Encryption of Color Images Based on Chaotic Attractors Generated by ODE Systems Containing Module Nonlinearities - Vasiliy Ye. Belozyorov; Natalia A. Guk; Danylo I. Yehoshkin (Journal of Optimization, Differential Equations and Their Applications)
The main objective of this work is to construct an algorithm for modeling chaotic attractors using special neural ODEs with antisymmetric matrices (antisymmetric neural ODEs) and modular power nonlinearities. These attractors are generated by a cascade of bifurcations of homoclinic orbits existing in the specified ODE system. This approach makes it possible to construct complex chaotic attractors containing many wings or many scrolls. The latter circumstance allows us to significantly complicate the encoding of documents with images transmitted over networks, which is the main criterion for the security of the information contained in these documents. This paper presents a method for encrypting color images using a cryptosystem based on on the properties of the well-known Lorenz attractor and new chaotic attractors generated by ODE systems with modulus-type nonlinearities. When encrypting color images, these attractors can generate parameters for changing pixel colors, which makes it difficult to restore the original image without knowing the exact characteristics of the attractors and starting points. To enhance the resilience of the encryption and protect against predictable patterns, a Block Cipher Mode of Operation is employed. The performance of the algorithm will be demonstrated both with and without the application of these modes, allowing for an assessment of their impact on the overall security of the system