在无PKI异步环境中亚立方硬币翻转
Subcubic Coin Tossing in Asynchrony without PKI
AI总结：
本文提出一种基于委员会的方法，将强二进制公共硬币转换为弱硬币，通信成本更低，首次实现无需PKI的异步公共硬币，通信成本低于n³，能有效对抗大量拜占庭故障。
摘要：
我们考虑一个由n个参与者组成的异步网络，通过安全通道连接，最多t个参与者是拜占庭故障。我们研究公共硬币翻转任务，即参与者试图就一个不可预测的随机值达成一致，由于拜占庭故障者的影响，存在一定失败的可能性。硬币翻转是一个广为人知且经常研究的任务，因其在拜占庭协议中的应用。在本工作中，我们提出一种基于委员会的方法，将强（几乎不失败）二进制公共硬币转换为较弱的硬币，其通信成本在渐近上要求更少。对于任何k>2和ε>0，我们可以将通信成本为O~(n^k)位的强二进制硬币转换为通信成本为O~(ε^{-2k}n^{3-2/k})位的弱二进制硬币。后者容忍的拜占庭故障者数量比其基础的强硬币少εn个，且失败概率为任意小的常数。通过我们的方法，我们获得了在t≤(1/4-ε)n故障情况下，通信成本为O~(n^{2.5})位的安全通道完美硬币，以及基于密码学哈希的在t≤(1/3-ε)n故障情况下，通信成本为O~(n^{7/3}κ)位的硬币。据我们所知，这些是首个无需PKI的异步公共硬币，其通信成本为o(n^3)位，但仍能以至少常数概率对抗t=Θ(n)的适应性拜占庭故障。
英文摘要：
We consider an asynchronous network of $n$ parties connected to each other via secure channels, up to $t$ of which are byzantine. We study common coin tossing, a task where the parties try to agree on an unpredictable random value, with some chance of failure due to the byzantine parties' influence. Coin tossing is a well-known and often-studied task due to its use in byzantine agreement. In this work, we present a committee-based method to transform strong (rarely failing) binary common coins into weaker ones that asymptotically require less communication. For any $k > 2$ and $\varepsilon > 0$, we can transform a strong binary coin that costs $\widetilde{O}(n^k)$ bits of communication into a weak binary coin that costs $\widetilde{O}(\varepsilon^{-2k}n^{3 - 2/k})$ bits. This latter coin tolerates $\varepsilon n$ fewer byzantine parties than the strong coin it is based on, and it fails with an arbitrarily small constant probability. With our method, we obtain a secure-channel-based perfectly secure coin for $t \leq (\frac{1}{4} - \varepsilon)n$ faults that costs $\widetilde{O}(n^{2.5})$ bits, as well as a coin based on cryptographic hashing for $t \leq (\frac{1}{3} - \varepsilon)n$ faults that costs $\widetilde{O}(n^{7/3}κ)$ bits. These are to our knowledge the first PKI-free asynchronous common coins that cost $o(n^3)$ bits of communication but still succeed with at least constant probability against $t = Θ(n)$ adaptive byzantine faults.
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。
