A novel multi‐image visually meaningful encryption algorithm based on compressive sensing and Schur decomposition

Abstract

Abstract Image encryption algorithm is an important telecommunication technology for protecting personal security. In this article, we propose a novel multi‐image visual encryption algorithm based on compressive sensing (CS) and Schur decomposition. First, multiple images are sparsed by a discrete wavelet transform, and the compressed images are obtained by zigzag confusion and CS. Second, these compressed images are combined according to random sequences and scrambled again to obtain the secret image. Third, the carrier image is subjected to a two‐level lifting wavelet transform where the low‐frequency and high‐frequency subbands are selected to perform a discrete cosine transform (DCT). Fourth, Schur decomposition is employed on the secret image to calculate an upper triangular matrix and a unitary matrix (orthogonal matrix) to be embedded into the DCT coefficients of the previous low‐frequency and high‐frequency subbands, respectively. With an inverse transformation, the final visually meaningful encrypted image is achieved. Here, the initial position of the zigzag confusion is related to the plain image, which can effectively resist known‐plaintext and chosen‐plaintext attacks. The simulation results demonstrate that the proposed algorithm has high security and good imperceptibility.