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Proof-of-stake blockchain protocols are becoming one of the most promisingalternatives to the energy-consuming proof-of-work protocols. However, oneparticularly critical threat in the PoS setting is the well-known long-rangeattacks caused by secret key leakage (LRSL attack). Specifically, an adversarycan attempt to control/compromise accounts possessing substantial stake at somepast moment such that double-spend or erase past transactions, violating thefundamental persistence property of blockchain. Puncturable signatures providea satisfying solution to construct practical proof-of-stake blockchainresilient to LRSL attack, despite of the fact that existent constructions arenot efficient enough for practical deployments.  In this paper, we provide an in-depth study of puncturable signatures andexplore its applications in the proof-of-stake blockchain. We formalize asecurity model that allows the adversary for adaptive signing and puncturingqueries, and show a construction with efficient puncturing operations based onthe Bloom filter data structure and strong Diffie-Hellman assumption. Thepuncturing functionality we desire is for a particular part of message, likeprefix, instead of the whole message. Furthermore, we use puncturablesignatures to construct practical proof-of-stake blockchain protocols that areresilient to LRSL attack, while previously the forward-secure signature is usedto immunize this attack. We implement our scheme and provide experimentalresults showing that in comparison with the forward-secure signature, ourconstruction performs substantially better on signature size, signing andverification efficiency, significantly on key update efficiency.

Puncturable Signatures and Applications in Proof-of-Stake Blockchain Protocol