Abstract
We associate with an integer lattice basis a scaled basis that has orthogonal vectors of nearly equal length. The orthogonal vectors or the QR-factorization of a scaled basis can be accurately computed up to dimension 216 by Householder reflexions in floating point arithmetic (fpa) with 53 precision bits.
We develop a highly practical fpa-variant of the new segment LLL- reduction of Koy and Schnorr [KS01]. The LLL-steps are guided in this algorithm by the Gram-Schmidt coefficients of an associated scaled basis. The new reduction algorithm is much faster than previous codes for LLL-reduction and performs well beyond dimension 1000.
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Koy, H., Schnorr, C.P. (2001). Segment LLL-Reduction with Floating Point Orthogonalization. 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_8
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DOI: https://doi.org/10.1007/3-540-44670-2_8
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