Periodicity in software vulnerability discovery, patching and exploitation

Periodicity in key processes related to software vulnerabilities need to be taken into account for assessing security at a given time. Here, we examine the actual multi-year field datasets for some of the most used software systems (operating systems and Web-related software) for potential annual variations in vulnerability discovery processes. We also examine weekly periodicity in the patching and exploitation of the vulnerabilities. Accurate projections of the vulnerability discovery process are required to optimally allocate the effort needed to develop patches for handling discovered vulnerabilities. A time series analysis that combines the periodic pattern and longer-term trends allows the developers to predict future needs more accurately. We analyze eighteen datasets of software systems for annual seasonality in their vulnerability discovery processes. This analysis shows that there are indeed repetitive annual patterns. Next, some of the datasets from a large number of major organizations that record the result of daily scans are examined for potential weekly periodicity and its statistical significance. The results show a 7-day periodicity in the presence of unpatched vulnerabilities, as well as in the exploitation pattern. The seasonal index approach is used to examine the statistical significance of the observed periodicity. The autocorrelation function is used to identify the exact periodicity. The results show that periodicity needs to be considered for optimal resource allocations and for evaluation of security risks.