Based on the Feistel network and dynamic deoxyribonucleic acid (DNA) encoding technology, an image encryption method is proposed using the "permutation-diffusionscrambling" structure. First, the SHA-3 algorithm is used to calculate the hash value of the plaintext image as the initial value of the hyperchaotic system, and the chaos-generated sequence is used to generate the Hill cipher matrix to replace the image pixel. Second, the DNA sequence operation is used as the F function of the Feistel network. The DNA sequence database is used as the key K of Feistel network, and the image pixel value diffusion is realized by the Feistel network. Finally, further diffusion is carried out through the ciphertext feedback and through the ciphertext confusion and diffusion of three rounds of "chaotic scrambling-DNA encoding-Feistel transformation-DNA decoding," making the ciphertext more random and resistant to attacks and ensuring that the encrypted ciphertext is more secure. The experimental results show that the proposed method can effectively encrypt the image and has prominent characteristics, such as strong plaintext sensitivity, a large key space, and excellent ciphertext statistical properties.

Image encryption is the most direct and effective technical means for protecting the security of image information. Based on the space filling property of the Hilbert curve and the infinite property of the H-geometric fractal, a new image encryption technique is proposed, which combines the pseudorandomness of a hyperchaotic system and the sensitivity to initial values. First, the hash value of a plaintext image is calculated using the secure hash algorithm 3 (SHA-3) as the initial value of the piece-wise linear chaotic map (PWLCM) and Rossler chaotic systems, which associates the key with the plaintext. In addition, the chaotic sequences that are generated by the chaotic systems are used to scramble the global pixel positions and the pixel values of the images, thereby disturbing the distribution of the pixel positions and the pixel values. Second, the Hilbert curve and H-fractal are alternately used to scramble the local pixel positions and diffuse the pixel values twice. Finally, the ciphertext feedback is used to further enhance the confusion and diffusion characteristics of the algorithm in order to achieve higher security. The experimental results and security analysis show that the encryption technique has enough key space to resist exhaustive attacks and can effectively resist statistical attacks, differential attacks, noise attacks, and cropping attacks. It can be used for military, judicial, and other privacy-related digital images secure storage and network security transmissions.

The squirrel search algorithm (SSA) is a recently proposed nature-inspired algorithm based on the dynamic foraging and gliding behavior of squirrels. Because of its simplicity and stability, the squirrel algorithm has attracted increasing research interest. However, the lack of exploration ability of the SSA may lead to premature convergence to the local optimum. To overcome this disadvantage, an improved SSA with reproductive behavior (RSSA) is proposed to solve the numerical optimization problem. First, the reproductive behavior of the invasive weed algorithm (IWO) is introduced to the conventional SSA to generate offspring individuals, and these offspring individuals are scattered into the search space by Gaussian distribution to complete the location update. This method makes it possible for individuals with poor fitness to enter the next generation search, improving the exploration ability of the SSA. Second, an adaptive step strategy is proposed to adaptively adjust the search step of squirrels according to the distance between each squirrel and other family members. This strategy effectively balances the exploration and exploitation of the algorithm. Finally, the performance of the proposed RSSA algorithm is evaluated using Wilcoxon's test on unimodal, multimodal, fixed-dimensional multimodal and CEC 2014 benchmark functions. Experimental results and statistical tests show that RSSA has better performance in terms of convergence, accuracy, and search capability compared with other state-of-the-art algorithms. INDEX TERMS Nature-inspired, squirrel search algorithm, exploration and exploitation, Wilcoxon's test, CEC 2014 benchmark functions.

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To improve the abilities of image encryption systems to resist plaintext attacks and differential attacks, a novel plaintext-related image encryption scheme based on Josephus traversing and pixel permutation is proposed. In this scheme, the step sizes of the Josephus traversing are associated with the pixel values, and the Josephus traversing method is improved, increasing the dependence of the cipher image on the plaintext image, further enhancing the plaintext sensitivity of the algorithm, and reducing the number of iterations of the index sequence generated by the chaotic system. By segmenting the image and combining a chaotic system, bit XOR and crossover operations between the modules are performed to achieve the effects of confusion and diffusion, and the randomness of the cipher image is improved. Finally, the confusing and spreading characteristics of the algorithm are further enhanced by cipher feedback. The experimental results and security analysis show that the proposed algorithm is sensitive to keys and can effectively resist attacks such as statistical attacks, selective-plaintext attacks and exhaustive attacks. The algorithm has high potential for real-time and secure image applications.

With the help of the fact that chaos is sensitive to initial conditions and pseudorandomness, combined with the spatial configurations in the DNA molecule's inherent and unique information processing ability, a novel image encryption algorithm based on bit permutation and dynamic DNA encoding is proposed here. The algorithm first uses Keccak to calculate the hash value for a given DNA sequence as the initial value of a chaotic map; second, it uses a chaotic sequence to scramble the image pixel locations, and the butterfly network is used to implement the bit permutation. Then, the image is coded into a DNA matrix dynamic, and an algebraic operation is performed with the DNA sequence to realize the substitution of the pixels, which further improves the security of the encryption. Finally, the confusion and diffusion properties of the algorithm are further enhanced by the operation of the DNA sequence and the ciphertext feedback. The results of the experiment and security analysis show that the algorithm not only has a large key space and strong sensitivity to the key but can also effectively resist attack operations such as statistical analysis and exhaustive analysis.

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