Two classes of power mappings with boomerang uniformity 2

Haode Yan; Zhen Li; Zhitian Song; Rongquan Feng

doi:10.3934/amc.2022046

Article Contents

2022, Volume 16, Issue 4: 1111-1120. Doi: 10.3934/amc.2022046

This issue Previous Article Maximal complete permutations over $ \mathbb{F}_2^n $ Next Article Kite-group divisible packings and coverings with any minimum leave and minimum excess

Two classes of power mappings with boomerang uniformity 2

1.
School of Mathematics, Southwest Jiaotong University, China
2.
The Experimental High School Attached to Beijing Normal University, China
3.
School of Mathematical Sciences, Peking University, China

^*Corresponding author: Haode Yan ([email protected])
^*Corresponding author: Haode Yan ([email protected])

Received: March 2022

Revised: May 2022

Early access: June 2022

Published: November 2022

H. Yan's research was supported by the National Natural Science Foundation of China (Grant No.11801468) and the Fundamental Research Funds for the Central Universities of China (Grant No.2682021ZTPY076)

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Abstract

Let $ q $ be an odd prime power. Let $ F_1(x) = x^{d_1} $ and $ F_2(x) = x^{d_2} $ be power mappings over $ \mathrm{GF}(q^2) $, where $ d_1 = q-1 $ and $ d_2 = d_1+\frac{q^2-1}{2} = \frac{(q-1)(q+3)}{2} $. In this paper, we study the boomerang uniformity of $ F_1 $ and $ F_2 $ via their differential properties. It is shown that the boomerang uniformity of $ F_i $ ($ i = 1,2 $) is 2 with some conditions on $ q $.

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Mathematics Subject Classification: Primary: 94A60; Secondary: 11T06.

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