Deterministic Channel Design for Minimum Leakage

This work explores the problem of designing a channel that leaks the least amount of information while respecting a set of operational constraints. This paper focuses on deterministic channels and deterministic solutions. This setting is relevant because most programs and many channel design problems are naturally modelled by deterministic channels. Moreover, the setting is also relevant when considering an attacker who can observe many outputs of an arbitrary channel while the secret input stays the same: when the number of observations is arbitrarily large, the channel of minimal leakage is deterministic. The deterministic channel design problem has different solutions depending on which leakage measure is chosen. The problem is shown to be NP-hard in general. However, for a particular class of constraints, called k-complete hypergraph constraints, a greedy algorithm is shown to provide the optimal solution for a wide class of leakage measures.