2015/07/19 by Morgan Barbier, Hayat Cheballah, Barbier, Morgan +4
Computer Science · #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #cs.CR #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1507.05316
arxiv created 2015/07/19 · openalex publication_date 2015/07/19 · arxiv updated 2015/07/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this transformation. This class -- which has been recently introduced -- has interesting properties, in particular if we want to control both the Hamming weight and the degree. We propose an innovative way to handle the Mobius transform which allows the composition between several Boolean functions and the use of Shannon or Reed-Muller decompositions. Thus we benefit from a better knowledge of coin-cident functions and introduce new properties. We show experimentally that for many features, coincident functions look like any Boolean functions.