Image encryption scheme based on compressed sensing and fractional quantum logistic-tent map

Abstract In this paper, we construct a quantum logistic-tent map and extend it to the fractional order. Using bifurcation portrait, Lyapunov exponent spectrum, and spectral entropy, its nonlinear characteristics are investigated. The analysis results illustrate that this fractional map possesses higher nonlinearity and is better suited for image encryption. Thus, the fractional quantum logistic-tent map as well as compressed sensing (CS) are utilized to create an image cryptosystem. The measurement matrix of CS is generated by this fractional map. Moreover, the map is also used for confusion and diffusion. In this encryption algorithm, the plaintext image is first sparsely represented with discrete wavelet transform (DWT). We then segment and reassemble the sparse image, and apply Arnold map to confuse the reassembled image. Next, a partial Hadamard matrix samples the image, and the pixel value is quantified with limited accuracy. Finally, the pixels of the image are diffused by two-way diffusion. This scheme integrates sparsity, block exchange, confusion, measurement acquisition, and diffusion. The simulation experiment finds that this image encryption approach possesses good security and compression performance.