Proof-of-stake blockchain protocols are becoming one of the most promising alternatives to the energy-consuming proof-of-work protocols. However, one particularly critical threat in the PoS setting is the well-known long-range attacks caused by secret key leakage (LRSL attack). Specifically, an adversary can attempt to control/compromise accounts possessing substantial stake at some past moment such that double-spend or erase past transactions, violating the fundamental persistence property of blockchain. Puncturable signatures provide a satisfying solution to construct practical proof-of-stake blockchain resilient to LRSL attack, despite of the fact that existent constructions are not efficient enough for practical deployments. In this paper, we provide an in-depth study of puncturable signatures and explore its applications in the proof-of-stake blockchain. We formalize a security model that allows the adversary for adaptive signing and puncturing queries, and show a construction with efficient puncturing operations based on the Bloom filter data structure and strong Diffie-Hellman assumption. The puncturing functionality we desire is for a particular part of message, like prefix, instead of the whole message. Furthermore, we use puncturable signatures to construct practical proof-of-stake blockchain protocols that are resilient to LRSL attack, while previously the forward-secure signature is used to immunize this attack. We implement our scheme and provide experimental results showing that in comparison with the forward-secure signature, our construction performs substantially better on signature size, signing and verification efficiency, significantly on key update efficiency.

中文翻译：

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权益证明区块链协议中的可伪签名及其应用

权益证明区块链协议正在成为耗能的工作量证明协议的最有希望的替代方案之一。但是，在PoS设置中，一个特别关键的威胁是由秘密密钥泄漏（LRSL攻击）引起的众所周知的远程攻击。具体来说，攻击者可能试图在过去的某个时刻控制/损害拥有大量股份的账户，从而使支出双倍支出或擦除过去的交易，从而违反了区块链的基本持久性。可穿刺签名提供了令人满意的解决方案，以构建可抵抗LRSL攻击的实用的权益证明区块链，尽管事实是，现有的构建对于实际部署而言效率不足。在本文中，我们提供了对可穿孔签名的深入研究，并探讨了其在权益证明区块链中的应用。我们将安全模型正式化，该模型允许对手进行自适应签名和删余查询，并基于Bloom过滤器数据结构和强大的Diffie-Hellman假设，展示了具有高效删余操作的结构。我们需要的打孔功能是针对消息的特定部分（例如前缀），而不是整个消息。此外，我们使用可穿孔签名来构建可抵抗LRSL攻击的实用的权益证明区块链协议，而以前使用前向安全签名来免疫此攻击。我们实施了该方案，并提供了实验结果，表明与前向安全签名相比，