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arXiv · 1805.03418

Computing an LLL-reduced basis of the orthogonal lattice

Jingwei Chen·Damien Stehlé·Gilles Villard
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Abstract

As a typical application, the Lenstra-Lenstra-Lovasz lattice basis reduction algorithm (LLL) is used to compute a reduced basis of the orthogonal lattice for a given integer matrix, via reducing a special kind of lattice bases. With such bases in input, we propose a new technique for bounding from above the number of iterations required by the LLL algorithm. The main technical ingredient is a variant of the classical LLL potential, which could prove useful to understand the behavior of LLL for other families of input bases.

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Jingwei Chen, Damien Stehlé, Gilles Villard. 2018-05-09. Computing an LLL-reduced basis of the orthogonal lattice. https://arxiv.org/abs/1805.03418

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