Integration of stiff chaotic models and numerical solvers into cryptographic frameworks

Abstract

This article addresses the actual scientific-technical problem of enhancing the efficiency of chaotic cryptographic frameworks by integrating stiff dynamical systems and their numerical solvers. A chaos-based cryptosystem has been developed and investigated, comprising a mathematical chaotic core, a numerical solver, and a keystream extraction module. Detailed design and analysis were conducted regarding the cryptographic and mathematical properties of chaotic cores based on nonautonomous oscillators: the Van der Pol, the nonlinear Van der Pol−Duffing, and the hybrid Rayleigh−Van der Pol−Duffing oscillators. Specialized solvers were created and tested, including a block k-point predictor-corrector method, a stabilized Skvortsov method, and a semi-implicit Rosenbrock method. Unlike classical explicit and implicit numerical schemes, these methods ensure the accurate numerical reproduction of chaotic dynamics and stability against external perturbations. The computational methods were parallelized, significantly boosting performance and ensuring the cryptosystem's scalability on multiprocessor architectures. It was demonstrated that block multi-point methods exhibit superior parallelism characteristics, featuring near-linear speedup and high scalability. An analysis of the key domain for each crypto-core was performed, covering the assessment of theoretical and effective capacity, the impact of correlation parameters, and stable regions of the phase space. Additionally, the statistical properties of the LSB-based step modification and its suitability for generating cryptographically secure sequences were investigated.