Bicategorical Semantics for Nondeterministic Computation

We present a topological bicategorical syntax for the interaction between public and private information in classical information theory. This allows high-level graphical definitions of encrypted communication and secret sharing, including a characterization of their security properties, which are automatically satisfied with no extra axioms required. This analysis shows that these protocols have an identical abstract form to the quantum teleportation and dense coding procedures, giving a concrete mathematical analogy between quantum and classical computing. Specific implementations of these protocols as nondeterministic classical procedures are recovered by applying our formalism in a symmetric monoidal bicategory of matrices of relations. http://www.elsevier.nl/locate/entcs.