Lattice Basis Reduction Using LLL Algorithm with Application to Algorithmic Lattice Problems

Sammanfattning

The LLL algorithm is recognized as one of the most important achievements of twentieth century with applications across many fields in mathematics. Yet, the subject is explained only on an advanced level in the current literature. We systematically present background and key concepts needed to understand the underlying problematic and afterwards give detailed proofs of all ideas needed to understand the algorithm. The paper focuses on application to lattice problems and proving results pre-sented in the original paper of A. K. Lenstra et al. published in 1982.