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.

翻译：我们运用范畴论形式化密码学中的模拟范式，并证明抵抗抽象攻击的协议构成对称幺半范畴，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、前提假设及多种攻击模型（如敌手合谋或独立行动的子集）。最后，我们利用弦图重新推导了一次一密的安全性质、Diffie-Hellman密钥交换的正确性，以及关于双参与三方密码学局限性的不可能性结果（排除了可组合承诺与广播等方案）。在此过程中，我们提出了两种可能具有独立价值的资源理论范畴构造：一种刻画多方共享资源，另一种描述渐近成功的资源转换。