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Results tagged with lenstra-lenstra-lovasz
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The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm efficiently finds a short, nearly orthogonal lattice basis form an arbitrary one
4
votes
Accepted
How does the lengths of the Gram-Schmidt orthogonal basis of a lattice basis change after ll...
Although there is not a formal result with respect to this question, there is a widely accepted empirical observation for "typical" lattices known as the Geometric Series Assumption (see the 8th slide …
- 26.4k
4
votes
Accepted
LLL on Knapsack-eque problem
If we have a target upper bound $X$ for the $|x_i|$, then we expect the contribution of the $x_i$ to the square of the $\mathcal L_2$ norm of the short vector to be less than $nX^2$. If we therefore i …
- 26.4k
2
votes
Algorithm to solve SVP (shortest vector problem) using LLL reduction
Although asymptotically strong, the AKS sieving algorithms and its generalisations should only be used for large dimensions. For smaller dimensions there are methods for constructing optimal bases in …
- 26.4k