2025/10/22 by James Kim, Kim, James
Computer Science · #Chaos-based Image/Signal Encryption #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2510.19885
openalex publication_date 2025/10/22 · openalex created_date 2025/10/25 · openalex updated_date 2026/07/28
Mathematically constructed S-boxes arise from algebraic structures and finite field theory to ensure strong, provable cryptographic properties. These mathematically grounded constructions allow for generation of thousands of S-Boxes with high nonlinearity, APN properties, and balanced avalanche characteristics, unlike fully random methods, which lack such theoretical guarantees in exchange for low complexity and more varied results. In this work, we compare mathematically constructed constructions with randomly generated ones to evaluate the relative weakness of the latter. We also establish an average measure of performance for randomly generated permutations, as well as random with forced cycle constraints, and compare them to well-established designs in a simple SPN setting.