Categorical composable cryptography

TL;DR

This paper introduces a category-theoretic framework for cryptography, modeling secure protocols as a symmetric monoidal category, which captures composable security and various attack models in a modular way.

Contribution

It formalizes cryptographic security using category theory, enabling a unified, abstract, and flexible approach to composable security definitions and attack models.

Findings

Protocols secure against abstract attacks form a symmetric monoidal category

Re-derivation of the security of the one-time pad using string diagrams

No-go results for certain cryptographic primitives like commitments and broadcasting

Abstract

We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in cryptography. Our model is able to incorporate computational security, set-up assumptions and various attack models such as colluding or independently acting subsets of adversaries in a modular, flexible fashion. We conclude by using string diagrams to rederive the security of the one-time pad and no-go results concerning the limits of bipartite and tripartite cryptography, ruling out e.g., composable commitments and broadcasting.