Software Security Growth Modeling: Examining Vulnerabilities with Reliability Growth Models

Abstract

The software engineering tools historically used to examine faults can also be used to examine vulnerabilities and the rate at which they are discovered. I discuss the challenges of the collection process and compare two sets of vulnerability characterization criteria. I collected fifty-four months of vulnerability data for OpenBSD 2.2 and applied seven reliability growth models to the two data sets. These models only passed applicability tests for the data set that omits dependent data points. Musa’s Logarithmic model has the best one-step-ahead predictive accuracy of the three acceptably accurate models for that data set. It estimated that fifty-four months after OpenBSD 2.2’s release, the mean time to vulnerability discovery for OpenBSD 2.2 was 42.5 days and that 58.4% of the vulnerabilities it contains had been found. However, a trend analysis cannot rule out the possibility that there is no trend at all in the rate of vulnerability detection, and this result casts doubts on the accuracy of the reliability growth models. The lack of a clear decreasing trend in that analysis highlights one of the challenges of using reliability growth models on vulnerability data: it may be a true reflection of the system or it may be caused by the changes over time in the effort invested in vulnerability detection.