2024/07/17 by Garg, Kirpa, Shabahat Hasan, Hasan, Sartaj Ul +4
Economics, Econometrics and Finance · Physics and Astronomy · #11T06 #12E20 #94A60 #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.2407.12617
openalex publication_date 2024/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-box, recently, three new tables have been introduced: the Extended Boomerang Connectivity Table (EBCT), the Lower Boomerang Connectivity Table (LBCT), and the Upper Boomerang Connectivity Table (UBCT). In fact, these tables offer improved methods over the usual Boomerang Connectivity Table (BCT) for analyzing the security of S-boxes against boomerang-style attacks. Here, we put in context these new EBCT, LBCT, and UBCT concepts by connecting them to the DDT for a differentially δ-uniform function and also determine the EBCT, LBCT, and UBCT entries of three classes of differentially 4-uniform power permutations, namely, Gold, Kasami and Bracken-Leander. We also determine the Double Boomerang Connectivity Table (DBCT) entries of the Gold function. As byproducts of our approach, we obtain some previously published results quite easily.