2023/04/30 by Augustine Musukwa, Musukwa, Augustine
Computer Science · Engineering · #06E30 #14G50 #94A60 #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2305.00582
openalex publication_date 2023/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine a connection between the weight of a Boolean function and the total weight of its first-order derivatives. The relationship established is used to study some cryptographic properties of Boolean functions. We establish a characterization of APN permutations in terms of the weight of the first-order derivatives of their components. We also characterize APN functions by the total weight of the second-order derivatives of their components. The total weight of the first-order and second-order derivatives for functions such as permutations, bent, partially-bent, quadratic, plateaued and balanced functions is determined.