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Secret leader election in consensus could protect leaders from Denial of Service (DoS) or bribery attacks, enhancing the blockchain system security. Single Secret Leader Election (SSLE), proposed by Boneh et al., supports electing a single random leader from a group of nodes while the leader’s identity remains secret until he reveals himself. Subsequent research endeavors have introduced distinct approaches to realize SSLE, yet most of these solutions consume relatively high communication complexity. In this paper, we propose an extended SSLE scheme, Secret Multiple Leaders Election (SMLE), based on linkable membership proof. A general SMLE scheme supports the one-time election of multiple consecutive secret leaders while reducing the average communication cost of a single leader election to constant complexity. In particular, SMLE is proven to satisfy a newly proposed consistent unpredictability property for each leader. Specifically, two concrete SMLE constructions are constructed. ....

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