Abstract: In this paper, an efficient image encryption scheme based on a novel mixed linear–nonlinear coupled map lattice (NMLNCML) system and DNA operations is presented. The proposed NMLNCML system strengthens the chaotic characteristics of the system, and is applicable for image encryption. The main advantages of the proposed method are embodied in its extensive key space; high sensitivity to secret keys; great resistance to chosen-plaintext attack, statistical attack, and differential attack; and good robustness to noise and data loss. Our image cryptosystem adopts the architecture of scrambling, compression, and diffusion. First, a plain image is transformed to a sparsity coefficient matrix by discrete wavelet transform, and plaintext-related Arnold scrambling is performed on the coefficient matrix. Then, semi-tensor product (STP) compressive sensing is employed to compress and encrypt the coefficient matrix. Finally, the compressed coefficient matrix is diffused by DNA random encoding, DNA addition, and bit XOR operation. The NMLNCML system is applied to generate chaotic elements in the STP measurement matrix of compressive sensing and the pseudo-random sequence in DNA operations. An SHA-384 function is used to produce plaintext secret keys and thus makes the proposed encryption algorithm highly sensitive to the original image. Simulation results and performance analyses verify the security and effectiveness of our scheme.

Key words: Compressive sensing; Coupled map lattice (CML); DNA operations; Semi-tensor product

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