Théorie Algébrique des Nombres et Applications notamment en Cryptographie / ICTP

Algebraic number theory is a very active field of mathematics. We plan to introduce the subject and its application to cryptography. After given courses in elementary arithmetic, algebraic numbers and p-adic numbers, we will focus on the basics of elliptic curves and finite fields. Applications will also figure prominently in the program as it is shown by the presence of the following courses : Introduction to cryptography, Elliptic curves and cryptography.
Moreover, we plan to cover the explicit construction of elliptic curves over finite fields with group of point of large prime order (as needed by cryptographic applications) via complex multiplication.