LLL Algorithm

A polynomial-time lattice basis reduction algorithm that, given a basis of a lattice in Euclidean space, outputs a reduced basis consisting of relatively short, nearly orthogonal vectors satisfying size-reduction and the Lovász condition for a chosen parameter δ∈(1/4,1].

A polynomial-time lattice-reduction algorithm that, given a basis of a Euclidean lattice, returns a reduced basis whose vectors are relatively short and nearly orthogonal according to the Lovász condition; widely used in computational number theory, algebra, and cryptanalysis.