecy and of our DPFSS are informally defined. Proofs of these properties are quite formal and depend on the design idea that every message in our scheme will be verified and the sender of a maliciously designed message will be removed from the protocol execution immediately.…”

“…Therefore, the secrecy of our DPFSS scheme holds throughout the execution. V. PERFORMANCE EVALUATION Like [17], [18], the efficiency of our DPFSS scheme DPFSS can be measured with its communication complexity and time complexity.…”

“…However, in many real-life scenarios [13]- [15], the participants may join and leave a data management system arbitrarily and thus result in dynamic groups of participants. Dynamic proactive secret sharing (DPSS) [16]- [18] allows a client to share a secret s among a committee C = {P 1 , . .…”

Multisecret‐sharing scheme with two‐level security and its applications in blockchain

“…Also, in recent years, many blockchain‐based SSSs were introduced to outcome the limitation of dishonest participants. To protect the secret from attackers, many authors used the threshold $$t/m$$ less than $$1/2$$ [14–18].…”