Biblio

In this paper, we consider a stochastic model to evaluate the system availability of an intrusion tolerant system (ITS), where the system undergoes the patch management with a periodic vulnerability checking strategy, i.e., a pull-type patch management. Based on the model, this paper discusses the appropriate timing for patch applying. In particular, the paper models the attack behavior of adversary and the system behaviors under reactive defense strategies by a composite stochastic reward net (SRN). Furthermore, we formulate the interval availability by applying the phase-type (PH) approximation to solve the Markov regenerative process (MRGP) models derived from the SRNs. Numerical experiments are conducted to study the sensitivity of the system availability with respect to the number of checking.

Computer security has gained more and more attention in a public over the last years, since computer systems are suffering from significant and increasing security threats that cause security breaches by exploiting software vulnerabilities. The most efficient way to ensure the system security is to patch the vulnerable system before a malicious attack occurs. Besides the commonly-used push-type patch management, the pull-type patch management is also adopted. The main issues in the pull-type patch management are two-fold; when to check the vulnerability information and when to apply a patch? This paper considers the security patch management for a virtual machine (VM) based intrusion tolerant system (ITS), where the system undergoes the patch management with a periodic vulnerability checking strategy, and evaluates the system security from the availability aspect. A composite stochastic reward net (SRN) model is applied to capture the attack behavior of adversary and the defense behaviors of system. Two availability measures; interval availability and point-wise availability are formulated to quantify the system security via phase expansion. The proposed approach and metrics not only enable us to quantitatively assess the system security, but also provide insights on the patch management. In numerical experiments, we evaluate effects of the intrusion rate and the number of vulnerability checking on the system security.