Differential and boomerang spectrums of some power permutations
| Autor: | Sha Jiang, Longjiang Qu, Kangquan Li, Yubo Li |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Combinatorics
Differential spectrum Physics Physics::General Physics Computational Theory and Mathematics Computer Networks and Communications Applied Mathematics Differential uniformity Spectrum (functional analysis) Astrophysics::Cosmology and Extragalactic Astrophysics Inverse function Differential (mathematics) Prime (order theory) |
| Zdroj: | Cryptography and Communications. 14:371-393 |
| ISSN: | 1936-2455 1936-2447 |
| Popis: | The differential (resp. boomerang) spectrum is an important parameter to estimate the resistance of cryptographic functions against some variants of differential (resp. boomerang) cryptanalysis. This paper aims to determine the differential and boomerang spectrums of some power permutations. In 1997, Helleseth and Sandberg proved that the differential uniformity of $x^{\frac {p^{n}-1}{2}+2}$ over $\mathbb {F}_{p^{n}}$ , where p is an odd prime, is less than or equal to 4. In this paper, we first determine the differential spectrum of $x^{\frac {3^{n}-1}{2}+2}$ over $\mathbb {F}_{3^{n}}$ with n odd and then compute its boomerang spectrum based on the differential spectrum. In addition, in 2018, Boura and Canteaut determined the boomerang spectrum of the inverse function over $\mathbb {F}_{2^{n}}$ with n even. Following their work, we characterize the boomerang spectrum of the inverse function $x^{p^{n}-2}$ over $\mathbb {F}_{p^{n}}$ for any odd prime p. |
| Databáze: | OpenAIRE |
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