Application of algebraic lattices in image encryption: methods comparison and analysis
Résumé
In this paper, we have introduced a novel color image encryption technique that relies on repairing a secret encryption key using algebraic lattices represented as Hasse diagrams and cryptography based on the matrices. The color images are converted into its RGB components ( Red, Green and Blue ) and each color is converted into a matrix of integers between 0 and 255. In this encryption process we proposed tow color images Lena of type JPEG and Baboon of type BMP with similar size, and we have involved the mathematical operations: addition, multiplication, and binary calculations, also be carried out a comparative study between certain encryption algorithms on this proposed color images. The experimental results reveal that the presented methods of image encryption has the advantages of large key space, strong robustness and good encryption and decryption performance. In addition, the product method has the merits of excellent performance of encryption.
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Références
G. Birkhoff, Lattice Theory, Amer. Math. Soc., New York, 1940.
H. R. Shakir, An image encryption method based on selective AES cod- ing of wavelet transform and chaotic pixel shuffling, Multimedia Tools and Applications 78(18) (2019) pp. 26073-26087.
S. Toughi, M.H. Fathi and Y.A. Sekhavat, “An image encryption scheme based on elliptic curve pseudo random and Advanced Encryption System,” Signal Processing 141 (2017) pp. 217-227, .
Nestor, T.; Belazi, A.; Abd-El-Atty, B.; Aslam, M.N.; Volos, C.; De Dieu, N.J.; Abd El-Latif, A.A. A new 4D hyperchaotic system with dynamics analysis, synchronization, and application to image encryption. Symmetry 2022, 14, 424.
Zhu, S.; Deng, X.; Zhang, W.; Zhu, C. Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding. Mathematics 2023, 11, 231.
Zeriouh, M., Chillali, A., and Boua, A. (2019). Cryptography based on the matrices. Bol. Soc. Paran. Mat, 3(3), 75-83.
C. Boyd and A. Mathuria, Protocols for Authentication and Key Establishment, Information Security and Cryptography Series; Springer-Verlag, Heidelberg, 2003.
Y. Qin, Z. Wang, Q. Pan, Q. Gong, Optical color-image encryption in the diffractive-imaging scheme, Opt. Lasers Eng. 77 (2016) 191–202.
S. Yuan, Y. Yang, X. Liu, X. Zhou, Z. Wei, Optical image transformation and encryption by phase-retrieval-based double random-phase encoding and compressive ghost imaging, Optics Lasers Eng. 100 (2018) 105–110.
X. Liao, M.A. Hahsmi, R. Haider, et al., An efficient mixed inter-intra pixels substitution at 2bits-level for image encryption technique using Dna and Chaos, Optik 153 (2018) 117–134.
Menezes A, Van Oorschot P, Vanstone S. Handbook of applied cryptography. Boca. Raton, FL: CRC Press; 1997
Jastrzebski K, Kotulski Z. On improved image encryption scheme based on chaotic map lattices. Eng Trans 2009;57(2):69–84.
Chung KL, Chang LC. Large encryption binary images with higher security. Pattern Recognit Lett 1998;19(56):461–8.
Hasse, H. Vorlesungen über Klassenkörpertheorie, Physica-Verlag: Würzburg, 1967.
Rival, I. In: Graphs and order; Rival, I., Ed.; D.Reidel Publishing Company: Dordrecht, 1985; pp. 103-133.
Birkhoff, G. Lattice theory, American Mathematical Society: Rhode Island; Vol: XXV, 1984.
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