Parametric Iteration in Resource Theories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908614815383552 |
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| author | Di Giorgio, Alessandro Sobocinski, Pawel Voorneveld, Niels |
| author_facet | Di Giorgio, Alessandro Sobocinski, Pawel Voorneveld, Niels |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parametric Iteration in Resource Theories Di Giorgio, Alessandro Sobocinski, Pawel Voorneveld, Niels Logic in Computer Science 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. |
| title | Parametric Iteration in Resource Theories |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2510.23413 |