A computational approach for the study of linear complexity of shrunken sequences

The shrinking generator is a pseudorandom bit generator based on the combination of two linear feedback shift registers of maximum period. These registers are synchronized with a common clock and produce binary sequences with good statistical properties. Due to its simplicity and efficient implement...

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Autores: Requena, Verónica, Gómez, Ana Isabel, Gómez Pérez, Domingo|||0000-0002-5780-2165
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:dnet:ucreareposit::7651a86cee6876bb9aed76b7a190463e
Acceso en línea:https://hdl.handle.net/10902/39871
Access Level:acceso abierto
Palabra clave:Shrinking generators
Linear complexity
Linear complexity profile
Multidimensional arrays
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spelling A computational approach for the study of linear complexity of shrunken sequencesRequena, VerónicaGómez, Ana IsabelGómez Pérez, Domingo|||0000-0002-5780-2165Shrinking generatorsLinear complexityLinear complexity profileMultidimensional arraysThe shrinking generator is a pseudorandom bit generator based on the combination of two linear feedback shift registers of maximum period. These registers are synchronized with a common clock and produce binary sequences with good statistical properties. Due to its simplicity and efficient implementation, the shrinking generator is particularly suitable for stream cipher cryptographic schemes and most proposed attacks rely on the properties of the generator. Furthermore, its analysis serves as the foundation for other interleave constructions. In our work, we present a new algorithm which allows to compute the linear complexity for shrunken sequences in an efficient way together with a closed formula for the linear complexity of its output in certain conditions. Additionally, we establish the first bound on its linear complexity profile and a conjecture about the values of the linear complexity of these sequences. Our techniques involve two-dimensional arrays and their interleave structure, which could prove valuable for other pseudorandom bit generators.The work of the first author is partially supported by grant PID2023-151238OA-I00 funded by MICIU/AEI /10.13039/501100011033 and by ERDF, EU. The work of the second author was supported contribution is part of the “CÁTEDRA UNIVERSIDAD DE CANTABRIA-INCIBE DE NUEVOS RETOS EN CIBERSEGURIDAD ”, financed by “European Union NextGeneration-EU, the Recovery Plan, Transformation and Resilience, through INCIBE. The work of the third author partially supported by the Spanish I+D+i project PID2022-142159OB-I00 of the Ministerio de Ciencia e Innovación, I+D+i project CIAICO/2022/167 of the Generalitat Valenciana, and the I+D+i project VIGROB-287 of the Universitat d’Alacant.SpringerUniversidad de Cantabria20262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/39871Cryptography and Communications, 2026, 18(1), 141-152reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:dnet:ucreareposit::7651a86cee6876bb9aed76b7a190463e2026-06-02T12:39:31Z
dc.title.none.fl_str_mv A computational approach for the study of linear complexity of shrunken sequences
title A computational approach for the study of linear complexity of shrunken sequences
spellingShingle A computational approach for the study of linear complexity of shrunken sequences
Requena, Verónica
Shrinking generators
Linear complexity
Linear complexity profile
Multidimensional arrays
title_short A computational approach for the study of linear complexity of shrunken sequences
title_full A computational approach for the study of linear complexity of shrunken sequences
title_fullStr A computational approach for the study of linear complexity of shrunken sequences
title_full_unstemmed A computational approach for the study of linear complexity of shrunken sequences
title_sort A computational approach for the study of linear complexity of shrunken sequences
dc.creator.none.fl_str_mv Requena, Verónica
Gómez, Ana Isabel
Gómez Pérez, Domingo|||0000-0002-5780-2165
author Requena, Verónica
author_facet Requena, Verónica
Gómez, Ana Isabel
Gómez Pérez, Domingo|||0000-0002-5780-2165
author_role author
author2 Gómez, Ana Isabel
Gómez Pérez, Domingo|||0000-0002-5780-2165
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Shrinking generators
Linear complexity
Linear complexity profile
Multidimensional arrays
topic Shrinking generators
Linear complexity
Linear complexity profile
Multidimensional arrays
description The shrinking generator is a pseudorandom bit generator based on the combination of two linear feedback shift registers of maximum period. These registers are synchronized with a common clock and produce binary sequences with good statistical properties. Due to its simplicity and efficient implementation, the shrinking generator is particularly suitable for stream cipher cryptographic schemes and most proposed attacks rely on the properties of the generator. Furthermore, its analysis serves as the foundation for other interleave constructions. In our work, we present a new algorithm which allows to compute the linear complexity for shrunken sequences in an efficient way together with a closed formula for the linear complexity of its output in certain conditions. Additionally, we establish the first bound on its linear complexity profile and a conjecture about the values of the linear complexity of these sequences. Our techniques involve two-dimensional arrays and their interleave structure, which could prove valuable for other pseudorandom bit generators.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/39871
url https://hdl.handle.net/10902/39871
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Cryptography and Communications, 2026, 18(1), 141-152
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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