Abstract
We present an efficient variant of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovász. We organize LLL-reduction in segments of size k. Local LLL-reduction of segments is done using local coordinates of dimension k.
We introduce segment LLL-reduced bases, a variant of LLL-reduced bases achieving a slightly weaker notion of reducedness, but speeding up the reduction time of lattices of dimension n by a factor n. We also introduce a variant of LLL-reduction using iterated segments. The resulting reduction algorithm runs in O(n 3 log2 n) arithmetic steps for integer lattices of dimension n with basis vectors of length 22.
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Koy, H., Schnorr, C.P. (2001). Segment LLL-Reduction of Lattice Bases. In: Silverman, J.H. (eds) Cryptography and Lattices. CaLC 2001. Lecture Notes in Computer Science, vol 2146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44670-2_7
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DOI: https://doi.org/10.1007/3-540-44670-2_7
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