Number-theoretic foundations of attribute-based encryption schemes
*Mohanad AlfirasCorresponding authorpresident@gulfuniversity.edu.bhDepartment of Electrical & Electronic EngineeringCollege of EngineeringGulf UniversitySanad, 26489, Kingdom of BahrainView full profile → , M. Thamizhsudarthamizhsudar@avit.ac.inDepartment of Humanities and Sciences (Mathematics Division)Aarupadai Veedu Institute of TechnologyVinayaka Mission’s Research Foundation (Deemed to be University)Paiyanoor, Chennai, Tamil Nadu, 603104, IndiaView full profile → , Amit Gauravcoe@niu.edu.inDepartment of Computer Science & EngineeringNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Manisha Sagar Pawarmanisha.pawar@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Manish Chhabrachmanish1610@vardhaman.orgDepartment of Computer Science and EngineeringVardhaman College of EngineeringShamshabad, Hyderabad, Telangana, 501218, IndiaView full profile → , Sardor Sabirovsabirov_sardor@mamunedu.uzDepartment of General Professional SciencesMamun UniversityKhiva, Uzbekistan0009-0004-1069-7865View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3009
- Pages:
- 3791–3801
Abstract
Attribute Based Encryption (ABE) has become a potent concept of access control on a fine-grained basis in a distributed and cloud setting. The paper will delve into number theoretic underpinnings of the ABE schemes, and in particular the role of the Euler theorems and Fermat’s little theorems and modular arithmetic in the key generation and encryption processes. It also explores the pairing-based cryptographic constructions that can be used to expressive access policies along bilinear mappings. The most important processes of secret keys reconstruction in the form of a poly-nominal interpolation and Lagrange coefficients are discussed. In addition, the optimization techniques, such as pre-computation and batching are also examined in order to enhance the computational efficiency and scalability. The results show that the integration of such powerful number theoretic concepts and powerful implementation mechanisms have much to do in improving the security, flexibility and performance of ABE systems in the real world.
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References
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