Application of fractional order chaotic systems to computer science

Due to the rapidly increasing data density in the virtual environment, larger storage areas and more secure transportation methods are needed. Along with the development of security measures, new methods of attack are developing at the same pace. For this reason, information security and encryption has been an important topic from the early ages to the present day and is still being intensively studied. Random number generators are an important area of study in cryptography. In a successful encryption application, randomness must be ensured and predictability must be reduced. In this thesis, a fractional order chaotic system based random number generator structure is proposed. By combining the success of fractional-order systems in modeling real-world problems with the inherent complexity and unpredictability of continuous-time chaotic systems, a robust design is achieved. As is known, chaotic systems are extremely sensitive to initial conditions and optimization algorithms have been used to take advantage of this situation. Optimization algorithms have been used to determine the initial conditions and fractional order values that satisfy the randomness conditions from infinite space. First, using particle swarm optimization and ant colony optimization, initial conditions appropriate for Lorenz, Chen and Rössler chaotic systems are calculated. Then, the values taken from the chaotic system output were converted into random numbers using Mod 2 and Mod 256. The randomness of these numbers has been tested with NIST, histogram analysis and sliding frequency analysis. A substitution box (s-box) has been designed with the generated random numbers. This architecture has been applied both for continuous time chaotic systems and for fractional order chaotic systems. The initial conditions and fractional order values of fractional order chaotic systems have been determined by optimization algorithms. Experimental studies show that implementations using continuous-time and fractional-order chaotic systems successfully pass all randomness tests. When the performance criteria of the generated s-boxes are examined, it is seen that they give very successful results compared to the chaotic system-based random number generators in the literature. In addition, the initial conditions of the Lorenz chaotic system were determined using the differential evolution algorithm due to its performance on continuous time data. Chi-square (𝜒2) test has been used as a randomness test and the test was successfully passed. In the last study, the initial conditions that can produce the most powerful s-box have been generated by optimization algorithms. The study has been performed for both continuous-time and fractional-order chaotic systems. All runs have been continued until the last iteration and more than one successful result was obtained. As a result, chaotic systembased s-boxes that successfully fulfill the performance criteria have been obtained.