Bicategorical Semantics for Nondeterministic Computation

TL;DR

This paper introduces a bicategorical framework for classical information protocols, revealing structural similarities with quantum protocols and enabling formal analysis of security and cryptography.

Contribution

It develops a bicategorical syntax for classical info interaction, unifying encryption, secret sharing, and cryptography within a high-level graphical formalism.

Findings

Protocols share an abstract form with quantum teleportation and dense coding

Formalism captures security properties of classical protocols

Implementation as nondeterministic classical procedures demonstrated

Abstract

We outline a bicategorical syntax for the interaction between public and private information in classical information theory. We use this to give high-level graphical definitions of encrypted communication and secret sharing protocols, including a characterization of their security properties. Remarkably, this makes it clear that the protocols have an identical abstract form to the quantum teleportation and dense coding procedures, yielding evidence of a deep connection between classical and quantum information processing. We also formulate public-key cryptography using our scheme. Specific implementations of these protocols as nondeterministic classical procedures are recovered by applying our formalism in a symmetric monoidal bicategory of matrices of relations.