A novel chaotic map application in image encryption algorithm

Research on chaos-based image encryption algorithms is a crucial field. However, existing chaos systems and image encryption algorithms still have significant room for improvement. To enhance the performance of chaos, we propose an improved chaos system, which experimental tests have shown to have better Lyapunov exponents, bifurcation diagrams, and other dynamic characteristics, passing NIST tests, and good correlation properties. To enhance the image encryption algorithm, we propose a novel image encryption algorithm based on our introduced chaotic system that is not only more secure but also more efficient. Firstly, we randomly select the least significant bit(LSB) of a pixel in the plaintext image for modification and extract the hashed value of the modified plaintext image as the parameter value and initial value of our proposed hyper-chaotic system, aiming to better resist plaintext attacks. Next, we enhance the confusion of pixels within the encrypted image by employing bit-plane shifts and using a novel crossover-boxes for pixel swapping. Lastly, we achieve higher security and improved efficiency by combining forward diffusion and backward diffusion(FDBD) with the addition of perturbation factors. Compared with peer algorithms, our proposed algorithm has advantages in encryption efficiency, local Shannon entropy, the correlation of adjacent pixels, as well as the measurement of sensitivity including the number of pixels change rate (NPCR) and unified averaged changed intensity (UACI). Furthermore, our proposed algorithm achieves a higher mean Shannon entropy (7.994), a lower mean Chi-square value (251.6247), and can achieve more ideal NPCR and UACI with a single encryption round.