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Main Authors: Kumari, Ruby, Rout, Tapas, Saini, Babul, Pandey, Jai Gopal, Karmakar, Abhijit
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.12359
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author Kumari, Ruby
Rout, Tapas
Saini, Babul
Pandey, Jai Gopal
Karmakar, Abhijit
author_facet Kumari, Ruby
Rout, Tapas
Saini, Babul
Pandey, Jai Gopal
Karmakar, Abhijit
contents Elliptic Curve Cryptography (ECC) is widely accepted for ensuring secure data exchange between resource-limited IoT devices. The National Institute of Standards and Technology (NIST) recommended implementation, such as B-163, is particularly well-suited for Internet of Things (IoT) applications. Here, Elliptic Curve Point Multiplication (ECPM) is the most time-critical and resource-intensive operation due to the finite field multiplier. This paper proposes a new implementation method of finite field multiplication using a hybrid Karatsuba multiplier, which achieves a significant improvement in computation time while maintaining a reasonable area footprint. The proposed multiplier, along with a finite field adder, squarer, and extended Euclidean inversion circuit, is used to implement an architecture for ECPM using the Montgomery algorithm. The architecture is evaluated for $GF(2^{163})$ on the Xilinx Virtex-7 FPGA platform, achieving a maximum frequency of 213~MHz and occupying 14,195 Lookup Tables (LUTs). The results demonstrate a significant speedup in computation time and overall performance compared to other reported designs.
format Preprint
id arxiv_https___arxiv_org_abs_2506_12359
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Efficient Hardware Implementation of Elliptic Curve Point Multiplication over $GF(2^m)$ on FPGA
Kumari, Ruby
Rout, Tapas
Saini, Babul
Pandey, Jai Gopal
Karmakar, Abhijit
Hardware Architecture
Elliptic Curve Cryptography (ECC) is widely accepted for ensuring secure data exchange between resource-limited IoT devices. The National Institute of Standards and Technology (NIST) recommended implementation, such as B-163, is particularly well-suited for Internet of Things (IoT) applications. Here, Elliptic Curve Point Multiplication (ECPM) is the most time-critical and resource-intensive operation due to the finite field multiplier. This paper proposes a new implementation method of finite field multiplication using a hybrid Karatsuba multiplier, which achieves a significant improvement in computation time while maintaining a reasonable area footprint. The proposed multiplier, along with a finite field adder, squarer, and extended Euclidean inversion circuit, is used to implement an architecture for ECPM using the Montgomery algorithm. The architecture is evaluated for $GF(2^{163})$ on the Xilinx Virtex-7 FPGA platform, achieving a maximum frequency of 213~MHz and occupying 14,195 Lookup Tables (LUTs). The results demonstrate a significant speedup in computation time and overall performance compared to other reported designs.
title An Efficient Hardware Implementation of Elliptic Curve Point Multiplication over $GF(2^m)$ on FPGA
topic Hardware Architecture
url https://arxiv.org/abs/2506.12359