SYSTEMATIC ANALYSIS OF MATHEMATICAL FUNDAMENTALS IN ELLIPTIC CURVE CRYPTOGRAPHY: CONCEPTS, APPLICATIONS, AND CHALLENGES

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Published: Nov 28, 2024

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Miftah Sigit Rahmawati
Universitas Muhammadiyah Sorong
Ierasath Bin Yousof
An-Nikmah Al-Islamiyah Institute, Malaysia

Abstract

This study aims to systematically analyze the mathematical fundamentals underpinning Elliptic Curve Cryptography (ECC) by reviewing its key concepts, applications, and challenges. Utilizing literature from Springer, Sagepub, and Mendeley databases, several essential mathematical concepts, such as the basic operations in ECC, including addition and multiplication. Furthermore, the challenges in solving the Elliptic Curve Discrete Logarithm Problem (ECDLP), which forms the foundation of ECC security, are discussed, along with the implementation of cryptographic protocols. This review also explores practical challenges in applying ECC to modern cryptographic systems, including key management and secure communications, and the theoretical implications of evolving algorithms. This article categorizes previous research into three main areas: (1) ECC concepts covering discussions on elliptic curves, cryptology, and pre-cryptological operations, (2) ECC applications in various encryption methods and models, such as the ECC encryption model, ECDSA, and ECDH, and (3) challenges in ECC implementation as a computational model. The results show that while the foundational algebraic theories supporting ECC have been developed, further research is required to enhance the effectiveness and efficiency of ECC in the future. This study serves as a groundwork for more in-depth research on algebraic structures in the formation of ECC.

Article Details

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ICEAST 2024
Section
Articles
Author Biography

Ierasath Bin Yousof, An-Nikmah Al-Islamiyah Institute, Malaysia

An-Nikmah Al-Islamiyah Institute, Malaysia

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