**
Teaching **

**
Number Theory and Applications to Cryptography **

** University of Luxembourg
Bachelor en Sciences et Ingénierie (Académique)
Mathématiques **

** Lecturer: ** Sara Arias-de-Reyna

** Type of teaching: ** Lecture with integrated exercises

** Credit-points (ECTS): ** 3

** Teaching language: ** English

** Targets: **

Number theory is one of the oldest disciplines in mathematics. Very recently, it found applications in cryptography and it is used in everyday life by all of us (even if we are not aware of it).
This course introduces the basic concepts of elementary number theory; in particular it covers the quadratic reciprocity law. It also contains a treatment of the Prime Number Theorem. Moreover, it addresses some aplications of the theory to cryptography: RSA, El Gamal, Diffie-Hellman and some primality testing.

** Contents
**

- Some aspects of elementary number theory
- RSA
- Finite fields
- Quadratic reciprocity
- Diffie-Hellman
- Primality testig
- The Prime Number Theorem