engleski

Color Avoiding Percolation

When assessing the security or robustness of a complex network, it is essential to take into account the fact that many nodes may fail together. For example, businesses within the same geographic area are subject to the same weather events, and computers running the same version of software may be subject to the same security vulnerabilities. Ignoring this heterogeneity of vulnerabilities leads to substantial overestimation of robustness, with potentially catastrophic consequences. Here, we develop a method to analyze this heterogeneity and show how it can be used to improve a system’s functionality. We color each node by its vulnerability and develop a “color-avoiding” percolation theory that allows us to determine the set of nodes that are connected while avoiding any single color. We apply our framework by proposing a new topological approach to cybersecurity, and we make use of data collected from the autonomous systems-level Internet. If there are entities that control many nodes or software bugs that affect many nodes, eavesdroppers to large sets of nodes may exist. In such a case, we propose splitting the message and transmitting each piece on a path that avoids all of the nodes that are vulnerable to one of the eavesdroppers. Our theory determines which nodes can securely communicate and which paths they should take. Our investigation is the first systematic study of the effect of vulnerability classes on robustness and security. We expect that our findings will open up a new frontier in the study of complex systems with important practical applications to cybersecurity as well as network robustness.

Complex systems ; Continuous percolation transition ; Network resilience ; Percolation phase transition ; Percolation theory

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