Image Encryption Algorithm Based on Substitution Principle and Shuffling Scheme

This research presents a method of image encryption that has been designed based on the algorithm of complete shuffling, transformation of substitution box, and predicated image crypto-system. This proposed algorithm presents extra confusion in the first phase because of including an S-box based on using substitution by AES algorithm in encryption and its inverse in Decryption. In the second phase, shifting and rotation were used based on secrete key in each channel depending on the result from the chaotic map, 2D logistic map and the output was processed and used for the encryption algorithm. It is known from earlier studies that simple encryption of images based on the scheme of shuffling is insecure in the face of chosen cipher text attacks. Later, an extended algorithm has been projected. This algorithm performs well against chosen cipher text attacks. In addition, the proposed approach was analyzed for NPCR, UACI (Unified Average Changing Intensity), and Entropy analysis for determining its strength.

Further Discussions of the Complex Dynamics of a 2D Logistic Map: Basins of Attraction and Fractal Dimensions

In this paper, we study the complex dynamic characteristics of a simple nonlinear logistic map. The map contains two parameters that have complex influences on the map’s dynamics. Assuming different values for those parameters gives rise to strange attractors with fractal dimensions. Furthermore, some of these chaotic attractors have heteroclinic cycles due to saddle-fixed points. The basins of attraction for some periodic cycles in the phase plane are divided into three regions of rank-1 preimages. We analyze those regions and show that the map is noninvertible and includes Z0,Z2 and Z4 regions.