The Cascade Vulnerability Problem

Abstract

A network of computers is vulnerable to the cascading problem when data of a security level d can be passed to a user with a lower security clearance u elsewhere on the network, without having to defeat any single component of the system that has an accreditation range great enough to allow users of level u and data of level d on a single system. An algorithm of time complexity order $\mathit{O}\mathrm{(}{\mathit{an}}^3\mathrm{)}$ and space complexity $\mathit{O}\mathrm{(}{\mathit{an}}^2\mathrm{)}$ is given to solve the cascade detection problem, where a is the number of security levels for data, and n is the number of nodes in the network. Also, the cascade correction problem, to remove all cascading paths from a network for a given cost, under restrictive conditions is shown to be NP-complete.