Vulnerability Discovery Model for a Software System Using Stochastic Differential Equation

Substantial growth in networking and our increasing dependence on it has led to the evolution of the security concerns to another level. With increasing vulnerabilities in the system, the number of possible security breaches also shows an upward trend. With such growing concern for security, the researchers began with the quantitative modeling of vulnerabilities termed as vulnerability discovery models (VDM). A vulnerability discovery model illustrates changes in the vulnerability detection rate in a software system during its lifecycle. They can be used to gauge risk based on which possible mitigation methodologies can be planned. It helps the IT managers and developers to allocate their resources optimally by timely development and application of patches. Such models also allow the end-users to assess security risk in their systems. In this paper, we have introduced a modified Alhazmi-Malaiya Logistic (AML) Model for vulnerability discovery process in the software systems. In addition, we formulate a stochastic differential equation based vulnerability discovery model (VDM) for quantitative assessment of vulnerabilities which effectively captures the current industrial scenario. The proposed VDM is obtained by using stochastic approach in the modified AML Model. The model developed is validated on real life software data sets.