可证私有分布式平均共识：一种信息论方法
Provably Private Distributed Averaging Consensus: An Information-Theoretic Approach
摘要：
在这项工作中，我们专注于以私人的方式解决分散的共识问题。具体来说，我们考虑一个设置，其中一组节点，通过网络连接，旨在计算其本地值的平均值，而不透露这些值给对方。分布式共识问题是一个经典的问题，已被广泛研究，其收敛特性是众所周知的。唉，最先进的共识方法建立在与相邻节点交换本地信息的基础上，这泄露了用户本地值的信息。我们提出了一个算法框架，能够实现经典的共识算法的收敛极限和速度，同时保持用户的本地值的私人。我们所提出的方法的关键思想是仔细设计噪声消息，从每个节点传递到它的邻居，使共识算法仍然精确地收敛到本地值的平均值，而最小量的信息泄漏的本地值。我们正式这精确地表征一个节点的私人消息和所有的消息，另一个对手收集随着时间的推移之间的互信息。我们证明了我们的方法是能够保护用户的隐私的任何网络没有所谓的“广义叶”，并形式化的隐私和收敛时间之间的权衡。与许多私有算法不同，我们的方法可以实现任何所需的准确性，并且所需的隐私级别只影响收敛时间。
英文摘要：
In this work, we focus on solving a decentralized consensus problem in a private manner. Specifically, we consider a setting in which a group of nodes, connected through a network, aim at computing the mean of their local values without revealing those values to each other. The distributed consensus problem is a classic problem that has been extensively studied and its convergence characteristics are well-known. Alas, state-of-the-art consensus methods build on the idea of exchanging local information with neighboring nodes which leaks information about the users' local values. We propose an algorithmic framework that is capable of achieving the convergence limit and rate of classic consensus algorithms while keeping the users' local values private. The key idea of our proposed method is to carefully design noisy messages that are passed from each node to its neighbors such that the consensus algorithm still converges precisely to the average of local values, while a minimum amount of information about local values is leaked. We formalize this by precisely characterizing the mutual information between the private message of a node and all the messages that another adversary collects over time. We prove that our method is capable of preserving users' privacy for any network without a so-called "generalized leaf", and formalize the trade-off between privacy and convergence time. Unlike many private algorithms, any desired accuracy is achievable by our method, and the required level of privacy only affects the convergence time.
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。
