Anne Broadbent ; Martti Karvonen - Categorical composable cryptography: extended version

lmcs:9979 - Logical Methods in Computer Science, October 22, 2024, Volume 19, Issue 4 - https://doi.org/10.46298/lmcs-19(4:30)2023
Categorical composable cryptography: extended versionArticle

Authors: Anne Broadbent ; Martti Karvonen

    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. This is a corrected version of the paper arXiv:2208.13232 published originally on December 18, 2023.


    Volume: Volume 19, Issue 4
    Published on: October 22, 2024
    Accepted on: October 10, 2023
    Submitted on: August 30, 2022
    Keywords: Computer Science - Cryptography and Security,Mathematics - Category Theory
    Funding:
      Source : OpenAIRE Graph
    • Funder: Natural Sciences and Engineering Research Council of Canada

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