Segment and Strong Segment LLL-Reduction of Lattice Bases
نویسندگان
چکیده
We present an efficient variant of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovász [LLL82]. We organize LLL-reduction in segments of size k. Local LLL-reduction of segments is done using local coordinates of dimension 2k. Strong segment LLL-reduction yields bases of the same quality as LLL-reduction but the reduction is n-times faster for lattices of dimension n. We extend segment LLL-reduction to iterated subsegments. The resulting reduction algorithm runs in O(n log n) arithmetic steps for integer lattices of dimension n with basis vectors of length 2, compared to O(n) steps for LLL-reduction.
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