Byzantine consensus allows n processes to decide on a common value, in spite of arbitrary failures. The seminal Dolev-Reischuk bound states that any deterministic solution to Byzantine consensus exchanges Omega(n^2) bits. In recent years, great advances have been made in deterministic Byzantine agreement for partially synchronous networks, with state-of-the-art cryptographic solutions achieving O(n^2 \kappa) bits (where $\kappa$ is the security parameter) and nearly matching the lower bound. In contrast, for synchronous networks, optimal solutions with O(n^2) bits, with no cryptography and the same failure tolerance, have been known for more than three decades. Can this gap in network models be closed? In this paper, we present Repeater, the first generic transformation of Byzantine agreement algorithms from synchrony to partial synchrony. Repeater is modular, relying on existing and novel algorithms for its sub-modules. With the right choice of modules, Repeater requires no additional cryptography, is optimally resilient (n = 3t+1, where t is the maximum number of failures) and, for constant-size inputs, preserves the worst-case per-process bit complexity of the transformed synchronous algorithm. Leveraging Repeater, we present the first partially synchronous algorithm that (1) achieves optimal bit complexity (O(n^2) bits), (2) resists a computationally unbounded adversary (no cryptography), and (3) is optimally-resilient (n = 3t+1), thus showing that the Dolev-Reischuk bound is tight in partial synchrony. Moreover, we adapt Repeater for long inputs, introducing several new algorithms with improved complexity and weaker (or completely absent) cryptographic assumptions.

翻译：拜占庭共识允许n个进程在存在任意故障的情况下就一个共同值达成一致。开创性的Dolev-Reischuk界指出，任何确定性拜占庭共识解决方案都需要交换\Omega(n^2)比特。近年来，确定性拜占庭协议在部分同步网络中取得了巨大进展，最先进的密码学解决方案实现了O(n^2 \kappa)比特（其中$\kappa$是安全参数），几乎达到了下界。相比之下，在同步网络中，最优解仅需O(n^2)比特，无需密码学且具有相同的容错能力，这一成果已为人所知三十余年。能否弥合网络模型之间的这一差距？在本文中，我们提出Repeater，这是首个将拜占庭协议算法从同步模型转换为部分同步模型的通用变换方法。Repeater采用模块化设计，其子模块依赖现有及新型算法。通过合理选择模块，Repeater无需额外密码学支持，具有最优弹性（n = 3t+1，其中t是最大故障数），并且对于恒定大小的输入，能保持所转换同步算法的最坏情况下单进程比特复杂度。借助Repeater，我们提出了首个部分同步算法，该算法（1）达到最优比特复杂度（O(n^2)比特），（2）能抵抗计算能力无上限的敌手（无需密码学），且（3）具有最优弹性（n = 3t+1），从而表明Dolev-Reischuk界在部分同步下是紧的。此外，我们针对长输入对Repeater进行了改进，引入了若干具有更优复杂度及更弱（或完全无需）密码学假设的新算法。