Modeling Ad-hoc rushing attack in a negligibility-based security framework

In this paper, we propose a formal notion of network security for ad hoc networks. We adopt a probabilistic security framework, that is, security is defined by a polynomially bounded adversary model, the cost of attack and the cost of defense. In a complex and probabilistic system, we speak of the "infeasibility" of breaking the security system rather than the "impossibility" of breaking the same system. Security is defined on the concept of "negligible", which is asymptotically sub-polynomial with respect to a pre-defined system parameter x. Intuitively, the parameter x in cryptography is the key length n. We apply the same bounds in ad hoc network security research, but in regard to scalability from now on. We propose an RP (n-runs) complexity class with a global virtual god oracle (GVG) to model a general class of network protocols. In GVG-RP (n-runs) class, the network scale (i.e., number of network members) N replaces the role of key length n in cryptography. From our formal rigorous treatment, we show that "rushing attack" is a severe attack that can reduce the success probability of common ad hoc routing schemes to negligible.Fortunately, countermeasures can be devised to answer this challenge. (1) Common network protocols are not designed to ensure that probability of security failure is negligible. In such designs, the system's security is not related to scalability. There is no asymptotic security guarantee in the network design; (2) We seek to devise security schemes to ensure that the probability of security failure is negligible in regard to network scale. In Theorem 2, we present an asymptotic invariant for scalable networks: "a polynomial-time network algorithm that ensures negligible probability of security failure at each step would stay in the state of ensuring negligible probability of security failure globally". This invariant demonstrates the existence of asymptotic security guarantee in ad hoc networks. It leads to the design of community-based secure routing to defend against rushing attacks. Nevertheless, it is unknown to us whether the ideal invariant can be practically implemented.