Lattices reduction, LLL algorithm and applications

Completed by: Etienne Helfer

Final report

This project is devoted to understand one of the key algorithm of modern discrete mathematics. The LLL algorithm is today a standard tool to deal with lattices and is used in problems from pure and applied mathematics. You will be asked

• to understand how the algorithm is working,
• study some of its applications (factoring polynomials, linear algebra over the integer ring, application to coding theory)
• implement them by yourself.

Prerequisites:

• Good mathematical aptitude (Algebra and number theory especially)