arXiv 2203.025532022-03cs.DCcs.CR

基于特征的最优时钟同步

Optimal Clock Synchronization with Signatures

Christoph Lenzen, Julian Loss

摘要：

加密签名可以通过增加可以容忍的错误方的数量来增加分布式系统对对抗性攻击的弹性。虽然这是很好的研究共识，它一直在容错时钟同步的上下文中，即使在完全连接的系统中探索不足。这里，$n$节点系统的诚实方需要计算小偏斜的输出时钟（即，最大相位偏移），尽管本地时钟速率在$1$和$\vartheta>1$之间变化，端到端通信延迟在$d-u$和$d$之间变化，以及来自恶意方的干扰。到目前为止，只知道偏斜$d$的时钟脉冲可以用$\lceil n/2\rceil-1$（PODC `19）的（普通最佳）弹性产生，在没有\emph{any}偏斜界限（STOC `84，PODC `85）的签名的情况下改进保持$\lceil n/3\rceil-1$的紧界限。由于通常为$d\gg u$和$\vartheta-1\ll 1$，因此这与即使在无故障情况（IPL `01）下也适用的$u+(\vartheta-1)d$的下限相差甚远。我们证明了匹配的上界和下界的$Θ(u+(\vartheta-1)d)$的偏斜的弹性范围从$\lceil n/3\rceil$到$\lceil n/2\rceil-1$。在假设对手不能伪造签名的情况下，显示上界的算法是确定性的。即使时钟最初是完全同步的，诚实节点之间的消息延迟是已知的，$\vartheta$任意接近1，并且同步算法是随机的，下限也保持不变。这对于寻求利用签名来提供更强大时间的网络设计者来说具有至关重要的意义。与没有签名的设置相反，它们必须确保攻击者无法轻松绕过具有故障端点的链路上的延迟下限。

英文摘要：

Cryptographic signatures can be used to increase the resilience of distributed systems against adversarial attacks, by increasing the number of faulty parties that can be tolerated. While this is well-studied for consensus, it has been underexplored in the context of fault-tolerant clock synchronization, even in fully connected systems. Here, the honest parties of an $n$-node system are required to compute output clocks of small skew (i.e., maximum phase offset) despite local clock rates varying between $1$ and $\vartheta>1$, end-to-end communication delays varying between $d-u$ and $d$, and the interference from malicious parties. So far, it is only known that clock pulses of skew $d$ can be generated with (trivially optimal) resilience of $\lceil n/2\rceil-1$ (PODC `19), improving over the tight bound of $\lceil n/3\rceil-1$ holding without signatures for \emph{any} skew bound (STOC `84, PODC `85). Since typically $d\gg u$ and $\vartheta-1\ll 1$, this is far from the lower bound of $u+(\vartheta-1)d$ that applies even in the fault-free case (IPL `01). We prove matching upper and lower bounds of $Θ(u+(\vartheta-1)d)$ on the skew for the resilience range from $\lceil n/3\rceil$ to $\lceil n/2\rceil-1$. The algorithm showing the upper bound is, under the assumption that the adversary cannot forge signatures, deterministic. The lower bound holds even if clocks are initially perfectly synchronized, message delays between honest nodes are known, $\vartheta$ is arbitrarily close to one, and the synchronization algorithm is randomized. This has crucial implications for network designers that seek to leverage signatures for providing more robust time. In contrast to the setting without signatures, they must ensure that an attacker cannot easily bypass the lower bound on the delay on links with a faulty endpoint.

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。

摘要：

英文摘要：

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