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Results tagged with lenstra-lenstra-lovasz
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user 25616
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm efficiently finds a short, nearly orthogonal lattice basis form an arbitrary one
5
votes
1
answer
992
views
Significance of Gram-Schmidt coefficients in LLL algorithm
Let $\{ {\bf v}_1,{\bf v}_2 \}$ be two linearly independent vectors. An orthogonal base $\{{\bf u}_1,{\bf u}_2 \}$ of the vector space $\mathrm{span}\{ {\bf v}_1,{\bf v}_2 \}$ can be computed using Gr …
- 919
11
votes
2
answers
3k
views
Why is the Lovász condition used in the LLL algorithm?
The LLL algorithm is used to approximate the Shortest Vector Problem, i.e., it outputs a reduced basis. Such a basis will satisfy two conditions:
$$ \forall i \gt j. \quad \lvert\mu_{ij}\rvert \le \ …
- 919