Leakage-Minimal Design: Universality, Limitations, and Applications

We consider a setting where a system has to interact, and hence create distinct outputs (observables), but subject to such operational constraints wants to minimize the leakage that such observables reveal about its secret input. It has been previously demonstrated that under some (highly symmetrical) constraints on the observables, it is possible to design systems that are universally optimal in the sense of leaking minimal information no matter how information is measured.,,In this work we make several contribution to this field. On universal (i.e., measure-invariant) optimality, we show its limitations through a counterexample where symmetry constraints are broken. Nevertheless, we also show two new universal optimality results: the first is in the presence of "graph like" constraints (that may lack symmetry). The second is universal optimality in the case of uncertainty about the prior. Furthermore, we prove that a generic class of leakage optimisation problems are convex problem, from which we derive that KKT conditions are necessary and sufficient for optimality. We demonstrate the practical value of the theory in the form of an application to timing attacks countermeasures.