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Pré-Publication, Document De Travail Année : 2010

Perturbation Analysis of the QR Factor R in the Context of LLL Lattice Basis Reduction

Xiao-Wen Chang
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Damien Stehlé
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Résumé

In 1982, Arjen Lenstra, Hendrik Lenstra Jr. and László Lovász introduced an efficiently computable notion of reduction of basis of a Euclidean lattice that is now commonly referred to as LLL-reduction. The precise definition involves the R-factor of the QR factorisation of the basis matrix. A natural mean of speeding up the LLL reduction algorithm is to use a (floating-point) approximation to the R-factor. In the present article, we investigate the accuracy of the factor R of the QR factorisation of an LLL-reduced basis. Our main contribution is the first fully rigorous perturbation analysis of the R-factor of LLL-reduced matrices under column-wise perturbations. Our results should be very useful to devise LLL-type algorithms relying on floating-point approximations.
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Dates et versions

ensl-00529425 , version 1 (25-10-2010)
ensl-00529425 , version 2 (07-04-2011)

Identifiants

  • HAL Id : ensl-00529425 , version 1

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Xiao-Wen Chang, Damien Stehlé, Gilles Villard. Perturbation Analysis of the QR Factor R in the Context of LLL Lattice Basis Reduction. 2010. ⟨ensl-00529425v1⟩
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