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arXiv · 2510.23413

Parametric Iteration in Resource Theories

Alessandro Di Giorgio·Pawel Sobocinski·Niels Voorneveld
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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.

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Alessandro Di Giorgio, Pawel Sobocinski, Niels Voorneveld. 2025-10-27. Parametric Iteration in Resource Theories. https://arxiv.org/abs/2510.23413

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