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.
Highlights
With the rapid development of the internet, the transmission of digital images is becoming more and more important for us
We give a necessary and sufficient condition for the general quadratic functions topologically conjugate with Logistic map L(x) = 4x(1 − x) and Tent map, and such functions can be used as pseudo-random sequence generators
We have presented a general condition for the quadratic functions f (x) = ax2 + bx + c topologically conjugate with Logistic map L(x) = 4x(1 − x) and Tent map
Summary
With the rapid development of the internet, the transmission of digital images is becoming more and more important for us. Chaotic systems are becoming important pseudo-random sequence generators. The quadratic function chaotic system will provide us reliable pseudo-random sequences for image encryption. The condition is proved to be necessary and sufficient for quadratic functions topologically conjugate with Logistic map L(x) = 4x(1 − x) and Tent map. This provides more support and choice for using quadratic function chaotic systems as pseudo-random sequence generators in the future. We improve the algorithm and use the quadratic function chaotic system to generate pseudo-random sequences. The results show that the improved scheme has good security and high efficiency
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