In a secret single leader election protocol (SSLE), one of the system members is chosen as a leader and no other member can know who the leader is, unless she decides to reveal herself. Leader-election oracles are known to be instrumental in designing efficient consensus protocols, and one can expect that secret leader election may help in developing long-lived blockchain systems that are secure with respect to the adaptive adversary. In this paper, we introduce secret leader sortition (SLS) that we believe to perfectly match progress and security expectations of proof-of-stake (PoS) blockchains. An SLS protocol produces an unpredictable permutation of system members that can be fed to an accompanying blockchain protocol in order to ensure deterministic finality. We describe Homomorphic Sortition, an SLS protocol based on Threshold Fully Homomorphic Encryption (ThFHE). An interesting novelty of our protocol is a cryptographic hash function evaluation under ThFHE and, somewhat surprisingly, we show that all ThFHE stimuli required for our protocol can be efficiently and proactively constructed in a parallelizable fashion. In contrast to existing secret leader election protocols, our SLS solution is purely asynchronous and it fairly leverages the stake distribution among the system members: the probability distribution for each position in the permutation is proportional to the stakes of remaining candidates. As we demonstrate, our SLS protocol seamlessly partners with a large family of PoS blockchain implementations.

翻译：在秘密的单一领导人选举协议(SSLE)中,系统成员之一被选为领导者,其他任何成员都无法知道领导者是谁,除非她自己决定露面。 众所周知,领导人选举或触碰会有助于设计高效共识协议,人们可以预计,秘密领导人选举会有助于开发长寿的连锁系统,这种系统对于适应性对手来说是安全的。在本文中,我们引入了秘密领导人排序(SLS),我们认为它能够完全匹配实证(POS)的链锁链的进展和安全期望。 SLS协议产生了一个无法预测的系统成员变换,可以被附在一个连锁协议上,以确保最终的确定性。 我们描述的是定型模式,一个基于超常状态完全民主的加密(THFHE)的SLS协议(SS),一个令人感兴趣的新事物是加密程序在THE(SFHE)下进行功能评估,并且有些令人惊讶的是,我们协议所需要的所有THE公司链链路段都能够高效和积极地以平行的方式构建一个系统。 与目前秘密选举协议分配的系统相比,SLSLS(S)的每一个的概率分配是比例。