In a single secret leader election protocol (SSLE), one of the system participants is chosen and, unless it decides to reveal itself, no other participant can identify it. SSLE has a great potential in protecting blockchain consensus protocols against denial of service (DoS) attacks. However, all existing solutions either make strong synchrony assumptions or have expiring registration, meaning that they require elected processes to re-register themselves before they can be re-elected again. This, in turn, prohibits the use of these SSLE protocols to elect leaders in partially-synchronous consensus protocols as there may be long periods of network instability when no new blocks are decided and, thus, no new registrations (or re-registrations) are possible. In this paper, we propose Homomorphic Sortition -- the first asynchronous SSLE protocol with non-expiring registration, making it the first solution compatible with partially-synchronous leader-based consensus protocols. Homomorphic Sortition relies on Threshold Fully Homomorphic Encryption (ThFHE) and is tailored to proof-of-stake (PoS) blockchains, with several important optimizations with respect to prior proposals. In particular, unlike most existing SSLE protocols, it works with arbitrary stake distributions and does not require a user with multiple coins to be registered multiple times. Our protocol is highly parallelizable and can be run completely off-chain after setup. Some blockchains require a sequence of rounds to have non-repeating leaders. We define a generalization of SSLE, called Secret Leader Permutation (SLP) in which the application can choose how many non-repeating leaders should be output in a sequence of rounds and we show how Homomorphic Sortition also solves this problem.

翻译：在单次秘密领导者选举协议（SSLE）中，系统参与者之一被选中，除非该参与者主动暴露身份，否则其他参与者无法识别其身份。SSLE在保护区块链共识协议免受拒绝服务（DoS）攻击方面具有巨大潜力。然而，现有解决方案要么要求强同步假设，要么具有注册过期特性——这意味着被选中的进程必须重新注册才能再次参与选举。这反过来阻碍了这些SSLE协议在部分同步共识协议中选举领导者，因为当网络长期不稳定、无法决定新区块时，就无法进行新注册（或重新注册）。本文提出同态抽签（Homomorphic Sortition）——首个具备非过期注册特性的异步SSLE协议，使其成为首个兼容基于部分同步领导者共识协议的解决方案。同态抽签基于阈值全同态加密（ThFHE），并针对权益证明（PoS）区块链进行定制，相较先前方案实现了多项重要优化。特别地，与大多数现有SSLE协议不同，它适用于任意权益分布，且无需持有多个币的用户进行多次注册。我们的协议具有高度并行性，且可在设置完成后完全在链外运行。某些区块链要求多轮次中不重复出现领导者。我们定义了SSLE的泛化形式——秘密领导者排列（SLP），使得应用可自主选择在连续轮次中需输出的不重复领导者数量，并证明同态抽签同样能解决该问题。