A stable meaningful image encryption scheme using the newly-designed 2D discrete fractional-order chaotic map and Bayesian compressive sensing

Abstract

In order to safely and covertly protect the digital image information during public channel transmission and localized storage, a stable image visually secure encryption algorithm by using 2D discrete fractional-order chaotic map (FOCM), Bayesian compressive sensing (BCS), and discrete V transform (DVT) is presented in this paper. First, the key-controlled measurement matrix constructed by the infinite collapse-Chebyshev-coupling chaotic map is employed to measure the scrambled wavelet packet coefficients of plain image in parallel. Then, the fractional-order chaotic map designed through piece-wise constant arguments method is employed to generate the secret code streams with assistance of the counter mode, and under its control, the compressed image is re-encrypted into the intermediate secret image. Next, the DVT-based embedding technology is proposed to stochastically embed the secret data into the non-secret-involved host image. Eventually, experimental results show that under the premise of ensuring security, the proposed algorithm improves the visual security around 1∼9 dB, and stabilizes its compression performance within 1 dB, compared with other existing related encryption algorithms.