New Perfect Nonlinear Functions and Their Semifields

2019/05/03 by Jinquan Luo, Luo, Jinquan, Junru Ma +1
Computer Science · Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Coding theory and cryptography #Combinatorics (math.CO) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1905.01041

openalex publication_date 2019/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, two new classes of perfect nonlinear functions over \mathbbF_p^2m are proposed, where p is an odd prime. Furthermore, we investigate the nucleus of the corresponding semifields of these functions and show that the semifields are not isotopic to all the known semifields. Particularly, the new perfect nonlinear functions are CCZ-inequivalent to other classes in general.

Citations

• Planar Functions and Planes of Lenz-Barlotti Class II
• Almost perfect and planar functions

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