Encryption of image data using compressive sensing and chaotic system

Abstract

An image cryptosystem using chaotic compressive sensing is designed to achieve simultaneous compression - encryption. Compressive sensing requires a measurement matrix to compressively sample a sparse signal and to guarantee its recovery at the receiver. In this paper, a new one-dimensional chaotic map is proposed which is used to construct the chaotic measurement matrix. Performance analysis demonstrates that the proposed chaotic map is highly chaotic, ergodic, highly sensitive to the initial conditions and suitable for chaotic compressive sensing. The parameters of the chaotic system are used as the secret key in the construction of measurement matrix and also the masking matrix. The sparse representation of the image is obtained using discrete wavelet transform. The sparse coefficients are then compressively sampled and encrypted using the chaotic measurement matrix and masking matrix. A parallel compressive sensing framework is employed which greatly improves the efficiency of the proposed chaotic compressive sensing scheme. Simulation results shows that the proposed scheme has good security performance against various attacks and better reconstruction performance, when compared with the commonly used random measurement matrix.