Author(s)

Xiaoyan Li ¹, Shi Wang ¹

Affiliation(s)

¹ Hainan Vocational University of Science and Technology, Haikou, Hainan, China

Corresponding Author

Xiaoyan Li

ABSTRACT

In the field of information security, the security of identity authentication is crucial. We focus on the application of algebraic curves in the field of identity authentication security and explore their core content in depth. Starting from the basic theory of algebraic curves, we explain the group structure and discrete logarithmic properties of elliptic curves. Then, we conduct a detailed analysis of its application mode, including key generation, encryption and decryption, and digital signature processes based on elliptic curve cryptography (ECC). This is aimed at building a secure defense line for identity authentication. Meanwhile, by using algebraic curves to construct a zero - knowledge identity authentication protocol, we can achieve identity verification under privacy protection. Compared to traditional methods, this application has obvious advantages and can effectively resist quantum computing attacks, improving efficiency with shorter key lengths and faster computation speeds. However, in the process of application promotion, there are challenges such as the urgent need to complete mathematical theories, optimize algorithms, and ensure compatibility.Conduct research on the application of algebraic curves in identity authentication security, providing both theoretical foundations and practical guidance for promoting technological innovation in this field and further enhancing the security and reliability of identity authentication.

KEYWORDS

Algebraic curve; Elliptic curve cryptography (ECC); Identity authentication; information security

CITE THIS PAPER

Xiaoyan Li, Shi Wang, Application and Research of Algebraic Curve in Identity Authentication Security. Journal of Electronics and Information Science (2025) Vol. 10: 82-88. DOI: http://dx.doi.org/10.23977/10.23977/jeis.2025.100111.

REFERENCES

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[3] Yang Guotao, Cao Chong, Han Tao, etc Password security authentication method based on hybrid encryption in the Internet of Things [J]. Application of microcontrollers and embedded systems, 2024,  000(4):7.
[4] Yang Qing, Wang Haoxuan, Liang Lei, etc Improved elliptic curve digital signature scheme and case analysis [J]. Computer applications and software, 2023, 40(1):327-330.
[5] Lin Tingting Secure execution of elliptic curve cryptography processes CN202210111179.2[2025-02-26].
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