Abstract
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The LLL algorithm is one of the most studied lattice basis
reduction algorithms in the literature. Among all of its variants, the
floating point version, also known as L2, is the most popular one, due to
its efficiency and its practicality. In its classic setting, the floating point
precision is a fixed value, determined by the dimension of the input
basis at the initiation of the algorithm. We observe that a fixed precision
overkills the problem, since one does not require a huge precision to
handle the process at the beginning of the reduction. In this paper, we
propose an adaptive way to handle the precision, where the precision
is adaptive during the procedure. Although this optimization does not
change the worst-case complexity, it reduces the average-case complexity
by a constant factor. In practice, we observe an average 20% acceleration
in our implementation.