From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology

Autores
de Micco, Luciana; Antonelli, Maximiliano; Rosso, Osvaldo Anibal
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.
Fil: de Micco, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; Argentina
Fil: Antonelli, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; Argentina
Fil: Rosso, Osvaldo Anibal. Universidade Federal de Alagoas; Brasil
Materia
PRNG
STATISTICAL PROPORTIES
NIST
DIEHARD
CHAOS
PERMUTATION ENTROPY
PERMUTATION COMPLEXITY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/174385

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network_name_str CONICET Digital (CONICET)
spelling From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodologyde Micco, LucianaAntonelli, MaximilianoRosso, Osvaldo AnibalPRNGSTATISTICAL PROPORTIESNISTDIEHARDCHAOSPERMUTATION ENTROPYPERMUTATION COMPLEXITYhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.Fil: de Micco, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; ArgentinaFil: Antonelli, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; ArgentinaFil: Rosso, Osvaldo Anibal. Universidade Federal de Alagoas; BrasilMolecular Diversity Preservation International2021-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/174385de Micco, Luciana; Antonelli, Maximiliano; Rosso, Osvaldo Anibal; From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology; Molecular Diversity Preservation International; Entropy; 23; 6; 5-2021; 1-171099-4300CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/23/6/671info:eu-repo/semantics/altIdentifier/doi/10.3390/e23060671info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:45:24Zoai:ri.conicet.gov.ar:11336/174385instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:45:25.129CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
title From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
spellingShingle From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
de Micco, Luciana
PRNG
STATISTICAL PROPORTIES
NIST
DIEHARD
CHAOS
PERMUTATION ENTROPY
PERMUTATION COMPLEXITY
title_short From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
title_full From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
title_fullStr From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
title_full_unstemmed From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
title_sort From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology
dc.creator.none.fl_str_mv de Micco, Luciana
Antonelli, Maximiliano
Rosso, Osvaldo Anibal
author de Micco, Luciana
author_facet de Micco, Luciana
Antonelli, Maximiliano
Rosso, Osvaldo Anibal
author_role author
author2 Antonelli, Maximiliano
Rosso, Osvaldo Anibal
author2_role author
author
dc.subject.none.fl_str_mv PRNG
STATISTICAL PROPORTIES
NIST
DIEHARD
CHAOS
PERMUTATION ENTROPY
PERMUTATION COMPLEXITY
topic PRNG
STATISTICAL PROPORTIES
NIST
DIEHARD
CHAOS
PERMUTATION ENTROPY
PERMUTATION COMPLEXITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.
Fil: de Micco, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; Argentina
Fil: Antonelli, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; Argentina
Fil: Rosso, Osvaldo Anibal. Universidade Federal de Alagoas; Brasil
description The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.
publishDate 2021
dc.date.none.fl_str_mv 2021-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/174385
de Micco, Luciana; Antonelli, Maximiliano; Rosso, Osvaldo Anibal; From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology; Molecular Diversity Preservation International; Entropy; 23; 6; 5-2021; 1-17
1099-4300
CONICET Digital
CONICET
url http://hdl.handle.net/11336/174385
identifier_str_mv de Micco, Luciana; Antonelli, Maximiliano; Rosso, Osvaldo Anibal; From continuous-time chaotic systems to pseudo random number generators: Analysis and generalized methodology; Molecular Diversity Preservation International; Entropy; 23; 6; 5-2021; 1-17
1099-4300
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/23/6/671
info:eu-repo/semantics/altIdentifier/doi/10.3390/e23060671
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Molecular Diversity Preservation International
publisher.none.fl_str_mv Molecular Diversity Preservation International
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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