An LLL Algorithm for Module Lattices

Explore an in-depth lecture on the LLL algorithm for module lattices presented by Alice Pellet-Mary from KU Leuven. Delve into the intricacies of lattice geometry, algorithms, and hardness as part of the "Lattices: Geometry, Algorithms and Hardness" series. Gain insights into the concept of smallness in K, previous works and results, and a comprehensive outline of the talk. Examine a high-level overview of LLL, inner product over R, QR factorization over R, and Euclidean division. Discover the use of Log space and the core idea behind the algorithm, including heuristics and underlying complexities. Conclude with a summary of the algorithm's impact and explore open problems in the field of module lattices.

An LLL algorithm for module lattices
What is small in K?
Previous works and result
Outline of the talk
High-level overview of LLL
Inner product over R
QR factorization over R
Euclidean division
Using the Log space
Idea of the algorithm
Heuristic
Under the carpet
Summary and impact
Open problems