A Chaos-Based Image Encryption Technique Utilizing Hilbert Curves and H-Fractals

Abstract

Image encryption is the most direct and effective technical means for protecting the security of image information. Based on the space filling property of the Hilbert curve and the infinite property of the H-geometric fractal, a new image encryption technique is proposed, which combines the pseudo-randomness of a hyperchaotic system and the sensitivity to initial values. First, the hash value of a plaintext image is calculated using the secure hash algorithm 3 (SHA-3) as the initial value of the piece-wise linear chaotic map (PWLCM) and Rossler chaotic systems, which associates the key with the plaintext. In addition, the chaotic sequences that are generated by the chaotic systems are used to scramble the global pixel positions and the pixel values of the images, thereby disturbing the distribution of the pixel positions and the pixel values. Second, the Hilbert curve and H-fractal are alternately used to scramble the local pixel positions and diffuse the pixel values twice. Finally, the ciphertext feedback is used to further enhance the confusion and diffusion characteristics of the algorithm in order to achieve higher security. The experimental results and security analysis show that the encryption technique has enough key space to resist exhaustive attacks and can effectively resist statistical attacks, differential attacks, noise attacks, and cropping attacks. It can be used for military, judicial, and other privacy-related digital images secure storage and network security transmissions.

Keywords

• Hilbert curve
• H-geometric fractal
• hyperchaotic system
• SHA-3
• image encryption
• chaotic cryptography