| Summary: | 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,
correctness of Diffie-Hellman key exchange and no-go results concerning the
limits of bipartite and tripartite cryptography, ruling out e.g., composable
commitments and broadcasting. On the way, we exhibit two categorical
constructions of resource theories that might be of independent interest: one
capturing resources shared among multiple parties and one capturing resource
conversions that succeed asymptotically.
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