Measuring, analyzing and predicting security vulnerabilities in software systems

In this work we examine the feasibility of quantitatively characterizing some aspects of security. In particular, we investigate if it is possible to predict the number of vulnerabilities that can potentially be present in a software system but may not have been found yet. We use several major operating systems as representatives of complex software systems. The data on vulnerabilities discovered in these systems are analyzed. We examine the results to determine if the density of vulnerabilities in a program is a useful measure. We also address the question about what fraction of software defects are security related, i.e., are vulnerabilities. We examine the dynamics of vulnerability discovery hypothesizing that it may lead us to an estimate of the magnitude of the undiscovered vulnerabilities still present in the system. We consider the vulnerability discovery rate to see if models can be developed to project future trends. Finally, we use the data for both commercial and open-source systems to determine whether the key observations are generally applicable. Our results indicate that the values of vulnerability densities fall within a range of values, just like the commonly used measure of defect density for general defects. Our examination also reveals that it is possible to model the vulnerability discovery using a logistic model that can sometimes be approximated by a linear model.