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 pseudo-randomness 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 image secure storage and network security transmissions.

Based on the Feistel network and dynamic DNA encoding technology, an image encryption method is proposed using the "permutation-diffusion-scrambling" structure. First, the SHA-3 algorithm is used to calculate the hash value of the plaintext image as the initial value of the hyper-chaotic 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.

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.

In this paper, an image encryption algorithm based on a hyperchaotic system and variable-step Josephus problem is proposed. Based on an in-depth analysis of the classic Josephus problem, a new variable-step Josephus problem that combines the pseudorandom sequence with the Josephus problem is proposed. Firstly, the hash value of the plaintext image is calculated, which is converted to the initial value of the chaotic system. Secondly, the chaotic system is iterated to generate four pseudorandom sequences X, Y, Z, and W. The sequences X, Y, and Z are input as parameters into the variable-step Josephus function to scramble the positions of the rows, pixel bits, and columns of the image, respectively. Finally, the elements of the sequence W and the image pixels are used to perform the addition operation. According to the experiments, the information entropy of the encrypted image with size 256256 reaches 7.997 and the adjacent correlations in three directions are within ±0.01. The experimental results show that image encryption algorithm proposed in this paper has plaintext sensitivity and can resist the common attacks.

Traditional encryption algorithms are inefficient when applied to image encryption because image data have the characteristics of large data sizes and strong correlations between adjacent pixels. The shortcomings of the traditional Data encryption standard (DES) encryption algorithm when applied to image encryption are analyzed, and a new image encryption algorithm based on the traditional DES encryption algorithm model, chaotic systems, DNA computing, and select cipher-text output is proposed. Select cipher-text output selects cipher image with the biggest entropy, and it can increase the randomness of cipher image and reduce the risk of encryption system being broken down. This algorithm overcomes the shortcomings of high computational complexity and inconvenient key management that the traditional text encryption algorithm has when applied to image encryption. The experimental results show that the security of this algorithm is verified by analyzing the information entropy, image correlation of adjacent pixels and other indexes. At the same time, this algorithm passes the noise attack test and the occlusion attack test, so it can resist common attacks.

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.