Byzantine agreement 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 agreement exchanges Omega(n^2) bits. In synchronous networks, solutions with optimal O(n^2) bit complexity, optimal fault tolerance, and no cryptography have been established for over three decades. However, these solutions lack robustness under adverse network conditions. Therefore, research has increasingly focused on Byzantine agreement for partially synchronous networks. Numerous solutions have been proposed for the partially synchronous setting. However, these solutions are notoriously hard to prove correct, and the most efficient cryptography-free algorithms still require O(n^3) exchanged bits in the worst case. In this paper, we introduce Oper, the first generic transformation of deterministic Byzantine agreement algorithms from synchrony to partial synchrony. Oper requires no cryptography, is optimally resilient (n >= 3t+1, where t is the maximum number of failures), and preserves the worst-case per-process bit complexity of the transformed synchronous algorithm. Leveraging Oper, we present the first partially synchronous Byzantine agreement algorithm that (1) achieves optimal O(n^2) bit complexity, (2) requires no cryptography, and (3) is optimally resilient (n >= 3t+1), thus showing that the Dolev-Reischuk bound is tight even in partial synchrony. Moreover, we adapt Oper for long values and obtain several new partially synchronous algorithms with improved complexity and weaker (or completely absent) cryptographic assumptions.

翻译：拜占庭协议允许n个进程在存在任意故障的情况下达成共同决定。经典的Dolev-Reischuk下界指出，任何确定性拜占庭协议解决方案都需要交换Ω(n²)比特。在同步网络中，具有最优O(n²)比特复杂度、最优容错性且无需密码学的解决方案已存在三十余年。然而，这些解决方案在不利网络条件下缺乏鲁棒性。因此，研究日益聚焦于部分同步网络的拜占庭协议。尽管已提出众多部分同步设置下的解决方案，但业界公认这些方案难以证明其正确性，且最高效的无密码学算法在最坏情况下仍需交换O(n³)比特。本文提出Oper——首个将确定性拜占庭协议从同步网络泛化转换至部分同步网络的通用方法。Oper无需密码学支持，具备最优容错性（n ≥ 3t+1，t为最大故障数），并保持被转换同步算法中每个进程的最坏情况比特复杂度。借助Oper，我们提出首个满足以下条件的部分同步拜占庭协议算法：(1) 实现最优O(n²)比特复杂度，(2) 无需密码学，(3) 具备最优容错性（n ≥ 3t+1），从而证明即使在部分同步条件下，Dolev-Reischuk下界依然是紧的。此外，我们针对长数值场景改进Oper，获得多个具有更优复杂度与更弱（或完全消除）密码学假设的新部分同步算法。