Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is to capture this phenomenon in a more abstract setting. We focus on resource theories -- general calculi of processes with a string diagrammatic syntax -- introducing a general parametric iteration construction. By instantiating this construction within the Markov category of probabilistic Boolean circuits and equipping it with a suitable metric, we are able to capture the notion of negligibility via asymptotic equivalence, in a compositional way. This allows us to use diagrammatic reasoning to prove simple cryptographic theorems -- for instance, proving that guessing a randomly generated key has negligible success.

翻译：许多算法是针对一个固定但未指定的参数而设计的。这种现象在密码学中尤为常见，协议通常包含一个安全参数，例如密钥的比特长度。我们的目标是在更抽象的背景下捕捉这一现象。我们专注于资源理论——一种具有字符串图语法的通用过程演算——引入了一种通用的参数化迭代构造。通过在概率布尔电路的马尔可夫范畴中实例化该构造，并为其配备合适的度量，我们能够以组合的方式，通过渐近等价来捕捉可忽略性的概念。这使我们能够利用图式推理来证明简单的密码学定理——例如，证明猜测随机生成的密钥具有可忽略的成功率。