2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption
Abstract 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 $$\:r$$ governs the system’s behavior, exhibiti...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2025-06-01
|
| Series: | Scientific Reports |
| Subjects: | |
| Online Access: | https://doi.org/10.1038/s41598-025-04702-0 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850136628872347648 |
|---|---|
| author | Raiz Ahmad Ghawar Said Aymen Flah Habib Kraiem Claude Ziad El bayeh Yousaf Hameed Khattak Faisal Baig |
| author_facet | Raiz Ahmad Ghawar Said Aymen Flah Habib Kraiem Claude Ziad El bayeh Yousaf Hameed Khattak Faisal Baig |
| author_sort | Raiz Ahmad |
| collection | DOAJ |
| description | Abstract 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 $$\:r$$ 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 $$\:{r}_{1}$$ =4, $$\:{r}_{2}$$ =3.8, and initial seed values $$\:{x}_{0}$$ =0.2350 and $$\:{y}_{0}$$ =0.3500, were run for $$\:{10}^{6}$$ 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. |
| format | Article |
| id | doaj-art-3ebca07bbb0a4f19a52206ca26ba6005 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-3ebca07bbb0a4f19a52206ca26ba60052025-08-20T02:31:04ZengNature PortfolioScientific Reports2045-23222025-06-0115111410.1038/s41598-025-04702-02D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryptionRaiz Ahmad0Ghawar Said1Aymen Flah2Habib Kraiem3Claude Ziad El bayeh4Yousaf Hameed Khattak5Faisal Baig6Federal Urdu University of Arts, Science & Technology IslamabadComputer Science Department, Iqra UniversityProcesses, Energy, Environment, and Electrical Systems, National Engineering School of Gabès, University of GabèsCenter for Scientific Research and Entrepreneurship, Northern Border UniversityCollege of Engineering and Technology, University of Doha for Science and TechnologyFederal Urdu University of Arts, Science & Technology IslamabadFederal Urdu University of Arts, Science & Technology IslamabadAbstract 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 $$\:r$$ 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 $$\:{r}_{1}$$ =4, $$\:{r}_{2}$$ =3.8, and initial seed values $$\:{x}_{0}$$ =0.2350 and $$\:{y}_{0}$$ =0.3500, were run for $$\:{10}^{6}$$ 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.https://doi.org/10.1038/s41598-025-04702-0EncryptionImage cryptographyChaotic mapTwo-dimensional logistic mapSecurity analysis |
| spellingShingle | Raiz Ahmad Ghawar Said Aymen Flah Habib Kraiem Claude Ziad El bayeh Yousaf Hameed Khattak Faisal Baig 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption Scientific Reports Encryption Image cryptography Chaotic map Two-dimensional logistic map Security analysis |
| title | 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_short | 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 |
| topic | Encryption Image cryptography Chaotic map Two-dimensional logistic map Security analysis |
| url | https://doi.org/10.1038/s41598-025-04702-0 |
| work_keys_str_mv | AT raizahmad 2dlogisticmapwithunittransferfunctionandmodulusoperationbasedpseudorandomnumbergenerationforimageencryption AT ghawarsaid 2dlogisticmapwithunittransferfunctionandmodulusoperationbasedpseudorandomnumbergenerationforimageencryption AT aymenflah 2dlogisticmapwithunittransferfunctionandmodulusoperationbasedpseudorandomnumbergenerationforimageencryption AT habibkraiem 2dlogisticmapwithunittransferfunctionandmodulusoperationbasedpseudorandomnumbergenerationforimageencryption AT claudeziadelbayeh 2dlogisticmapwithunittransferfunctionandmodulusoperationbasedpseudorandomnumbergenerationforimageencryption AT yousafhameedkhattak 2dlogisticmapwithunittransferfunctionandmodulusoperationbasedpseudorandomnumbergenerationforimageencryption AT faisalbaig 2dlogisticmapwithunittransferfunctionandmodulusoperationbasedpseudorandomnumbergenerationforimageencryption |