On the Differential Properties of the Power Mapping x^pm+2

2022/04/18 by Yuying Man, Yongbo Xia, Man, Yuying +5
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Coding theory and cryptography #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2204.08118

openalex publication_date 2022/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let m be a positive integer and p a prime. In this paper, we investigate the differential properties of the power mapping x^pm+2 over \mathbbF_pⁿ, where n=2m or n=2m-1. For the case n=2m, by transforming the derivative equation of x^pm+2 and studying some related equations, we completely determine the differential spectrum of this power mapping. For the case n=2m-1, the derivative equation can be transformed to a polynomial of degree p+3. The problem is more difficult and we obtain partial results about the differential spectrum of x^pm+2.

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