Categorical composable cryptography

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 use the one time pad as our main example: in abstract terms, its composable security follows from the axioms of a Hopf algebra with an integral, which concretely speaking corresponds to a group structure on the message space and a uniformly random key.

Time permitting, we will also discuss no-theorems concerning composable two- and three-party cryptography.

Joint work with Anne Broadbent. Based on https://arxiv.org/abs/2208.13232