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Adapted spectral-differential method for construction of differentially 4-uniform piecewise-linear permutations, orthomorphisms, and involutions of the field F2n

  • Andrey V. Menyachikhin EMAIL logo
Published/Copyright: February 12, 2025

Abstract

We propose a method to construct permutations of the field F2n with low value of the Δ-uniformity such that their restrictions to the cosets of the group F2n× by some of its subgroup H are linear. Using the proposed method, we construct a large number of new CCZ-nonequivalent differentially 4-uniform permutations, orthomorphisms, and involutions over the field F2n with n = 6, 8.


Originally published in Diskretnaya Matematika (2023) 35, №2, 42–77 (in Russian).


Acknowledgment

The author is grateful to A. E. Trishin for introduction in this field, to his advisor B. A. Pogorelov for his help and support in all aspects, and to D. A. Burov for valuable comments and interest in this study.

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Applications

Examples of differentially 4-uniform piecewise-linear permutations constructed via the adapted spectral-differential method

Received: 2023-01-11
Published Online: 2025-02-12
Published in Print: 2025-02-25

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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