Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption
A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis...
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MDPI AG
2020-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/4/474 |
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doaj-c8e187df96c844908a6b85da8e115a1b2020-11-25T02:54:35ZengMDPI AGEntropy1099-43002020-04-012247447410.3390/e22040474Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image EncryptionLazaros Moysis0Christos Volos1Sajad Jafari2Jesus M. Munoz-Pacheco3Jacques Kengne4Karthikeyan Rajagopal5Ioannis Stouboulos6Laboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceLaboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceNonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, VietnamFaculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, MexicoDepartment of Electrical Engineering, University of Dschang, Dschang P.O. Box 134, CameroonCenter for Nonlinear dynamics, Defence University, Mekelle 1020, EthiopiaLaboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceA modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.https://www.mdpi.com/1099-4300/22/4/474chaoslogistic mapbifurcation analysisfuzzy numbersRBGimage encryption |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Lazaros Moysis Christos Volos Sajad Jafari Jesus M. Munoz-Pacheco Jacques Kengne Karthikeyan Rajagopal Ioannis Stouboulos |
| spellingShingle |
Lazaros Moysis Christos Volos Sajad Jafari Jesus M. Munoz-Pacheco Jacques Kengne Karthikeyan Rajagopal Ioannis Stouboulos Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption Entropy chaos logistic map bifurcation analysis fuzzy numbers RBG image encryption |
| author_facet |
Lazaros Moysis Christos Volos Sajad Jafari Jesus M. Munoz-Pacheco Jacques Kengne Karthikeyan Rajagopal Ioannis Stouboulos |
| author_sort |
Lazaros Moysis |
| title |
Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption |
| title_short |
Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption |
| title_full |
Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption |
| title_fullStr |
Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption |
| title_full_unstemmed |
Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption |
| title_sort |
modification of the logistic map using fuzzy numbers with application to pseudorandom number generation and image encryption |
| publisher |
MDPI AG |
| series |
Entropy |
| issn |
1099-4300 |
| publishDate |
2020-04-01 |
| description |
A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption. |
| topic |
chaos logistic map bifurcation analysis fuzzy numbers RBG image encryption |
| url |
https://www.mdpi.com/1099-4300/22/4/474 |
| work_keys_str_mv |
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