Deterministic chaos game: A new fractal based pseudo-random number generator and its cryptographic application

Abstract

In this paper, a digital image encryption algorithm is proposed based on the generalized model of the chaos game. The chaos game is a well-known fractal, which acts as a pseudo-random number generator (PRNG) in the proposed encryption algorithm. The foundation of the chaos game is based on basic points and its distance ratio that determine the basis of how they distribute random values in 2D or 3D space. These basic points are entered by the user interface and are the result of an encrypted image with a fractal structure. The use of the bifurcation diagram and Lyapunov exponent analysis showed that the proposed chaos game has the dynamical behavior, and fully chaotic characteristic, and can be used as a secure PRNG in cryptography systems. In the proposed method, the region of interest is determined by a number of Bases, and the fractal mechanism of chaos game for the encryption process is performed on the image. This process is very sensitive to any changes in keys and refers to confusion. The evaluation results of security and performance analysis on standard images confirm the efficiency of the proposed method and demonstrate that the proposed method is robust against attacks.