Yoneda Hacking: The Algebra of Attacker Actions

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