Parametric Iteration in Resource Theories
Abstract
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.
Cite
@article{arxiv.2510.23413,
title = {Parametric Iteration in Resource Theories},
author = {Alessandro Di Giorgio and Pawel Sobocinski and Niels Voorneveld},
journal= {arXiv preprint arXiv:2510.23413},
year = {2025}
}