Elliptic Curves and Cryptography
Elliptic curve cryptography (ECC) is a cornerstone of modern cryptographic systems, offering enhanced security and efficiency compared to traditional methods such as RSA. This course provides a comprehensive introduction to the mathematical foundations of elliptic curves and their application in cryptography.
The journey begins with the algebraic and geometric properties of elliptic curves, including their group law and key theorems, laying the groundwork for understanding their utility in secure communication. We then explore the core principles of public-key cryptography, illustrating how elliptic curves enable compact and high-strength cryptographic primitives. If time permits, we will introduce its applications in post-quantum cryptography.
By the end of the course, participants will gain the theoretical and practical knowledge needed to leverage elliptic curves in designing and analyzing cryptographic systems, ensuring robust protection against emerging security threats. This course is ideal for students, researchers, and professionals seeking a solid foundation in cryptography with a focus on ECC.
The journey begins with the algebraic and geometric properties of elliptic curves, including their group law and key theorems, laying the groundwork for understanding their utility in secure communication. We then explore the core principles of public-key cryptography, illustrating how elliptic curves enable compact and high-strength cryptographic primitives. If time permits, we will introduce its applications in post-quantum cryptography.
By the end of the course, participants will gain the theoretical and practical knowledge needed to leverage elliptic curves in designing and analyzing cryptographic systems, ensuring robust protection against emerging security threats. This course is ideal for students, researchers, and professionals seeking a solid foundation in cryptography with a focus on ECC.
讲师
日期
2025年03月25日 至 06月17日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 09:50 - 11:25 | A3-3-201 | ZOOM 02 | 518 868 7656 | BIMSA |
修课要求
linear algebra, basis algebraic curves.
参考资料
1. J. H. Silverman. The Arithmetic of Elliptic Curves. Graduate texts in mathematics, vol, 106. Springer(1986)
2. R. Hartshorne. Algebraic Geometry. Springer-Verlag, New York, 1977. Graduate texts in mathematics.
3. J. Hoffstein, J. Pipher and J. H. Silverman. An introduction to mathematic cryptography. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2008
2. R. Hartshorne. Algebraic Geometry. Springer-Verlag, New York, 1977. Graduate texts in mathematics.
3. J. Hoffstein, J. Pipher and J. H. Silverman. An introduction to mathematic cryptography. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2008
听众
Advanced Undergraduate
, Graduate
视频公开
公开
笔记公开
公开
语言
中文
讲师介绍
Peigen Li received his bachelor's degree from the Harbin Institute of Technology and his Ph.D. from the Department of Mathematical Sciences at Tsinghua University. He subsequently worked as a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and Tsinghua University. In 2024, he joined BIMSA as an Assistant Professor. His current research interests include post-quantum cryptography, algebraic geometry, and number theory.