### Keep A Secret? Thanks To Number Theory!

This mathematics workshop allow students to learn how number theory is applied to secure communications. Through practical exercises such as decryption of a coded message with a cipher wheel, the student will discover how an encryption algorithm works and understand the underlying number theory.

They will tackle different mathematical concepts:

- the Euclidean division (division with remainder)
- the greatest common divisor
- Fermat’s little theorem
- fast modular exponentiation
- the RSA algorithm

If the teachers wish to prepare their classes before the workshop, corresponding materials that can be used to work with the students will be provided. (For more details see the Prerequisite tab)

This workshop is suited for pupils from 3^{e} onwards. The workshop is flexible and the pace is adapted to the level of each class.

### Language

This workshop can be offered in Luxembourgish, French, German and English.

### Time schedule

The workshops take place from 9:00h till 15:30h with a lunch break of one hour. During the lunch break the students can get some food from the restaurants that are located on Campus Belval and in Belval Plaza, or they can use the canteen.

### Prerequisites

If you wish to prepare the class before the workshop, you can review or introduce the following concepts:

- The Euclidean division (i.e. the division with remainder) and the Euclidean algorithm (for the division, the case of a negative dividend/divisor should also be considered).
- The greatest common divisor (gcd) of two integers and Bézout’s identity that gives the gcd of two integers as a linear combination of these integers. (For example 3 = gcd(6, 15) = -12*6 + 5*15). Such a linear combination can be obtained by means of the extended Euclidean algorithm.
- The definition of a prime number.
- The basic rules of exponentiation.

Materials that can be used for the preparation will be provided.

### Location

The workshops in mathematics take place in the Maison du Savoir (MSA) on Campus Belval.

If you arrive by car or coach, take the A4 and keep it until the end, then follow the signs towards “Belval”. On the campus, there are no signs to indicate the way to Maison du Savoir. Please use the map below to find your way.

If you arrive by train, the stop is “Belval Université”. Our building is 10 minutes away from the train station by foot. There are also several buses that you can take to arrive on the campus.

Schedule