Categorical composable cryptography
This work offers a foundational framework for composable security in cryptography, addressing the problem of modular and flexible security definitions for researchers and practitioners in the field.
The authors formalized the simulation paradigm of cryptography using category theory, demonstrating that protocols secure against abstract attacks form a symmetric monoidal category, which provides an abstract model for composable security definitions. They applied this model to rederive the security of the one-time pad and establish no-go results for composable commitments and broadcasting in bipartite and tripartite 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 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.