A Combinatorics Proliferation Model with Threshold for Malware Countermeasure

Security software such as anti-virus software and personal firewall are usually installed in every host within an enterprise network. There are mainly two kinds of security software: signature-based software and anomaly-based software. Anomaly-based software generally has a “threshold” that discriminates between normal traffic and malware communications in network traffic observation. Such a threshold involves the number of packets used for behavior checking by the anomaly-based software. Also, it indicates the number of packets sent from an infected host before the infected host is contained. In this paper, we propose a mathematical model that uses discrete mathematics known as combinatorics, which is suitable for situations in which there are a small number of infected hosts. Our model can estimate the threshold at which the number of infected hosts can be suppressed to a small number. The result from our model fits very well with the result of computer simulation using typical existing scanning malware and a typical network