Eligibility Analysis of Different Chaotic Systems Derived from Logistic Map for Design of Cryptographic Components

One of the topics that have successful applications in engineering technologies and computer science is chaos theory. The remarkable area among these successful applications has been especially the subject of chaos-based cryptology. Many practical applications have been proposed in a wide spectrum from image encryption algorithms to random number generators, from block encryption algorithms to hash functions based on chaotic systems. Logistics map is one of the chaotic systems that has been the focus of attention of researchers in these applications. Since, Logistic map can be shown as the most widely used chaotic system in chaos-based cryptology studies due to its simple mathematical structure and its characterization as a strong entropy source. However, in some studies, researchers stated that the behavior displayed in relation to the dynamics of the Logistic map may pose a problem for cryptology applications. For this reason, alternative studies have been carried out using different chaotic systems. In this study, it has been investigated which one is more suitable for cryptographic applications for five different derivatives of the Logistic map. In the study, a substitution box generator program has been implemented using the Logistic map and its five different derivatives. The generated outputs have been tested for five basic substitution box design criteria. Analysis results showed that the proposals for maps derived from Logistic map have a more robust structure than many studies in the literature.