打破$O(\sqrt n)$比特壁垒：每方仅需Polylog比特的Byzantine Agreement
Breaking the $O(\sqrt n)$-Bit Barrier: Byzantine Agreement with Polylog Bits Per Party
AI总结：
研究Byzantine Agreement中通信不对称性是否必然，提出SRDS原语构建首个$\tilde O(1)$平衡通信协议，打破$O(\sqrt n)$壁垒并回答开放问题。
摘要：
Byzantine agreement (BA)（拜占庭协议），即$n$个方面对恶意代理时就其输入比特之一达成一致的任务，是位于大量分布式协议核心的强大原语。有趣的是，在总通信量最优的协议中，各方的需求高度不平衡：每方摊销成本为$\tilde O(1)$比特，但某些方必须发送$Ω(n)$比特。在已知最佳的平衡协议中，总通信量次优，每方通信$\tilde O(\sqrt{n})$。在此工作中，我们探讨不对称性是否为实现总通信量优化所固有。我们在这方面的贡献如下：1）我们定义了一种密码学原语，即简洁重构分布式签名（SRDS），足以构建$\tilde O(1)$平衡BA。我们基于不同的密码学和公钥基础设施（PKI）假设提供了两种SRDS构造。2）基于SRDS的BA遵循从“几乎处处”一致提升至完全一致的范式，并在单轮内完成。我们证明，在每方发送$o(n)$消息的此类协议中，PKI设置和密码学假设是必需的。3）我们进一步探索了实现SRDS的自然方法与特定类型NP完全问题（推广Subset-Sum和Subset-Product）的平均情况简洁非交互式论证系统（SNARGs）之间的联系。我们的结果为最小化BA的每方通信提供了新方法，以及局限性和壁垒。特别是，我们构建了前两个具有$\tilde O(1)$平衡通信的BA协议，在设置和密码学假设之间提供权衡，并回答了King和Saia（DISC'09）提出的开放问题。
英文摘要：
Byzantine agreement (BA), the task of $n$ parties to agree on one of their input bits in the face of malicious agents, is a powerful primitive that lies at the core of a vast range of distributed protocols. Interestingly, in protocols with the best overall communication, the demands of the parties are highly unbalanced: the amortized cost is $\tilde O(1)$ bits per party, but some parties must send $Ω(n)$ bits. In best known balanced protocols, the overall communication is sub-optimal, with each party communicating $\tilde O(\sqrt{n})$. In this work, we ask whether asymmetry is inherent for optimizing total communication. Our contributions in this line are as follows: 1) We define a cryptographic primitive, succinctly reconstructed distributed signatures (SRDS), that suffices for constructing $\tilde O(1)$ balanced BA. We provide two constructions of SRDS from different cryptographic and Public-Key Infrastructure (PKI) assumptions. 2) The SRDS-based BA follows a paradigm of boosting from "almost-everywhere" agreement to full agreement, and does so in a single round. We prove that PKI setup and cryptographic assumptions are necessary for such protocols in which every party sends $o(n)$ messages. 3) We further explore connections between a natural approach toward attaining SRDS and average-case succinct non-interactive argument systems (SNARGs) for a particular type of NP-Complete problems (generalizing Subset-Sum and Subset-Product). Our results provide new approaches forward, as well as limitations and barriers, towards minimizing per-party communication of BA. In particular, we construct the first two BA protocols with $\tilde O(1)$ balanced communication, offering a tradeoff between setup and cryptographic assumptions, and answering an open question presented by King and Saia (DISC'09).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
