A New Representation of Binary Sequences by means of Boolean Functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913074161647616 |
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| author | Cardell, S. D. Fúster-Sabater, A. Requena, V. Beltrá, M. |
| author_facet | Cardell, S. D. Fúster-Sabater, A. Requena, V. Beltrá, M. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_05374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Representation of Binary Sequences by means of Boolean Functions Cardell, S. D. Fúster-Sabater, A. Requena, V. Beltrá, M. Cryptography and Security Information Theory 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. |
| title | A New Representation of Binary Sequences by means of Boolean Functions |
| topic | Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2506.05374 |