A Fuzzy Hypergraph-Based Framework for Secure Encryption and Decryption of Sensitive Messages

Annamalai Meenakshi, Obel Mythreyi, Leo Mrsic, Antonios Kalampakas and Sovan Samanta ()
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Annamalai Meenakshi: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai 600062, India
Obel Mythreyi: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai 600062, India
Leo Mrsic: Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia
Antonios Kalampakas: College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait
Sovan Samanta: Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia

Mathematics, 2025, vol. 13, issue 7, 1-20

Abstract: The growing sophistication of cyber-attacks demands encryption processes that go beyond the confines of conventional cryptographic methods. Traditional cryptographic systems based on numerical algorithms or standard graph theory are still open to structural and computational attacks, particularly in light of advances in computation power. Fuzzy logic’s in-built ability to manage uncertainty together with the representation ability of fuzzy hypergraphs for describing complex interrelations offers an exciting avenue in the direction of developing highly evolved and secure cryptosystems. This paper lays out a new framework for cryptography using fuzzy hypergraph networks in which a hidden value is converted into a complex structure of dual fuzzy hypergraphs that remains completely connected. This technique not only increases the complexity of the encryption process, but also significantly enhances security, thus making it highly resistant to modern-day cryptographic attacks and appropriate for high security application. This approach improves security through enhanced entropy and the introduction of intricate multi-path data exchange through simulated nodes, rendering it highly resistant to contemporary cryptographic attacks. It ensures effective key distribution, accelerated encryption–decryption processes, and enhanced fault tolerance through dynamic path switching and redundancy. The adaptability of the framework to high-security, large-scale applications further enhances its robustness and performance.

Keywords: encryption; decryption; fuzzy hypergraph; dual fuzzy hypergraph; secure network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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