LLL Demonstration

WORK IN PROGRESS

This is a demo of the LLL algorithm. You can check the debug box to step through the algorithm to see exactly how LLL works.

Set \(k=2\).

While \(k\leq n\)

    For \(j\) from \(k-1\) down to \(1\)

        Set \(\vec{v}_k=\vec{v}_k-\lfloor \mu_{k,j} \rceil \vec{v}_j\)

    EndFor

    If \( \|\vec{v}_k^*\|^2\geq (\delta-\mu_{k,k-1}^2)\|v_{k-1}^*\|^2 \):

        Set \(k=k+1\)

    Else

        Swap \(\vec{v}_k\) and \(\vec{v}_{k-1}\)
        Set \(k=\max(k-1,2)\)

    EndIf
EndWhile

Output LLL-reduced basis \(\{\vec{v}_1,\cdots ,\vec{v}_n\}\)

Orthogonality Defect:

Number of lattice points rendered per direction:

LLL \(\delta\):

Debug

k=; Current step:

Gram-Schmidt Coefficient Matrix: