Isogeny-based Cryptography and Quaternion Algebra
This course covers isogeny-based cryptography and its underlying mathematical framework—quaternion algebras.
Supersingular elliptic curves have endomorphism rings isomorphic to maximal orders in quaternion algebras. The Deuring correspondence links supersingular elliptic curves to quaternion algebra ideals, forming the foundation of most isogeny-based protocols. Topics include: Elliptic curves, isogenies; Quaternion algebras, orders, and ideals; The Deuring correspondence and its algorithms; Cryptographic protocols: SIDH, CSIDH, and SQIsign; Recent advances in signatures and cryptanalysis.
Students will learn the full mathematical framework and gain practical insight into protocol design and security.
Supersingular elliptic curves have endomorphism rings isomorphic to maximal orders in quaternion algebras. The Deuring correspondence links supersingular elliptic curves to quaternion algebra ideals, forming the foundation of most isogeny-based protocols. Topics include: Elliptic curves, isogenies; Quaternion algebras, orders, and ideals; The Deuring correspondence and its algorithms; Cryptographic protocols: SIDH, CSIDH, and SQIsign; Recent advances in signatures and cryptanalysis.
Students will learn the full mathematical framework and gain practical insight into protocol design and security.
讲师
日期
2026年09月21日 至 12月15日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周二 | 15:20 - 16:55 | A3-3-201 | ZOOM 08 | 787 662 9899 | BIMSA |
修课要求
Linear algebra and basis algebra geometry.
参考资料
1. J. Silverman. The arithmetic of elliptic curves, volume 106. Springer, 2009.
2. J. Voight. Quaternion Algebras, Springer.
2. J. Voight. Quaternion Algebras, Springer.
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
, Researcher
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.