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：我们用范畴论形式化了密码学中的模拟范式，并证明抵抗抽象攻击的协议构成一个对称幺半范畴，从而为密码学中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、灵活的方式融入计算安全性、设定假设以及各种攻击模型（例如共谋或独立行动的敌手子集）。最后，我们利用弦图重新推导了一次一密的安全性、Diffie-Hellman密钥交换的正确性，以及关于二方与三方密码学极限的不可行性结果，从而排除了例如可组合承诺和广播等方案。在此过程中，我们展示了两个可能具有独立价值的资源理论范畴构造：一个用于捕获多方共享的资源，另一个用于捕获渐近成功的资源转换。