 | A CIMPA research school on Arithmetic, coding and cryptography National Higher School of Mathematics Sidi Abdellah (Algiers), Algeria April 5-16 2026 |
 |
|
| 
The scientific program will feature a foundational course in algebraic number theory, focusing on key topics such as the ramification of primes, Frobenius elements, and the structure of decomposition and inertia groups. In parallel, the theory of elliptic curves will be examined in depth, covering, among others, their group structure, torsion points, isogenies, endomorphism rings, the Weil pairing, the Mordell-Weil theorem, elliptic curves over finite fields, which are essential concepts for understanding their applications in cryptography. The course on isogeny-based cryptography will begin by exploring the algorithmic aspects of elliptic curves and isogenies, using these foundations to introduce simple elliptic curve-based cryptographic schemes, such as the Diffie-Hellman key exchange and the Charles-Goren-Lauter hash function. It will then move to more advanced topics, including the Deuring correspondence and the class group action of complex multiplication, and the cryptographic applications that emerge from these ideas. Additionally, coding theory will be approached from an algebraic-geometric perspective, with particular emphasis on the construction of error-correcting linear codes. Students will also explore modern cryptographic protocols, learning how elliptic curves and isogenies play a central role in designing secure communication systems. Hands-on computational sessions using tools like GP Pari or Sage will provide practical experience, enabling students to implement cryptographic algorithms and perform elliptic curve computations..
|