A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915008278953984 |
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| author | Steiner, Matthias Johann |
| author_facet | Steiner, Matthias Johann |
| contents | Let $\mathbb{F}_q$ be a finite field of characteristic $p$. In this paper we prove that the $c$-Boomerang Uniformity, $c \neq 0$, for all permutation monomials $x^d$, where $d > 1$ and $p \nmid d$, is bounded by $d^2$. Further, we utilize this bound to estimate the $c$-boomerang uniformity of a large class of Generalized Triangular Dynamical Systems, a polynomial-based approach to describe cryptographic permutations, including the well-known Substitution-Permutation Network. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_12621 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials Steiner, Matthias Johann Number Theory Cryptography and Security Information Theory Algebraic Geometry 11T06, 14G50, 14H50, 94A60 Let $\mathbb{F}_q$ be a finite field of characteristic $p$. In this paper we prove that the $c$-Boomerang Uniformity, $c \neq 0$, for all permutation monomials $x^d$, where $d > 1$ and $p \nmid d$, is bounded by $d^2$. Further, we utilize this bound to estimate the $c$-boomerang uniformity of a large class of Generalized Triangular Dynamical Systems, a polynomial-based approach to describe cryptographic permutations, including the well-known Substitution-Permutation Network. |
| title | A Degree Bound For The c-Boomerang Uniformity Of Permutation Monomials |
| topic | Number Theory Cryptography and Security Information Theory Algebraic Geometry 11T06, 14G50, 14H50, 94A60 |
| url | https://arxiv.org/abs/2307.12621 |