We consider the privacy of interactions between individuals in a network. For many networks, while nodes are anonymous to outside observers, the existence of a link between individuals implies the possibility of one node revealing identifying information about its neighbor. Moreover, while the identities of the accounts are likely hidden to an observer, the network of interaction between two anonymous accounts is often available. For example, in blockchain cryptocurrencies, transactions between two anonymous accounts are published openly. Here we consider what happens if one (or more) parties in such a network are deanonymized by an outside identity. These compromised individuals could leak information about others with whom they interacted, which could then cascade to more and more nodes' information being revealed. We use a percolation framework to analyze the scenario outlined above and show for different likelihoods of individuals possessing information on their counter-parties, the fraction of accounts that can be identified and the idealized minimum number of steps from a deanonymized node to an anonymous node (a measure of the effort required to deanonymize that individual). We further develop a greedy algorithm to estimate the \emph{actual} number of steps that will be needed to identify a particular node based on the noisy information available to the attacker. We apply our framework to three real-world networks: (1) a blockchain transaction network, (2) a network of interactions on the dark web, and (3) a political conspiracy network. We find that in all three networks, beginning from one compromised individual, it is possible to deanonymize a significant fraction of the network ($>50$%) within less than 5 steps. Overall these results provide guidelines for investigators seeking to identify actors in anonymous networks, as well as for users seeking to maintain their privacy.

中文翻译：

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渗透框架揭示了阴谋、暗网和区块链网络中隐私的局限性

我们考虑网络中个人之间交互的隐私。对于许多网络，虽然节点对外部观察者来说是匿名的，但个体之间存在联系意味着一个节点可能会泄露有关其邻居的识别信息。此外，虽然账户的身份可能对观察者隐藏，但两个匿名账户之间的交互网络通常是可用的。例如，在区块链加密货币中，两个匿名账户之间的交易是公开发布的。在这里，我们考虑如果这样一个网络中的一个（或多个）当事方被外部身份去匿名化会发生什么。这些受感染的个人可能会泄露与他们互动的其他人的信息，然后这些信息可能会级联到越来越多的节点信息被泄露。我们使用渗透框架来分析上面概述的场景，并针对个人拥有其交易对手信息的不同可能性、可以识别的账户比例以及从去匿名节点到匿名节点的理想化最小步骤数显示（对该个人去匿名化所需努力的衡量标准）。我们进一步开发了一种贪婪算法来估计基于攻击者可用的噪声信息来识别特定节点所需的 \emph{actual} 步数。我们将我们的框架应用于三个现实世界的网络：（1）区块链交易网络，（2）暗网上的交互网络，以及（3）政治阴谋网络。我们发现在所有三个网络中，从一个受感染的个人开始，可以在不到 5 个步骤内对网络的很大一部分（$>50$%）进行去匿名化。总体而言，这些结果为寻求识别匿名网络中的参与者的调查人员以及寻求维护其隐私的用户提供了指导。