A Note on the Walsh Spectrum of Power Residue S-Boxes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909838996406272 |
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| author | Steiner, Matthias Johann |
| author_facet | Steiner, Matthias Johann |
| contents | Let $\mathbb{F}_q$ be a prime field with $q \geq 3$, and let $d, m \geq 1$ be integers such that $\gcd \left( d, q \right) = 1$ and $m \mid (q - 1)$. In this paper we bound the absolute values of the Walsh spectrum of S-Boxes $S (x) = x^d \cdot T \left( x^\frac{q - 1}{m} \right)$, where $T$ is a function with $T (x) \neq 0$ if $x \neq 0$. Such S-Boxes have been proposed for the Zero-Knowledge-friendly hash functions Grendel and Polocolo. In particular, we prove the conjectured correlation of the Polocolo S-Box. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on the Walsh Spectrum of Power Residue S-Boxes Steiner, Matthias Johann Number Theory Cryptography and Security Let $\mathbb{F}_q$ be a prime field with $q \geq 3$, and let $d, m \geq 1$ be integers such that $\gcd \left( d, q \right) = 1$ and $m \mid (q - 1)$. In this paper we bound the absolute values of the Walsh spectrum of S-Boxes $S (x) = x^d \cdot T \left( x^\frac{q - 1}{m} \right)$, where $T$ is a function with $T (x) \neq 0$ if $x \neq 0$. Such S-Boxes have been proposed for the Zero-Knowledge-friendly hash functions Grendel and Polocolo. In particular, we prove the conjectured correlation of the Polocolo S-Box. |
| title | A Note on the Walsh Spectrum of Power Residue S-Boxes |
| topic | Number Theory Cryptography and Security |
| url | https://arxiv.org/abs/2507.06808 |