A THEORY OF NETWORK SECURITY: PRINCIPLES OF NATURAL SELECTION AND COMBINATORICS

摘要

We propose the definition of security of networks against the cascading failure models of deliberate attacks. We propose a model of networks by the natural selection of homophyly/kinship, randomness, and preferential attachment, referred to as the security model. We show that the networks generated by the security model are provably secure against any attacks of sizes poly(log n) under the cascading failure models, for which the principles of natural selection and the combinatorial principles of the networks of the security model, including a power law, a self-organizing principle, a small-diameter property, a local navigation law, a degree-priority principle, an inclusion-exclusion principle, and an infection priority tree principle, etc., are the underlying principles. Furthermore, we show that the networks generated by the security model have an expander core. This property ensures that the networks of the security model satisfy the requirement of global communications in engineering. Based on our theory, we propose a security protocol for computer networks. Our theory demonstrates that security of networks can be achieved by a merging of natural selection and combinatorial principles, and that both natural selection principles, and combinatorial principles are essential to security of networks.