Modelling and Analysis of Network Security - an Algebraic Approach

TL;DR

This paper introduces a unified algebraic framework based on probabilistic process calculus for modeling and analyzing various network security games, enabling efficient computation of Nash equilibria and optimal strategies.

Contribution

It proposes a novel algebraic approach using PVCCSG for uniformly modeling different security game scenarios and provides an algorithm for computing Nash equilibria strategies.

Findings

Effective in modeling diverse security scenarios

Algorithm successfully computes Nash equilibria

Demonstrated with four real-world case studies

Abstract

Game theory has been applied to investigate network security. But different security scenarios were often modeled via different types of games and analyzed in an ad-hoc manner. In this paper, we propose an algebraic approach for modeling and analyzing uniformly several types of network security games. This approach is based on a probabilistic extension of the value-passing Calculus of Communicating Systems (CCS) which is regarded as a Generative model for Probabilistic Value-passing CCS (PVCCSG for short). Our approach gives a uniform framework, called PVCCSG based security model, for the security scenarios modeled via perfect and complete or incomplete information games. We present then a uniform algorithm for computing the Nash equilibria strategies of a network security game on its PVCCSG based security model. The algorithm first generates a transition system for each of the PVCCSG based security models, then simplifies this transition system through graph-theoretic abstraction and bisimulation minimization. Then, a backward induction method, which is only applicable to finite tree models, can be used to compute all the Nash equilibria strategies of the (possibly infinite) security games. This algorithm is implemented and can also be tuned smoothly for computing its social optimal strategies. The effectiveness and efficiency of this approach are further demonstrated with four detailed case studies from the field of network security.