Design and analysis of cryptographic protocols based on fractional order models

The first chapter covers system theory, chaotic systems, chaos theory, and cryptology in detail. The second chapter introduces fundamental mathematical concepts such as Gamma and Beta functions, Laplace transforms, and transfer functions. The third chapter explores the mathematical foundations and engineering applications of fractional-order systems and functions, with detailed explanations of Gründwald-Letnikov, Riemann-Liouville, and Caputo definitions, as well as the Chareff method. The fourth chapter analyzes the mathematical models and Simulink simulations of fractional-order Lorenz and Chen systems and their applications in cryptography. The final chapter highlights the superior performance of fractional-order chaotic systems in security and encryption and discusses potential application areas for future research. The thesis demonstrates that fractional-order chaotic systems can offer innovative and secure solutions in cryptography and security protocols.