A novel image encryption algorithm using chaotic compressive sensing and nonlinear exponential function

Abstract

This paper presents an optically secure image cryptosystem in the compressed-sensing (CS) domain by using a chaos driven nonlinear function. First, the original image is divided into non-overlapping blocks of uniform size, and then the discrete cosine transform (DCT) is used for obtaining sparse representation of these blocks. A logistic map-based circulant sensing measurement matrix is used to compress the sparse representations of the blocks. This partial cipher is further processed for encryption using a nonlinear function based on a dynamic invertible exponential function. The decorrelation of values is done by applying the Arnold 2-D map on the cipher. The seed values to the logistic equation and the parameters of the Arnold map are based on the original image, which makes the proposed algorithm robust in terms of plain text sensitivity. Not only does the algorithm achieve a considerable amount of security, but it also conceals the original image identity by the compression introduced, thereby reducing the storage and transmission cost. The decryption of the cipher is done using a smooth l0 approximation, giving high-quality reconstruction results. The extensive simulation results and performance analysis illustrates the excellent security and reconstruction results of the proposed scheme in comparison with the existing algorithms.