This article introduces a simple and effective new algorithm for image encryption using a chaotic system which is based on the magic squares. This novel 3D chaotic system is invoked to generate a random key to encrypt any color image. A number of chaotic keys equal to the size of the image are generated by this chaotic system and arranged into a matrix then divided into non-overlapped submatrices. The image to be encrypted is also divided into sub-images, and each sub-image is multiplied by a magic matrix to produce another set of matrices. The XOR operation is then used on the resultant two sets of matrices to produce the encrypted image. The strength of the encryption method is tested in two folds. The first fold is the security analysis which includes key space analysis and sensitivity analysis. In the second fold, statistical analysis was performed, which includes the correlation coefficients, information entropy, the histogram, and analysis of differential attacks. Finally, the time of encryption and decryption was computed and show very good results.

We present a new general complex integral transform in this study. This complex transform properties are studied. The main problem is reduced to a simple algebraic equation using this complex integral transformation. By solving this algebraic equation and using the inverse of the general complex integral transform, the answer to this main problem can be found. Finally, the solution to linear higher order ordinary differential equation is found by using the new general complex integral transform. We also present and discuss a number of key real-life problems, such as pharmacokinetics and nuclear physics.

Currently, images are very important with the rapid growth of communication networks. Therefore, image encryption is a process to provide security for private information and prevent unwanted access to sensitive data by unauthorized individuals. Chaos systems provide an important role for key generation, with high randomization properties and accurate performance. In this study, a new four-dimensional hyper-chaotic system has been suggested that is used in the keys generation, which are utilized in the image encryption process to achieve permutation and substitution operations. Firstly, color bands are permuted using the index of the chaotic sequences to remove the high correlation among neighboring pixels. Secondly, dynamic S-boxes achieve the principle of substitution, which are utilized to diffuse the pixel values of the color image. The efficiency of the proposed method is tested by the key space, histogram, and so on. Security analysis shows that the proposed method for encrypting images is secure and resistant to different attacks. It contains a big key space of (2627) and a high sensitivity to a slight change in the secret key, a fairly uniform histogram, and entropy values nearby to the best value of 8. Moreover, it consumes a very short time for encryption and decryption.

A dynamic S-box generation based on a hybrid method of new chaotic system and DNA computing

Image Encryption Algorithm Based on a Novel Six-Dimensional Hyper- Chaotic System