A Novel S-Box Design Based on Quantum Tent Maps and Fractional Stochastic Models With an Application in Image Encryption

dc.authorid Yalcin, Mustak Erhan/0000-0003-3377-2560
dc.authorscopusid 57205348801
dc.authorscopusid 57191577688
dc.authorscopusid 6602685919
dc.authorscopusid 7005476038
dc.authorwosid Yalcin, Mustak Erhan/O-2257-2015
dc.contributor.author Hematpour, Nafiseh
dc.contributor.author Gharari, Fatemeh
dc.contributor.author Ors, Berna
dc.contributor.author Yalcin, Mustak E.
dc.date.accessioned 2024-06-23T21:36:55Z
dc.date.available 2024-06-23T21:36:55Z
dc.date.issued 2023
dc.department Kadir Has University en_US
dc.department-temp [Hematpour, Nafiseh; Ors, Berna; Yalcin, Mustak E.] Istanbul Tech Univ, Fac Elect & Elect Engn, TR-34469 Istanbul, Turkiye; [Hematpour, Nafiseh] Kadir Has Univ, Dept Mechatron Engn, Istanbul, Turkiye; [Gharari, Fatemeh] Univ Mohaghegh Ardabili, Dept Stat & Comp Sci, Ardebil, Iran en_US
dc.description Yalcin, Mustak Erhan/0000-0003-3377-2560 en_US
dc.description.abstract In this article, we propose an approach to create a high-quality quantum tent map by utilizing the generalized quantum dot system. Our objective is to determine if its chaos surpasses that of the traditional classic tent. To achieve this, we first introduce a quantum tent map, showcasing its chaotic behavior in relation to control parameters and initial conditions. We validate the presence of chaos by calculating the Lyapunov exponent and analyzing the time series. Next, we design a chaotic S-box based on this new map. Subsequently, we explore the possibility of obtaining strong S-boxes by employing two fractional stochastic models and three components of the proposed quantum tent map. Our primary question is whether the combination of fractional stochastic models and quantum tent maps can result in superior S-boxes. The answer to this question is a resounding "Yes." The performance of these S-boxes exceeds that of previously proposed models. Finally, we evaluate a mixed S-box as the foundation for achieving highly secure image encryption. Among the models presented in this article, the best-performing S-box is produced through the combination of the fractional gamma distribution (FGD) with parameters alpha = 1.06 and beta = 2.8, along with the X-quantum tent map dimension. This model achieves an SAC (Strict Avalanche Criterion) value of 0.5, surpassing even AES (Advanced Encryption Standard). Its non-linearity value is 106.625, indicating excellent performance. Additionally, the model has an LP (Linear Property) value of 0.128906 and a DP (Differential Properties) score of 12. Furthermore, we obtain BIC-SAC 0.503209 and BIC-Non-linearity 103.679. Lastly, we present an image encryption algorithm to demonstrate the effectiveness of the mixed S-box, evaluating its performance against various attacks. The results affirm the suitability of this encryption method, with the generated image encryption offering a key space of 216960, ensuring high security. The example image exhibits an entropy value of 7.9311. Moreover, it demonstrates correlations in different orientations: horizontal (0.0076), vertical (-0.00048659), and diagonal (0.00020717). The image also achieves NPCR (Number of Pixel Change Rate) at %99.63 and UACI (Unified Average Changing Intensity) at %33.96. Notably, the algorithm executes in an impressive time of 0.810653, particularly considering the utilization of new 64 S-boxes instead of a fixed one. Even the correlation value for some standard photos approaches 0.0000667, demonstrating smallest correlation. This article underscores the effectiveness of combining new methods to generate an S-box. en_US
dc.description.sponsorship Trkiye Bilimsel ve Teknolojik Arascedil;tirma Kurumu en_US
dc.description.sponsorship No Statement Available en_US
dc.identifier.citationcount 0
dc.identifier.doi 10.1007/s00500-023-09478-x
dc.identifier.issn 1432-7643
dc.identifier.issn 1433-7479
dc.identifier.scopus 2-s2.0-85179658233
dc.identifier.scopusquality Q2
dc.identifier.uri https://doi.org/10.1007/s00500-023-09478-x
dc.identifier.uri https://hdl.handle.net/20.500.12469/5670
dc.identifier.wos WOS:001130364400002
dc.identifier.wosquality Q2
dc.language.iso en en_US
dc.publisher Springer en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.scopus.citedbyCount 4
dc.subject Quantum tent map en_US
dc.subject Fractional stochastic models en_US
dc.subject Substitution boxes (S-boxes) en_US
dc.subject Cryptography en_US
dc.subject Performance analysis en_US
dc.title A Novel S-Box Design Based on Quantum Tent Maps and Fractional Stochastic Models With an Application in Image Encryption en_US
dc.type Article en_US
dc.wos.citedbyCount 6
dspace.entity.type Publication

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