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.
Lecturer
Date
21st September ~ 15th December, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Tuesday | 15:20 - 16:55 | A3-3-201 | ZOOM 08 | 787 662 9899 | BIMSA |
Prerequisite
Linear algebra and basis algebra geometry.
Reference
1. J. Silverman. The arithmetic of elliptic curves, volume 106. Springer, 2009.
2. J. Voight. Quaternion Algebras, Springer.
2. J. Voight. Quaternion Algebras, Springer.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese
Lecturer Intro
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.