Efficient scalar multiplication algorithms on elliptic curves over prime fields for resource-constrained cryptographic devices
M. Sreenivasa Reddydypc@adityauniversity.inDepartment of Mechanical EngineeringAditya UniversitySurampalem, Andhra Pradesh, 533437, IndiaView full profile → , *Fazil HasanCorresponding authorfazil@niu.edu.inDepartment of AgricultureNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Shivangi Guptashivangi.gupta@quantumeducation.inQuantum University Research CenterQuantum UniversityRoorkee, Uttarakhand, 247667, India0009-0005-4285-8974View full profile → , Shivam P. Chaudharyshivamchaudhary@gokuluniversity.ac.inFaculty of EngineeringGokul Global UniversitySidhpur, Gujarat, 384151, IndiaView full profile → , Manisha Sagar Pawarmanisha.pawar@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Shaziya Islamshaziya.islam@rungta.orgDepartment of Computer Science & EngineeringRungta College of Engineering & TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, 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-3060
- Pages:
- 4397–4406
Abstract
Although Elliptic Curve Cryptography (ECC) over prime fields is computationally efficient in many cryptographic operations, scalar multiplication remains a computational bottleneck, particularly in resource-constrained devices such as IoT nodes and embedded systems. The paper addresses the issue of decreasing the computation time, memory and energy usage and maintaining the cryptographic security. It is proposed to use a hybrid optimization system that is based on windowed techniques, Montgomery ladder to perform periodically and parallelized arithmetical operations. Its algorithm allows it to use optimized modular arithmetic and reduced point operations to achieve maximum performance. Experimental results indicate that the time of scalar multiplication is decreased by 34.8 percent, additions of points are decreased by 28.5 percent, and the amount of energy used is lowered by 22.7 percent when traditional methods of double-and-add are used. The proposed solution is resistant to side-channel attacks, in addition to being more efficient. The results indicate that it can be used in real-time embedded system cryptography that is secure and low-power.
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References
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