Differential Spectrum and Boomerang Spectrum of Some Power Mapping

2025/06/06 by Cui, Yuehui, Jinquan Luo, Luo, Jinquan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory #FOS: Computer and information sciences #Information Theory (cs.IT) #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2506.05738

openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(x)=x^s(pm-1) be a power mapping over \mathbbF_pⁿ, where n=2m and gcd(s,p^m+1)=t. In \citekpm-1, Hu et al. determined the differential spectrum and boomerang spectrum of the power function f, where t=1. So what happens if t≥1? In this paper, we extend the result of \citekpm-1 from t=1 to general case. We use a different method than in \citekpm-1 to determine the differential spectrum and boomerang spectrum of f by studying the number of rational points on some curves. This method may be helpful for calculating the differential spectrum and boomerang spectrum of some Niho type power functions.

Citations

• The differential spectrum and boomerang spectrum of a class of locally-APN functions
• Two Classes of Power Mappings with Boomerang Uniformity 2

Related

• The differential spectrum and boomerang spectrum of a class of locally-APN functions
• The Differential Spectrum of the Power Mapping x^pn-3
• Boomerang Spectra of Two Classes of Power Functions via Their Differential Spectra
• On the Niho type locally-APN power functions and their boomerang spectrum
• On the Differential Properties of the Power Mapping x^pm+2