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Lenstra–Lenstra–Lovász lattice basis reduction algorithm

The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis B = { b 1 , b 2 , … , b d } {\displaystyle \mathbf {B} =\{\mathbf {b} _{1},\mathbf {b} _{2},\dots ,\mathbf {b} _{d}\}} with n-dimensional integer…

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LLL reduction

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Properties of LLL-reduced basis

LLL algorithm pseudocode

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Lenstra–Lenstra–Lovász lattice basis reduction algorithm

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Avg. degree1.96
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basis displaystyle algorithm lll lattice mathbf delta lll-reduced leq mathcal integer reduction vert vector short applications first -1 n-1 cdot

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