Practical algorithms for constructing HKZ and Minkowski reduced bases
نویسندگان
چکیده
In this paper, three practical lattice basis reduction algorithms are presented. The first algorithm constructs a Hermite, Korkine and Zolotareff (HKZ) reduced lattice basis, in which a unimodular transformation is used for basis expansion. Our complexity analysis shows that our algorithm is significantly more efficient than the existing HKZ reduction algorithms. The second algorithm computes a Minkowski reduced lattice basis. It is the first practical algorithm for Minkowski reduced bases for lattices of arbitrary dimensions. The third algorithm is an improvement of the second algorithm by drastically reducing the number of lattice points being searched. Since the original LLL algorithm is no longer applicable to the third algorithm, we propose a notion of quasi-LLL reduction to accelerate the computation.
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Practical HKZ and Minkowski Lattice Reduction Algorithms
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