Analysis of the Impact of Logistic Map with Gaussian Membership Function for Cryptography

Abstract

This paper deals with the integration of the as logistic map with the different fuzzy number generators, resulting in a hybrid approach of encryption that can leverage the strengths and randomness of both chaotic dynamics and fuzzy logic. The chaotic maps are influenced by the Gaussian fuzzification, which produces bifurcation diagrams that have the fundamental structure of the system’s dynamics. By analyzing the chaotic behavior of the various maps and their impact on generating the pseudo-random sequences which can be suitable for the encryption, the fuzzy numbers are added to modify the chaotic systems. The proposed hybrid encryption approach is expected to address the limitations of single chaotic map usage and thus to represent a more effective and efficient encryption approach. The proper security analysis and cryptanalysis of the chaotic encryption algorithms are very important to recognize probable vulnerabilities at the very beginning. Optimization methods for a particular device i.e., GPUs (Graphics Processing Units) or FPGAs, as well as parallel processing exploration, will be the key to improving these algorithms in real-world applications.