A new one-dimensional cosine polynomial chaotic map and its use in image encryption

• Published in: The Visual computer Vol. 37; no. 3; pp. 541 - 551
• Main Authors: Talhaoui, Mohamed Zakariya, Wang, Xingyuan, Midoun, Mohamed Amine
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2021; Springer Nature B.V
• Subjects: Artificial Intelligence; Chaos theory; Computer Graphics; Computer Science; Cryptography; Data encryption; Dynamical systems; Entropy; Image Processing and Computer Vision; Original Article; Permutations; Polynomials; Security; Statistical analysis; Substitutes; Image encryption; Secure real-time communication; Cryptography; Chaos theory; One-dimensional chaotic map
• ISSN: 0178-2789; 1432-2315
• DOI: 10.1007/s00371-020-01822-8

In this paper, we propose a new real one-dimensional cosine polynomial (1-DCP) chaotic map. The statistical analysis of the proposed map shows that it has a simple structure, a high chaotic behavior, and an infinite chaotic range. Therefore, the proposed map is a perfect candidate for the design of chaos-based cryptographic systems. Moreover, we propose an application of the 1-DCP map in the design of a new efficient image encryption scheme (1-DCPIE) to demonstrate the new map further good cryptographic proprieties. In the new scheme, we significantly reduce the encryption process time by raising the small processing unit from the pixels level to the rows/columns level and replacing the classical sequential permutation substitution architecture with a parallel permutation substitution one. We apply several simulation and security tests on the proposed scheme and compare its performances with some recently proposed encryption schemes. The simulation results prove that 1-DCPIE has a better security level and a higher encryption speed.