A novel image encryption scheme based on logistic map and dynatomic modular curve

Abstract

A new image encryption and decryption algorithm based on chaotic map and dynatomic modular curve is proposed in this paper. Firstly, the definition of dynatomic modular curve and its periodic points are introduced, and a property of the dynatomic modular curve is proved. Secondly, the relationship between the Logistic map and the dynatomic modular curve is discussed. Finally, the encryption algorithm which is composed of permutation of pixels and substitution is given. In order to eliminate sufficiently the relation between adjacent pixels in the image, pixel values of the original image are sorted as index function, which derives from Logistic map and dynatomic modular curve. And XOR operation is performed between the scrambled pixel sequence and projective transformation sequence. Simulation experiments and nonparametric hypothesis test demonstrate that the proposed algorithm is secure to resist different types of attacks and it can be applied to real-time encryption.