Quadratic Function Chaotic System and its Application on Digital Image Encryption

Abstract

To obtain chaotic systems with good properties to help chaos based image encryption, this paper first study the condition under which quadratic functions can be used as pseudo-random sequence generator. We give a necessary and sufficient condition for quadratic functions topologically conjugate with the most frequently used Logistic map and Tent map. Since topological conjugacy maintains chaotic characteristics, more quadratic functions can be used as pseudo-random sequence generators in the digital image encryption. Then, it analyzes a diffusion algorithm with a good effect but poor in resisting the chosen plaintext attack. It is also verified by simulation. The quadratic function chaotic system is applied in the improvement of the diffusion algorithm. Furthermore, the improved algorithm contains plaintext related and cyclic shift operations. Finally, the performance analysis shows that the improved scheme has good security and high efficiency.

Keywords

• Quadratic function
• logistic map
• topological conjugacy
• chaotic image encryption