Faster LLL-type Reduction of Lattice Bases

@inproceedings{Neumaier2016FasterLR,
  title={Faster LLL-type Reduction of Lattice Bases},
  author={Arnold Neumaier and Damien Stehl{\'e}},
  booktitle={ISSAC},
  year={2016}
}
We describe an asymptotically fast variant of the LLL lattice reduction algorithm. It takes as input a basis B ∈ Z<sup>n x n</sup> and returns a (reduced) basis C of the Euclidean lattice L spanned by B, whose first vector satisfies |c<sub>1</sub>| ≤ (1+c) (4/3)<sup>(n-1)/4</sup> (det L)<sup>1/n</sup> for any fixed c>0. It terminates within O(n<sup>4+ε</sup> β<sup>1+ε</sup>) bit operations for any ε >0, with β = log max<sub>i</sub> |b<sub>i</sub>|. It does rely on fast integer arithmetic but… CONTINUE READING

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