Image encryption based on compressive sensing and chaos systems

Abstract

Recently, a new image encryption technique based on compressive sensing (CS) has been proposed. CS allows the signal to be sampled at a much lower rate than the Nyquist- Shannon rate. Furthermore, the signal can be sampled and compressed in a single step using the sparsity of the signal which represents the signal with a reduced number of samples. The signal can be sparse in its original domain or in another domain such as Discrete Cosine Transform (DCT), Discrete Fourier Transform (DFT) or Discrete Wavelet Transform (DWT). In addition, CS can be used for encryption by using a good measurement matrix as the secret key of the encryption algorithm, so that CS samples, compresses and encrypts in a one-step process.This paper introduces a new algorithm based on CS for image encryption. Plain image is sparse in the DCT domain, and the combination of pixels is used to reduce the dimension of the image DCT. The measurement matrix is generated using a three-dimensional chaotic system, and for further encryption, pixel scrambling is applied using a one-dimensional chaotic system to generate the scrambling vector. Experimental and analysis results show that the proposed algorithm has good performance in terms of security and image compression, as well as low time complexity.