Representations of Generalized Self-Shrunken Sequences
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Título: | Representations of Generalized Self-Shrunken Sequences |
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Autor/es: | Cardell, Sara D. | Climent, Joan-Josep | Fúster Sabater, Amparo | Requena Arévalo, Verónica |
Grupo/s de investigación o GITE: | Grupo de Álgebra y Geometría (GAG) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Generalized self-shrinking generator | PN-sequence | Binomial sequence | Additive group | Coset |
Área/s de conocimiento: | Álgebra |
Fecha de publicación: | 19-jun-2020 |
Editor: | MDPI |
Cita bibliográfica: | Cardell SD, Climent J-J, Fúster-Sabater A, Requena V. Representations of Generalized Self-Shrunken Sequences. Mathematics. 2020; 8(6):1006. doi:10.3390/math8061006 |
Resumen: | Output sequences of the cryptographic pseudo-random number generator, known as the generalized self-shrinking generator, are obtained self-decimating Pseudo-Noise (PN)-sequences with shifted versions of themselves. In this paper, we present three different representations of this family of sequences. Two of them, the p and G-representations, are based on the parameters p and G corresponding to shifts and binary vectors, respectively, used to compute the shifted versions of the original PN-sequence. In addition, such sequences can be also computed as the binary sum of diagonals of the Sierpinski’s triangle. This is called the B-representation. Characteristics and generalities of the three representations are analyzed in detail. Under such representations, we determine some properties of these cryptographic sequences. Furthermore, these sequences form a family that has a group structure with the bit-wise XOR operation. |
Patrocinador/es: | This research is partially supported by Ministerio de Economía, Industria y Competitividad (MINECO), Agencia Estatal de Investigación (AEI), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS, reference TIN2017-84844-C2-1-R. It is also supported by Comunidad de Madrid (Spain) under project CYNAMON (P2018/TCS-4566), co-funded by FSE and European Union FEDER funds. The first author is supported by CAPES (Brazil). Finally, the second and fourth author are partially supported by Spanish grant VIGROB-287 of the Universitat d’Alacant. |
URI: | http://hdl.handle.net/10045/107613 |
ISSN: | 2227-7390 |
DOI: | 10.3390/math8061006 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.3390/math8061006 |
Aparece en las colecciones: | INV - GAG - Artículos de Revistas |
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