A novel fuzzy graph based cryptographic framework for secure communication in computer and electronic systems using discrete mathematical structures
*K. Kishore KumarCorresponding authorkishorekamarajugadda@gmail.comDepartment of Electronics & Communication EngineeringFaculty of Science & Technology (ICFAI Tech)ICFAI Foundation for Higher EducationHyderabad, Telangana, 501203, IndiaView full profile → , Raghavendra Kulkarniraghavendrakulkarni@my.amrita.eduDepartment of Computer ScienceSchool of ComputingAmrita Vishwa VidyapeethamMysuru, Karnataka, 570026, IndiaView full profile → , S. Kayalvizhikayalvizhiscse12@sethu.ac.inDepartment of Computer Science & DesignSethu Institute of TechnologyVirudhunagar, Tamil Nadu, 626115, IndiaView full profile → , Divya Sharmaer.divyasharma@gmail.comDepartment of Computer Science & EngineeringNew Horizon College of EngineeringBengaluru, Karnataka, 560103, IndiaView full profile → , S. Pushparanidrpushparanis@veltech.edu.inDepartment of Computer Science and EngineeringSchool of ComputingVel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and TechnologyAvadi, Chennai, Tamil Nadu, 600062, IndiaView full profile → , Yamini Tondepusmile.yamini@gmail.comDepartment of Computer Science and EngineeringKoneru Lakshmaiah Education FoundationVaddeswaram, Andhra Pradesh, 522302, IndiaView full profile → , Gadi Mounicamounica.gadi1@gmail.comDepartment of Computer Science and EngineeringAditya College of Engineering and Technology (A)Surampalem, Andhra Pradesh, 533437, IndiaView full profile → , Bandla Srinivasa Raosreenibandla@gmail.comDepartment of Computer Science and EngineeringTeegala Krishna Reddy Engineering CollegeHyderabad, Telangana, 500097, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Oct 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2782
- Pages:
- 3543–3552
Abstract
This paper presents the Fuzzy Graph–Based Cryptographic Framework (FGCF), which couples continuous-valued membership functions from fuzzy graph theory with a discrete finite-field encryption core to yield a key generation engine whose entropy significantly exceeds that of binary-graph precursors. A fuzzy graph G̃ = (V, E, μ, ρ) is parameterized with Gaussian vertex memberships μ(v) ∈ [0,1] and edge memberships ρ(e) ≤ min(μ(u), μ(v)); its chromatic number, structural entropy, and fuzzy connectivity are jointly hashed into a 384-bit master key. Block encryption proceeds through modular multiplication over a prime field Zp, augmented by a depth-first search permutation layer that exploits the graph’s traversal ordering for diffusion. Testing on 10,000 randomized plaintext samples gives a Shannon entropy of 7.9999 bits/byte, an avalanche effect of 50.6±0.3%, a maximum differential probability of 2–6.2 and a key space of 2384. Throughput reaches 131 Mbps for 256-bit blocks on standard hardware and 47 Mbps on ARM Cortex-A72 at |V| = 8, confirming IoT viability.
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References
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