Image Encryption Algorithm Based on Factorial Decomposition

This study proposes a highly efficient image encryption algorithm by employing a rapid key generation approach and permutation structure. The image is converted to a matrix, and then an encryption algorithm based on factorial decomposition permutation is applied. Two variants of the algorithm have been proposed in this study, where each variant is distinguished by the elements of the matrix to be permutated. The first variant is based on the permutation of the pixels of the image. In the second variant, the permutation is applied to both columns and rows of the matrix. These variants of the algorithm have been tested and compared. To create a permutation of a collection of elements, the factorial decomposition mathematical technique is applied, where the Euclidian division of a given key is obtained by adding the factorials of all the integers. The experimental results indicate that the proposed approach provides sufficient and optimistic results in terms of computational complexity, Keyspace analysis, Statistical analysis, and Sensitivity analysis attacks. The statistical analysis shows the superiority of the algorithm using two permutation methods, where sensitivity analysis indicates that the number of pixels changing rate (NPCR) achieved around 99.7 and the unified average changed intensity (UACI) is around 33.5, which showed better performance than the other approaches in the literature. Moreover, the proposed approach provided less computational complexity compared with the existing approaches.