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Due to the fact that many classical numerical methods have not yet mature quantum counterparts, quantum circuit design is very important in quantum image processing. In this paper, using the novel enhanced quantum representation (NEQR) model, an image encryption algorithm based on Feistel structure is carried out in quantum computer by giving the encryption quantum circuits. First, the modified Feistel structure for image encryption is proposed. It is a 128-bit block cipher and requires 16-bit subkeys to encrypt the image, and it is a mixture of Feistel and substitution–permutation network; then, the detailed quantum circuits design of the encryption algorithm are given. Through numerical simulation and analysis, it is verified that the proposed quantum image encryption algorithm is effective and can resist statistical attacks effectively. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive generalised function projective synchronisation scheme of fractional-order chaotic systems with different dimensions and orders and fully unknown parameters is presented. On the basis of the Lyapunov method of fractional-order systems, a stability theorem of the fractional-order system with non-identical orders is proven. Using the fractional-order controller and adaptive control theory, sufficient conditions for synchronisation and unknown parameters update rules are obtained. Theoretical analysis and numerical simulations are provided to verify the validity of the proposed scheme. Moreover, synchronisation results are applied to secure communication via modified chaotic masking (MCM) method. The unpredictability of the scaling function matrix and the use of fractional-order systems with different orders can increase the security of the cryptosystem. The security analysis shows that the introduced algorithm has large key space, high sensitivity to encryption keys, higher security and the acceptable encryption speed. [ABSTRACT FROM AUTHOR]

As a symmetric encryption algorithm, multiple-parameter fractional Fourier transform (MPFRFT) is proposed and applied to image encryption. The MPFRFT with two vector parameters has better security, which becomes the main technical means to protect information security. However, our study found that many keys of the MPFRFT are invalid, which greatly reduces its security. In this paper, we propose a new reformulation of MPFRFT and analyze it using eigen-decomposition-type fractional Fourier transform (FRFT) and weighted-type FRFT as basis functions, respectively. The results show that the effective keys are extremely limited. Furthermore, we analyze the extended encryption methods based on MPFRFT, which also have the security risk of key invalidation. Theoretical analysis and numerical simulation verify our point of view. Our discovery has important reference value for a class of generalized FRFT image encryption methods. [ABSTRACT FROM AUTHOR]