Chapitre D'ouvrage Année : 2025

Another L Makes It Better? Lagrange Meets LLL and May Improve BKZ Pre-Processing

Résumé

We present a new variant of the LLL lattice reduction algorithm, inspired by Lagrange notion of pair-wise reduction, called L4. Similar to LLL, our algorithm is polynomial in the dimension of the input lattice, as well as in , where is an upper-bound on the norm of the longest vector of the input basis. We experimentally compared the norm of the first basis vector obtained with LLL and L4 up to dimension 200. On average we obtain vectors that are up to 16% shorter. We also used our algorithm as a pre-processing step for the BKZ lattice reduction algorithm with blocksize 24. In practice, up to dimension 140, this allows us to reduce the norm of the shortest basis vector on average by 3%, while the runtime does not significantly increases. In 10% of our tests, the whole process was even faster. This paper has been awarded the “Code and Data Available” and “Results Reproduced” badges as recognition that the author(s) have followed reproducibility principles. Code and data that allow readers to reproduce the results in this paper are available at https://zenodo.org/records/13847623. Participation in the ALENEX artifact evaluation phase was optional and performed at the request of the author(s).
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Dates et versions

hal-04879590 , version 1 (10-01-2025)

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Citer

Sébastien Balny, Claire Delaplace, Gilles Dequen. Another L Makes It Better? Lagrange Meets LLL and May Improve BKZ Pre-Processing. 2025 Proceedings of the Symposium on Algorithm Engineering and Experiments (ALENEX), Society for Industrial and Applied Mathematics, pp.181-193, 2025, ⟨10.1137/1.9781611978339.15⟩. ⟨hal-04879590⟩

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