Securing digital images: A chaos-driven scrambling algorithm using the Rössler system

A wide range of mathematical constructs, theories, and algorithms have been leveraged by cryptographers to secure valuable and sensitive digital images. Among these, image encryption based on scrambling algorithms has been extensively utilized. These scrambling techniques operate on 1D, 2D, and 3D constructs, relying on pixel-level swapping to enhance security. This research introduces a novel scrambling algorithm that employs a row- and column-based scrambling approach. The encryption process begins with an input image, from which a 2D scrambled image is generated. The columns of pixels from the input image are randomly placed into the columns of the scrambled image. Once all columns are inserted, the process is repeated to intensify the scrambling effect. A similar procedure is then applied to the rows of the image. To further enhance security, a diffusion process is applied using an XOR operation between the scrambled image and a random number stream. These random numbers are generated using the 3D Rössler chaotic system, where two chaotic streams contribute to the scrambling effect, and a third stream is used for diffusion. Both machine simulations and exhaustive security analyses demonstrate that the proposed image cipher is highly resistant to various cryptanalytic attacks, including brute-force attacks, differential attacks, and noise and data cropping attacks. Given these promising results, we recommend the proposed method for real-world applications to fully utilize its security potential.