2020/04/23 by Christian Kaspers, Yue Zhou, Kaspers, Christian +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Cryptographic Implementations and Security #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.CO #math.IT
paper · pdf · doi:10.48550/arxiv.2004.11896
38 pages. arXiv admin note: text overlap with arXiv:2002.00673
openalex publication_date 2020/04/23 · arxiv created 2020/11/29 · arxiv updated 2020/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Almost perfect nonlinear (APN) functions play an important role in the design of block ciphers as they offer the strongest resistance against differential cryptanalysis. Despite more than 25 years of research, only a limited number of APN functions are known. In this paper, we show that a recent construction by Taniguchi provides at least (φ(m))/(2)\lceil (2m+1)/(3m) \rceil inequivalent APN functions on the finite field with 22m elements, where φ denotes Euler's totient function. This is a great improvement of previous results: for even m, the best known lower bound has been (φ(m))/(2)(\lfloor (m)/(4)\rfloor +1), for odd m, there has been no such lower bound at all. Moreover, we determine the automorphism group of Taniguchi's APN functions.