Lattices and applications

Goal:

Lattice reduction (the LLL algorithm) is a powerful tool to find short vectors in lattices with plenty of applications. There are many good implementations of LLL, for example in SageMath.

The aim of this project is to apply the LLL algorithm (using a chosen implementation as a `black box') to various problems such as (simultaneous) Diophantine approximation and attacking the RSA cryptographic scheme, which is used by anybody with a computer or a smartphone every day.

Schedule: To be determined.

Supervisors: Gabor Wiese

Difficulty level: Introductory.

Tools: Any computer language.

Results: [too be completed at the end of the project.]

FSCT -- University of Luxembourg