Fixed Point Based Secure Key Generation in Generalized Fuzzy Metric Spaces for Cryptographic Applications

Abstract

This research introduces a novel cryptographic framework based on fixed point theory in generalized fuzzy metric spaces. The proposed model combines concepts of fuzzy distance, nonlinear contractions, and iterative fixed point mappings to generate secure cryptographic keys. The framework improves uncertainty handling, resistance against attacks, and secure communication in distributed systems. Existence and uniqueness of fixed points are established using generalized fuzzy contraction mappings. Applications in symmetric key generation, authentication systems, and secure communication are discussed.