A Fast Image Encryption Algorithm Based on Logistic Mapping and Hyperchaotic Lorenz System for Clear Text Correlation

Image encryption (IE) technology is vital to privacy, but the parameter range of the traditional image encryption technology is limited. So it is important to enhance the performance of IE methods. In this study, a plaintext associative IE based on the improved logistic map and hyperchaotic system is proposed. The improved logistic map scrambles the pixels of the image. Then the hyperchaotic system performs diffusion and confusion operations on the image. For parameters
$\mu $
and
$r$
, the sequence generated by the improved logistic map can traverse and uniformly distribute in the space (0,1). The Lyapunov exponent of the improved logistic map is greater than 21.5. The correlation coefficients of the encrypted image pixels after encryption are all less than 0.05. The UACI and NPCR indices of the improved encryption method are close to their theoretical values of 98.6133 and 33.1287, respectively, which are higher than those of the reference methods. The improved encryption method overcomes the limitations in the parameter range of traditional image and text encryption techniques, slow encryption speed, and uneven chaotic sequences. This method has higher security and sensitivity, andit can be used to establish a plaintext associative IE method.