Multi-image encryption scheme with quaternion discrete fractional Tchebyshev moment transform and cross-coupling operation

• Published in: Signal processing Vol. 211; p. 109107
• Main Authors: Zhou, Nan-Run, Tong, Liang-Jia, Zou, Wei-Ping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2023
• Subjects: Chaotic map; Cross-coupling operation; Multi-image encryption; Quaternion discrete fractional Tchebyshev moment transform; Chaotic map; Cross-coupling operation; Quaternion discrete fractional Tchebyshev moment transform; Multi-image encryption
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2023.109107

•The discrete fractional Tchebyshev transform is extended to the QDFrTMT.•The QDFrTMT with quaternion symplectic form enhances the computational efficiency.•Sine-logistic exponential chaotic map and piece-wise linear chaotic map are cross-coupled.•Double layers permutation-diffusion operations are performed for better robustness. With quaternion theory, the traditional discrete fractional Tchebyshev transform is extended to the quaternion algebra domain for multi-image processing. A new multi-image encryption scheme based on quaternion discrete fractional Tchebyshev moment transform (QDFrTMT) and the cross-coupling chaotic system is suggested. The original images are first confused by fractal sorting square matrix and sine-logistic exponential chaotic map, and then the resulting image is divided into four matrices. With the quaternion symplectic form representation, a quaternion signal can be formed by the divided matrices, which can reduce the number of the discrete fractional Tchebyshev transforms used and enhance the computational efficiency. Subsequently, the quaternion array is encrypted with the proposed QDFrTMT. To overcome the weakness of the permutation-diffusion operation based on a single chaotic map, a Logistic-sine exponential chaotic map and a piece-wise linear chaotic map are cross-coupled. The final ciphertext images can be acquired by carrying out the dual-layer encryption processes in horizontal and vertical directions. Numerical simulations and security analyses verify the effectiveness of the multi-image encryption algorithm and its strong ability to counteract common attacks.