Fuzzy algebraic structure based cryptographic key generation
Pravin Vishnu Shindepravin.shinde@sakec.ac.inDepartment of Artificial Intelligence and Data ScienceShah and Anchor Kutchhi College of EngineeringMumbai, Maharashtra, 400088, IndiaView full profile → , Manoj Patilmanoj.patil@mctrgit.ac.inDepartment of Computer EngineeringRajiv Gandhi Institute of TechnologyMumbai, Maharashtra, 400053, IndiaView full profile → , Rahul S. Pachaderahulpachade24@gmail.comDepartment of Artificial Intelligence & Data ScienceShah and Anchor Kutchhi College of EngineeringMumbai, Maharashtra, 400088, IndiaView full profile → , Vaishali Ranevaishalirane@tsecmumbai.inDepartment of Computer EngineeringThakur Shyamnarayan Engineering CollegeMumbai, Maharashtra, 400101, IndiaView full profile → , *Altaf Osman MulaniCorresponding authordraomulani.vlsi@gmail.comDepartment of Electronics & Telecommunication EngineeringSKN Sinhgad College of EngineeringPandharpur, Maharashtra, 413304, IndiaView full profile → , Manish Ranamanishrana23@gmail.comDepartment of Artificial Intelligence and Data ScienceWadala EastShah and Anchor Kutchhi Engineering CollegeMumbai, Maharashtra, 400088, 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-2783
- Pages:
- 3553–3562
Abstract
This paper introduces the Fuzzy Algebraic Key Generation Scheme (FAKGS), which embeds graded membership functions into the operations of groups and rings, producing key sequences whose structural complexity and statistical randomness measurably exceed those of deterministic algebraic counterparts. A fuzzy group (G, μG) is constructed by assigning vertex-strength memberships μG(x) ∈ [0,1] to each group element x ∈ G, subject to the subgroup-analogue condition μG(xy–1) ≥ min(μG(x), μG(y)). A companion fuzzy ring (R, μR) encodes additive and multiplicative membership separately, and a structure-preserving fuzzy homomorphism φ: (G, μG) → (R, μR) maps group coset information into the ring’s multiplication domain. Nonlinear key sequences are then derived from this mapping via a combinatorial Latin-square permutation layer and an affine transformation over GL(n, Zp). Testing on 10,000 independent key instantiations confirms that FAKGS achieves a NIST SP 800-22 average pass rate of 99.6%, Shannon entropy of 7.9998 bits/byte, avalanche effect of 50.8 ± 0.28%, and a 384-bit effective key space. Key generation time is O(|G| log|G|), confirmed empirically at 125 Mbps throughput for 256-bit blocks on standard hardware. Algebraic attack resistance, measured by the cost of the XL algorithm on the induced equation system, exceeds the baseline graph-cipher by a factor of 216 at equation degree 12. The FAKGS is validated on constrained IoT hardware (ARM Cortex-A72) at 44 Mbps, confirming embedded-system viability.
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References
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