LLL Algorithm

This lecture covers the LLL (Lenstra–Lenstra–Lovász) algorithm, which is used to find a reduced basis in a lattice. The algorithm iteratively transforms a given basis to a new basis with certain properties, aiming to reduce the size of the basis vectors. Through a series of steps involving Gram-Schmidt orthogonalization and basis reduction, the algorithm ensures that the resulting basis is shorter and more orthogonal. The lecture also discusses the termination conditions of the algorithm and the concept of LLL-reduced bases. Various examples and operations are presented to illustrate the algorithm's application and effectiveness.