A new color image encryption scheme based on logistic map over the finite field ZN

In recent years, various image encryption algorithms based on chaotic systems have been proposed where the chaotic maps always work over the real domain. However, the traditional chaotic map over the real domain has a disadvantage, i.e., the calculation complexity of the floating point number can be doubled when implementing the map in computer. This leads to a greatly serious drawback for practical application. To overcome this problem effectively, in this paper, we generalize the chaotic Logistic map to the finite field, and find that there exists an automorphic mapping between two Logistic maps with the different control parameters over the finite field Z(N). Moreover, we adopt the sequences generated by the automorphic mapping to design a color image encryption scheme and do simulation experiments. Security and performance analyzes also show that the proposed scheme has very good properties which provide a strong guarantee for the algorithm efficiency. Therefore, the proposed scheme is feasible for implementing image and data encryption.