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

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 sinelogistic 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 Logisticsine 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. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper extends the traditional discrete fractional Tchebyshev transform to the quaternion algebra domain for multi-image processing using quaternion theory. A new multi-image encryption scheme based on quaternion discrete fractional Tchebyshev moment transform (QDFrTMT) and the cross-coupling chaotic system is proposed. Numerical simulations and security analyses show the effectiveness of the algorithm and its ability to resist common attacks.