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 (≈ can be composed sequentially and in parallel). This gives an abstract model of composable security definitions in cryptography that is not tied to any particular machine model. 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.
In this talk, I will give an overview of techniques to compile Sigma protocols—a popular class of interactive cryptographic proofs—to non-interactive proofs that guarantee security when used in any larger protocol context. The aim of the talk will be to provide an introduction to the area to system designers who typically use cryptographic tools as a black box, while also providing insight into some interesting technical subtleties that I uncovered in a recent work.