2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption

[EN] This study presents a novel approach to generating high-quality random numbers using a two-dimensional logistic map with a unit transfer function (2DLMUTF). The method is built upon the chaotic dynamics of the logistic map, where the parameter \documentclass[12pt]{minimal} \usepackage{amsmath}...

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Detalles Bibliográficos
Autores: Ahmad, Raiz, Said, Ghawar, Flah, Aymen, Kraiem, Habib, El Bayeh, Claude Ziad, Baig, Faisal, Khattak, Yousaf Hameed|||0000-0002-7565-192X
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/224403
Acceso en línea:https://riunet.upv.es/handle/10251/224403
Access Level:acceso abierto
Palabra clave:Encryption
Image cryptography
Chaotic map
Two-dimensional logistic map
Security analysis
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oai_identifier_str oai:riunet.upv.es:10251/224403
network_acronym_str ES
network_name_str España
repository_id_str
dc.title.none.fl_str_mv 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
title 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
spellingShingle 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
Ahmad, Raiz
Encryption
Image cryptography
Chaotic map
Two-dimensional logistic map
Security analysis
title_short 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
title_full 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
title_fullStr 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
title_full_unstemmed 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
title_sort 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
dc.creator.none.fl_str_mv Ahmad, Raiz
Said, Ghawar
Flah, Aymen
Kraiem, Habib
El Bayeh, Claude Ziad
Baig, Faisal
Khattak, Yousaf Hameed|||0000-0002-7565-192X
author Ahmad, Raiz
author_facet Ahmad, Raiz
Said, Ghawar
Flah, Aymen
Kraiem, Habib
El Bayeh, Claude Ziad
Baig, Faisal
Khattak, Yousaf Hameed|||0000-0002-7565-192X
author_role author
author2 Said, Ghawar
Flah, Aymen
Kraiem, Habib
El Bayeh, Claude Ziad
Baig, Faisal
Khattak, Yousaf Hameed|||0000-0002-7565-192X
author2_role author
author
author
author
author
author
dc.contributor.none.fl_str_mv Instituto de Diseño para la Fabricación y Producción Automatizada
European Commission
Northern Border University
Ministry of the Environment, República Checa
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Encryption
Image cryptography
Chaotic map
Two-dimensional logistic map
Security analysis
topic Encryption
Image cryptography
Chaotic map
Two-dimensional logistic map
Security analysis
description [EN] This study presents a novel approach to generating high-quality random numbers using a two-dimensional logistic map with a unit transfer function (2DLMUTF). The method is built upon the chaotic dynamics of the logistic map, where the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:r$$\end{document} governs the system's behavior, exhibiting chaotic nature in the range of 3.57 to 4. By applying a unit transfer function and modulus operation, the system's output is constrained within the [0, 1] range, altering the phase space dynamics compared to traditional 2D logistic maps. Numerical simulations in MATLAB, with parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{r}_{1}$$\end{document}=4, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{r}_{2}$$\end{document}=3.8, and initial seed values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{0}$$\end{document}=0.2350 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{y}_{0}$$\end{document}=0.3500, were run for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{10}<^>{6}$$\end{document} iterations. Statistical testing using the NIST SP 800 - 22 test suite showed superior randomness, with the method passing all 15 tests. Additionally, uniformity, autocorrelation, cross-correlation, and entropy analyses confirmed the method's suitability for cryptographic applications. The generated random numbers were used to create substitution boxes (S-boxes) for image encryption, demonstrating strong encryption performance. Overall, 2DLMUTF offers a computationally efficient and secure solution for random number generation which is suitable for cryptographic and image encryption applications.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-06-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/224403
url https://riunet.upv.es/handle/10251/224403
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv MZP MZP CZ.10.03.01%2F00%2F22_003%2F0000048
NBU NBU NBU-FFR-2025-2484-05
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/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
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Nature Publishing Group
publisher.none.fl_str_mv Nature Publishing Group
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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spelling 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryptionAhmad, RaizSaid, GhawarFlah, AymenKraiem, HabibEl Bayeh, Claude ZiadBaig, FaisalKhattak, Yousaf Hameed|||0000-0002-7565-192XEncryptionImage cryptographyChaotic mapTwo-dimensional logistic mapSecurity analysis[EN] This study presents a novel approach to generating high-quality random numbers using a two-dimensional logistic map with a unit transfer function (2DLMUTF). The method is built upon the chaotic dynamics of the logistic map, where the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:r$$\end{document} governs the system's behavior, exhibiting chaotic nature in the range of 3.57 to 4. By applying a unit transfer function and modulus operation, the system's output is constrained within the [0, 1] range, altering the phase space dynamics compared to traditional 2D logistic maps. Numerical simulations in MATLAB, with parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{r}_{1}$$\end{document}=4, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{r}_{2}$$\end{document}=3.8, and initial seed values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{0}$$\end{document}=0.2350 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{y}_{0}$$\end{document}=0.3500, were run for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{10}<^>{6}$$\end{document} iterations. Statistical testing using the NIST SP 800 - 22 test suite showed superior randomness, with the method passing all 15 tests. Additionally, uniformity, autocorrelation, cross-correlation, and entropy analyses confirmed the method's suitability for cryptographic applications. The generated random numbers were used to create substitution boxes (S-boxes) for image encryption, demonstrating strong encryption performance. Overall, 2DLMUTF offers a computationally efficient and secure solution for random number generation which is suitable for cryptographic and image encryption applications.The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research work through the project number. NBU-FFR-2025-2484-05., also the authors declare that the article has been produced with the financial support of the European Union under the REFRESH - Research Excellence For Region Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition and paper was supported by the following project TN02000025 National Centre for Energy II awarded to HK.Nature Publishing GroupInstituto de Diseño para la Fabricación y Producción AutomatizadaEuropean CommissionNorthern Border UniversityMinistry of the Environment, República ChecaRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-06-02journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/224403reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMZP MZP CZ.10.03.01%2F00%2F22_003%2F0000048NBU NBU NBU-FFR-2025-2484-05open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2244032026-06-13T07:49:27Z
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