##  [LLL Algorithm](/lll-algorithm) 

  ##  [LLL Algorithm](https://mathlogic.quantumdictionary.io/lll-algorithm-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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].

 

 

 

 

 





 

 



 ##  [LLL Algorithm](https://algebra.quantumdictionary.io/lll-algorithm-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.