Torsion subgroups and their cryptographic implications
Pragati Dubeypragatidubey25@gmail.comDepartment of Computer Science and ApplicationsRamdeobaba University (RBU)Nagpur, Maharashtra, 440013, IndiaView full profile → , *Dewanand Atmaram MeshramCorresponding authormeshramda@gmail.comDepartment of Information TechnologyRMD Sinhgad School of EngineeringSavitribai Phule Pune UniversityPune, Maharashtra, 411058, IndiaView full profile → , Rekha A Kulkarnirakulkarni@pict.eduDepartment of Computer EngineeringSCTR’s Pune Institute of Computer TechnologyPune, Maharashtra, 411043, IndiaView full profile → , Amruta Vijay Suranaamruta.surana@gmail.comDepartment of Computer Science and EngineeringYashoda Mahadeo Kakade College of EngineeringTalegaon Dabhade, Pune, Maharashtra, 410507, IndiaView full profile → , Khushal Khairnarkhushal.khairnar@mitaoe.ac.inDepartment of Computer Science & Engineering (AI and ML)MIT Academy of EngineeringAlandi, Pune, Maharashtra, 412105, IndiaView full profile → , Kalyani Ghugeghugeks896@gmail.comDepartment of Computer Science & Engineering (Artificial Intelligence & Machine Learning)Vishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Chandrakant Deelip Kokanecdkokane1992@gmail.comDepartment of Computer Science and Engineering (Artificial Intelligence)Vishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView 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-3051
- Pages:
- 4289–4298
Abstract
Torsion subgroups are important in algebraic structures, and in the current cryptographic systems, especially elliptic curve systems. In this paper the theoretical background of the torsion subgroups is addressed in the framework of the structure theorem of finite abelian groups and extended to the argument of an elliptic curve and algebraic groups. The focus is on the definition of the torsion points and their algebraic properties that carry the interesting implication on the security and efficiency of cryptographic protocols. Torsion subgroups play an important role in elliptic curve cryptography (ECC) since they are applicable to key generation, subgroup confinement and subgroup resistance to small subgroup attacks. Their generalizability to zero-knowledge proofs is also covered, and specifically in the construction of secure and verifiable protocols. The paper contains both, analytical and comparative analysis showing how torsion-based properties can be utilized to provide robustness, scalability and provide a better cryptographic security to the modern distributed and privacy preserving systems.
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References
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