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 pseudorandomness 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.

Digital Cosine Chaotic Map for Cryptographic Applications

“…where k ∈ [10,24] is a control parameter and F refers to a chaotic map. We select k in the range [10,24] for two reasons: Firstly, when the angle of the cosine function is sufficiently large, even small differences in F(x n ) will lead to wildly diverging outputs. For example, if the angle is small, the difference between cos(2 1 ) = −0.416146836 and cos(2 1+0.00001 ) = −0.416159442 is small.…”

“…Chaotic systems have many desirable features such as sensitivity to initial conditions and parameters, ergodicity, topological transitivity mixing, unpredictability, and aperiodic dense orbits. Thus, chaotic systems have been broadly used in a number of areas such as secure communication [5], engineering [6], and cryptographic applications [7]- [10]. There are many commonalities between chaotic systems and cryptographic algorithms such as key sensitivity (parameter sensitivity), uniform data distribution (ergodicity), random-like behavior (chaoticity) and many more.…”

A New Composite Fractal Function and Its Application in Image Encryption

“…Bit-level permutation [19][20][21], and (2). Pixel-based permutation [22][23][24]. A bit is considered as the smallest operating element.…”

Anti Mandelbrot Sets via Jungck-M Iteration

“…in hosiery and grocery) to design on coffee cups, jugs, bed sheets and shirts. The fractals found many applications in image encryption [8] or compression [9], cryptography [10], art and design [11] due to their unique and self-similar behavior. There are many applications of fractals in electrical and electronics engineering presented in [12].…”