A Theory of Network Security: Principles of Natural Selection and Combinatorics

Q3 Mathematics
Angsheng Li, Yicheng Pan
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引用次数: 8

Abstract

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 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 principle and combinatorial principles are essential to security of networks.
网络安全理论:自然选择与组合原理
针对故意攻击的级联失效模型,提出了网络安全的定义。我们提出了一个由同质/亲缘关系、随机性和优先依恋的自然选择构成的网络模型,称为安全模型。我们证明了在级联失效模型下,由安全模型生成的网络对任何规模为poly(log n)的攻击都是安全的,其中安全模型网络的自然选择原则和组合原则包括幂律、自组织原则、小直径特性、局部导航原则、度优先原则、包容-排斥原则和感染优先树原则等。是基本原则。此外,我们还证明了由该安全模型生成的网络具有扩展核。这种特性保证了安全模型的网络满足工程中全局通信的要求。在此基础上,提出了一种计算机网络安全协议。我们的理论表明,网络的安全性可以通过自然选择原理和组合原理的结合来实现,而自然选择原理和组合原理对网络的安全性都是必不可少的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
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