https://doi.org/10.1140/epjp/s13360-025-06326-9
Regular Article
A novel image encryption scheme based on elliptic curves, Hilbert matrices and chaotic maps for better visual sentimental performance of telecommunication systems
1
Department of Mathematical Sciences, Faculty of Science and Technology, Fatima Jinnah Women University, Rawalpindi, Pakistan
2
Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia
3
Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia
Received:
11
January
2025
Accepted:
13
April
2025
Published online:
13
May
2025
Chaos-based image encryption techniques have gained attention due to their potential for generating highly complex and unpredictable encryption algorithms. These algorithms leverage chaotic systems’ attributes, which are sensitive to initial conditions and exhibit complex, non-repeating behavior, enabling them attractive candidate for encryption purposes. The intricate dynamics of chaotic systems makes it difficult for intruders to predict or crack the encryption without the proper decryption key. The use of piecewise linear chaotic map for image permutation introduces nonlinearity and randomness to the encryption process. Additionally, utilizing an elliptic curve and a Hilbert matrix for generating the encryption key brings a different layer of complexity. The chaotic logistic map further contributes to the encryption process by generating a sequence crucial for diffusion of pixels. To guarantee that the suggested encryption mechanism is robust and secure, various analyses like information entropy, statistical analysis of histograms, pixel correlation and sensitivity analysis are carried out. Through the result of these analyses, it is evident that this proposed technique is a promising approach to address security concerns in transmitting images over public networks. The proposed work attains high NPCR (99.63%), UACI (33.47%) and entropy (7.9991) that ensures resilience against statistical and differential attacks. Comparing the suggested study with the literature existing research shows that it is a reliable and safe real-time image encryption system.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
