Quantum Image Encryption Based on Baker Map and 2D Logistic Map

This paper presents a quantum image encryption algorithm based on Baker map and 2D logistic map. The encrypted image is represented with NEQR model and the presented scheme adopts the strategy of selective encryption. Given a threshold value T, when CYX′≥T(CYX′<T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C^{\prime }_{YX}\geq T (C^{\prime }_{YX}< T)$\end{document}, the proposed scheme performs U⊕k(U⊕A) on quantum state |I′〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$|I^{\prime }\rangle $\end{document}. The final ciphertext quantum image is obtained through performing nine times quantum Baker map (QBM). The quantum circuits of encryption and decryption procedure are given. Multiple images were tested for security performance, including entropy, correlation coefficient (CC), Number of Pixel Change Rate (NPCR) and the Unified Averaged Changed Intensity (UACI). The best values of entropy, CC, NPCR and UACI are 7.9888, -0.0005, 99.58%, 33.17% respectively. Simulation results show that the proposed quantum image scheme has good performance in the aspect of security. By comparison with other schemes, the main indicators of the proposed scheme are roughly the same.