2025/05/30 by Sara D. Cardell, Cardell, S. D., A. Fuúter-Sabater +5
Computer Science · #Advanced Algebra and Logic #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2506.05374
openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a connection between them which allows us to study some properties of Boolean functions through binary sequences and vice versa. Then, we define a new representation of sequences, based on Boolean functions and derived from the algebraic normal form, named reverse-ANF. Next, we study the relation between such a representation and other representations of Boolean functions as well as between such a representation and the binary sequences. Finally, we analyse the generalized self-shrinking sequences in terms of Boolean functions and some of their properties using the different representations.