A New Representation of Binary Sequences by means of Boolean Functions
This work provides a theoretical framework for linking Boolean functions and binary sequences, which may be useful for cryptographers studying sequence properties, but the results are theoretical and no concrete improvements or numbers are presented.
The paper introduces a new bijection between Boolean functions and binary sequences with period a power of two, and defines a reverse-ANF representation for sequences. It explores relationships between this representation and existing ones, and analyzes generalized self-shrinking sequences using these tools.
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.