Yoneda Hacking: The Algebra of Attacker Actions

Abstract

Our work focuses on modeling security of systems from their component-level designs. Towards this goal we develop a categorical formalism to model attacker actions. Equipping the categorical formalism with algebras produces two interesting results for security modeling. First, using the Yoneda lemma, we are able to model attacker reconnaissance missions. In this context, the Yoneda lemma formally shows us that if two system representations, one being complete and the other being the attacker's incomplete view, agree at every possible test, then they behave the same. The implication is that attackers can still successfully exploit the system even with incomplete information. Second, we model the possible changes that can occur to the system via an exploit. An exploit either manipulates the interactions between system components, for example, providing the wrong values to a sensor, or changes the components themselves, for example, manipulating the firmware of a global positioning system (GPS). One additional benefit of using category theory is that mathematical operations can be represented as formal diagrams, which is useful for applying this analysis in a model-based design setting. We illustrate this modeling framework using a cyber-physical system model of an unmanned aerial vehicle (UAV). We demonstrate and model two types of attacks (1) a rewiring attack, which violates data integrity, and (2) a rewriting attack, which violates availability.