Hyper Static Analysis of Programs - An Abstract Interpretation-Based Framework for Hyperproperties Verification

In the context of systems security, information flows play a central role. Unhandled information flows potentially leave the door open to very dangerous types of security attacks, such as code injection or sensitive information leakage. Information flows verification is based on a notion of dependency between a system’s objects, which requires specifications expressing relations between different executions of a system. Specifications of this kind, called hyperproperties, go beyond classic trace properties, defined in terms of predicate over single executions. The problem of trace properties verification is well studied, both from a theoretical as well as a practical point of view. Unfortunately, very few works deal with the verification of hyperproperties. Note that hyperproperties are not limited to information flows. Indeed, a lot of other important problems can be modeled through hyperproperties only: processes synchronization, availability requirements, integrity issues, error resistant codes check, just to name a few. The sound verification of hyperproperties is not trivial: it is not easy to adapt classic verification methods, used for trace properties, in order to deal with hyperproperties. The added complexity derives from the fact that hyperproperties are defined over sets of sets of executions, rather than sets of executions, as happens for trace properties. In general, passing to powersets involves many problems, from a computability point of view, and this is the case also for systems verification. In this thesis, it is explored the problem of hyperproperties verification in its theoretical and practical aspects. In particular, the aim is to extend verification methods used for trace properties to the more general case of hyperproperties. The verification is performed exploiting the framework of abstract interpretation, a very general theory for approximating the behavior of discrete dynamic systems. Apart from the general setting, the thesis focuses on sound verification methods, based on static analysis, for computer programs. As a case study – which is also a leading motivation – the verification of information flows specifications has been taken into account, in the form of Non-Interference and Abstract Non-Interference. The second is a weakening of the first, useful in the context where Non-Interference is a too restrictive specification. The results of the thesis have been implemented in a prototype analyzer for (Abstract) Non-Interference which is, to the best of the author’s knowledge, the first attempt to implement a sound verifier for that specification(s), based on abstract interpretation and taking into account the expressive power of hyperproperties.