On Some Information Geometric Approaches to Cyber Security

Various contexts of relevance to cyber security involve the analysis of data that has a statistical character and in some cases the extraction of particular features from datasets of fitted distributions or empirical frequency distributions. Such statistics, for example, may be collected in the automated monitoring of IP-related data during accessing or attempted accessing of web-based resources, or may be triggered through an alert for suspected cyber attacks. Information geometry provides a Riemannian geometric framework in which to study smoothly parametrized families of probability density functions, thereby allowing the use of geometric tools to study statistical features of processes and possibly the representation of features that are associated with attacks. In particular, we can obtain mutual distances among members of the family from a collection of datasets, allowing, for example, measures of departures from Poisson random or uniformity, and discrimination between nearby distributions. Moreover, this allows the representation of large numbers of datasets in a way that respects any topological features in the frequency data and reveals subgroupings in the datasets using dimensionality reduction. Here some results are reported on statistical and information geometric studies concerning pseudorandom sequences, encryption-decryption timing analyses, comparisons of nearby signal distributions and departure from uniformity for evaluating obscuring techniques.