Abstract
In this thesis, we propose Latent behaviour analysis (LBA): a method to study changes in the observable behaviour of a transition system when in the presence of an external force, e.g., an attack or a fault. In LBA, we model these external forces using spa tial transformations, while preserving the original transition dynamics of the system. We use the framework of universal coalgebra to model the transition system as an F coalgebra (X, c : X ? F(X)) for some functor F, and the external force as a spatial transformation m: X ? X, which lets us seamlessly combine the two into what we call the latent F-coalgebra (X, c ? m). The latent F-coalgebra (X, c ? m) implements the transition system in the presence of the force modelled by m. Latent coalgebras are compatible with the usual verification and testing methods for coalgebras and transi tion systems, and the properties satisfied by latent coalgebras prove properties about the original system: if the latent coalgebra (X, c ? m) satisfies some property P, then the original system (X, c) satisfies P in the presence of the force modelled by m. Since the set of spatial transformations is a monoid under function composition, we can combine these transformations to model interesting interactions. For example, if m: X ? X models an attack and w: X ? X models a counterattack, then (X, c?w?m) is the latent system whose behaviour is that of the system (X, c) under the effects of the attack m and the effects of the counterattack w. This example illustrates the versatility of spatial transformations: attackers can use them to break security requirements, and designers can use them to enforce security properties. In this work, we show how to use LBA to approach three cybersecurity problems. The first problem is the classifica tion of attacker models. We provide a method to systematically generate and compare attacker models for a system based on their potentially harmful effects by modelling their attacks using spatial transformations. The second problem is the quantification of robustness in Cyber-physical Systems (CPSs). We propose a methodology for the sys tematic generation of attacks in CPSs to quantify the robustness of a system, and we propose a notion of latent robustness which considers the use of counterattacks (also modelled using spatial transformations). Finally, we study the problem of timing side channel repair, for which we propose using a spatial transformation to enforce constant memory access patterns while preserving the functionality of the program.