An image compression-encryption scheme based on compressive sensing and hyperchaotic system

This paper proposes an image compression-encryption scheme based on compressive sensing, a seven-dimensional (7-D) hyperchaotic system, and the Josephus problem with Linear Feedback Shift Register (LFSR). Firstly, the plain image is transformed into a sparse matrix using a discrete wavelet transform. Then, the scrambling process is applied to the rows and columns using the Josephus sequences. This method demonstrates good scrambling performance and effectively breaks correlations between values with simple steps. Additionally, the shift number required in Josephus sequences is generated by an LFSR instead of being defined by a single value, thereby increasing the complexity and security of the algorithm. Secondly, to reduce the size of the image, CS is applied to the scrambling matrix where the measurement matrix is constructed using the first four variables of the 7-D hyperchaotic system to obtain the compressed image. Finally, to enhance the security of the compressed image, the XOR operation is applied between the compressed image and the mask matrix which is generated by the last three variables of the 7-D hyperchaotic system to obtain the final cipher image. Experimental and analyses results show that the proposed algorithm has good performance in terms of security and image compression, as well as low time complexity.