On some quadratic APN functions

  • Hiroaki TaniguchiEmail author


A construction of APN functions using the bent function \(B(x,y)=xy\) is proposed in Carlet (Des Codes Cryptogr 59:89–109, 2011). At this time, two families of APN functions using this construction are known, that is, the family of Carlet (2011) and the family of Zhou and Pott (Adv Math 234:43–60, 2013). In this note, we propose another family of APN functions with this construction, which are not CCZ equivalent to the former two families on \({{\mathbb {F}}}_{2^8}\). We also propose a family of presemifields and determined the middle, left, right nuclei and the center of the associated semifields.


APN function Semifield Projective polynomial 

Mathematics Subject Classification

11T71 06E30 12K10 51A35 



The author thanks the referees for many helpful comments and advices.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Institute of Technology, Kagawa CollegeTakamatsuJapan

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