Abstract:
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. 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.