1*Assistant Professor, Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai
Email Id: drarchanag@veltech.edu.in
Scopus Id: 57822786800
Orcid Id: 0009-0002-7623-1334
Elliptic curve cryptography (ECC) has now gained widespread acceptance as an encryption protocol of choice in the public-key cryptographic model since it can provide better security with considerably smaller key sizes and comparatively lower computation cost than most of the standard algorithms. This review discusses the mathematical ideas applied to the elliptic curves and how the elliptic curve discrete logarithm problem has been employed to offer a guarantee of cryptographic security. Key exchange, authentication and secure data transmission functions of major ECC algorithms, such as ECDH, ECDSA, ECIES and EdDSA, are discussed. More efficient methods of ECC performance and resilience, including efficient scalar multiplication, intelligent key generation schemes, pairing-based cryptography, and isogeny-based schemes, are also discussed. The review further evaluates common security threats affecting ECC implementations, including side-channel attacks, protocol-level vulnerabilities, hardware-related risks, and emerging quantum-computing challenges. Practical applications of ECC across secure communication protocols, blockchain systems, Internet of Things environments, and cloud platforms demonstrate its adaptability in modern digital infrastructures. Despite the fact that some implementation complexities and future quantum risks are still quite significant issues, ECC still provides a good balance between efficiency and security. The results underscore the current significance of the elliptic curve-based methods in modern cryptographic systems and their applicability to the creation of next-generation secure communication systems.
Keywords: elliptic curve cryptography, elliptic curve discrete logarithm problem, public-key cryptography, cryptographic security, post-quantum cryptography
How to cite this article: Gurulakshmi GA. Cryptography with Elliptic Curves: Enhancing Security through Advanced Mathematical Techniques. Int J Drug Deliv Technol. 2026;16(10s): 365-374; DOI: 10.25258/ijddt.16.10s.48.
Source of support: Nil.
Conflict of interest: None