Elliptic curve cryptography over binary extension fields
Mohammad Shkoukanim.shkokani@asu.edu.joDepartment of Computer ScienceFaculty of Information TechnologyApplied Science Private University (ASU)Amman, 11931, JordanView full profile → , *Namrata GainCorresponding authordr.namrata.gain@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , Vikram V. Patelvikrampatel@gokuluniversity.ac.inFaculty of EngineeringGokul Global UniversitySiddhpur, Gujarat, 384151, IndiaView full profile → , Manjushree Ram Ghogaregaikwadmanjushree3@gmail.comDepartment of Civil EngineeringS. B. Patil College of EngineeringIndapur, Maharashtra, 413106, IndiaView full profile → , Bodireddy Vamalathabodireddyvamalathaaa@proton.meCentre for Multidisciplinary ResearchAnurag UniversityHyderabad, Telangana, 500088, IndiaView full profile → , Priyanka Shashikant Kshirsagarkshirsagar.shashikant@vit.eduDepartment of Chemical EngineeringVishwakarma 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-3056
- Pages:
- 4347–4356
Abstract
Binary extension field-based Elliptic Curve Cryptography (ECC) offers secure and efficient capabilities to resource-constrained systems such as embedded systems and IoT. In this paper, a specific research is provided on ECC as characterized in finite fields F2m, and the mathematical structure, arithmetic and cryptographic resiliency are discussed. The representations of polynomials and normal basis are also discussed and some of the basic field operations like addition, multiplication, and inversion are carried out. It also examines the elliptic curve constructions in binary fields, in which the different kinds of curves have been supersingular and non-supersingular. Good group law arithmetic to compute point addition and point doubling are considered to optimize the performance of scalar multiplication. Lower computational complexity and improved energy efficiency, over prime field implementations, has been demonstrated experimentally. The results prove the suitability of binary field ECC in high-speed low-power cryptography applications and simultaneously, they are very resistant to classical cryptanalysis attacks and have high security assurance.
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References
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