Abstract
The famous lattice basis reduction algorithm of L. Lovasz transforms a given integer lattice basis b1,...,bn ∈ ℤn into a reduced basis, and does this by O(n4 log B) arithmetic operations on O(n log B)-bit integers. Here B bounds the euclidean length of the input vectors, i.e. ∥b1∥2,...,∥bn∥2 ≦ B. The new algorithm operates on integers with at most O(n + log B) bits and uses at most O(n4 log B) arithmetic operations on such integers. This reduces the number of bit operations for reduction by a factor n2 if n is proportional to log B and if standard arithmetic is used. For most practical cases reduction can be done without very large integer arithmetic but with floating point arithmetic instead.
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