一句话：用范畴论形式化密码学模拟范式，证明抗抽象攻击的协议构成对称幺半范畴，并给出可组合安全性的抽象模型。
该文将密码学的模拟范式（simulation paradigm）置于范畴论框架中：把能够抵御抽象攻击的协议视为态射，证明它们构成对称幺半范畴，从而为密码学中的可组合安全定义提供抽象模型。该模型能以模块化、灵活的方式纳入计算安全性、设置假设以及合谋或独立行动等攻击模型。作为应用，作者用串图重新推导一次性密码本的安全性、Diffie-Hellman 密钥交换的正确性，以及两方/三方密码学限制相关的不可能性结果，排除可组合承诺与广播等原语。文中还给出两种资源理论的范畴构造，分别刻画多方共享资源与渐近成功的资源转换。
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.
@article{paperbot2164,
title = {Categorical composable cryptography: extended version},
author = {Anne Broadbent and Martti Karvonen},
journal = {Logical Methods in Computer Science},
volume = {Volume 19, Issue 4},
year = {2023},
doi = {10.46298/lmcs-19(4:30)2023}
}