A New Representation of Binary Sequences by means of Boolean Functions

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.

@article{cardell2025_2506.05374,
  title={ A New Representation of Binary Sequences by means of Boolean Functions },
  author={ S.D. Cardell and A. Fuúter-Sabater and V. Requena and M. Beltrá },
  journal={arXiv preprint arXiv:2506.05374},
  year={ 2025 }
}