Number-theoretic transformations in public key encryption
*M. ThamizhsudarCorresponding authorthamizhsudar@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 → , Tanveer Ahmad Wanitanveer.ahmad@niu.edu.inDepartment of PhysicsNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Savinder Kaursavinder.kaur.orp@chitkara.edu.inCentre for Research Impact and OutcomeChitkara UniversityRajpura, Punjab, 140417, IndiaView full profile → , Mahendihasan S. Heeramahendihasan.gcca@gokuluniversity.ac.inFaculty of Computer Science and ApplicationsGokul Global UniversitySidhpur, Gujarat, 384151, IndiaView full profile → , B. Anandkumaranand1710@vardhaman.orgDepartment of Computer Science and EngineeringVardhaman College of EngineeringShamshabad, Hyderabad, Telangana, 501218, IndiaView full profile → , Vella Satyanarayanaasece_vella@adityauniversity.inDepartment of Electronics and Communication EngineeringAditya UniversitySurampalem, Kakinada District, Andhra Pradesh, 533437, 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-3042
- Pages:
- 4179–4188
Abstract
NTTs have proven to be an important calculator in modern public key encryption, particularly in lattice-based and post-quantum cryptography. Mathematical backgrounds and algorithms implementations of NTTs in the context of efficient arithmetic of polynomials over finite field are discussed in this paper. The study addresses the flaws of the conventional convolution algorithms, and suggests simplified Cooley Tukey founded NTT algorithms, which can translate to a lot when it comes to computational complexity. Additionally, it also talks about how NTT can be integrated into the environment of algebraic structures (rings and modules) so as to enable safe and dimensionless encryption. Benchmarking at the experimental level demonstrates the improvements in the computational efficiency, as much as 45 per cent reduction in the processing time as compared to the traditional methods. The results introduce better throughput, reduced latency and capability to run in resource limited environments.
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References
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