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：我们利用范畴论对密码学中的模拟范式进行了形式化，并证明抵御抽象攻击的协议构成一个对称幺半范畴，从而为密码学中的可组合安全性定义提供了抽象模型。我们的模型能够以模块化、灵活的方式纳入计算安全性、设置假设以及各种攻击模型（例如敌手的共谋子集或独立行动子集）。最后，我们通过弦图重新推导了一次一密的安全性、迪菲-赫尔曼密钥交换的正确性，以及关于双参与方与三参与方密码学局限性的不可能性结果（排除了例如可组合承诺和广播）。在此过程中，我们展示了两种可能具有独立意义的资源理论的范畴构造：一种用于刻画多方共享的资源，另一种用于刻画渐近成功的资源转化。