A lower bound on the number of inequivalent APN functions

2020/02/03 by Christian Kaspers, Yue Zhou, Kaspers, Christian +1 · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Cryptographic Implementations and Security #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2002.00673

openalex publication_date 2020/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish a lower bound on the total number of inequivalent APN functions on the finite field with 2^2m elements, where m is even. We obtain this result by proving that the APN functions introduced by Pott and the second author, that depend on three parameters k, s and α, are pairwise inequivalent for distinct choices of the parameters k and s. Moreover, we determine the automorphism group of these APN functions.

Citations

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