NTK-3D chaotic map and a non-associative LA-field sequences for image encryption

Abstract

The imperative protection of digital information and its secure transmission has evolved into a complex challenge. Within this context, non-linear dynamical systems assume a pivotal role in fortifying content security by their unpredictable behavior and susceptibility to initial conditions. This study introduces an innovative 3D-chaotic system. The proposed map is then examined through bifurcation diagrams and randomness tests, revealing an intricate chaotic behavior of the system. Moreover, an advanced method of securing information is introduced, incorporating a non-associative LA-field sequences-oriented affine transformation. The initial procurement of a non-associative LA field through computational approaches is succeeded by utilizing sequences of its components to establish an affine transformation. This transformative process serves as the central aspect of the suggested color image encryption method. In this strategy, the NTK-3D map and the innovative affine transformation collaborate to introduce both confusion and diffusion, thereby fortifying the overall security stance. The non-associative behavior of the involved algebraic structure, combined with a dynamical system, results in highly resilient encryption. The proposed scheme is not only time-efficient but also has an expanded key space. The results of some performance assessments demonstrate that the suggested encryption technique for the digital medium is capable of resisting well-known attacks.