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Evaluation of linear relations between vectors of a lattice in euclidean space

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Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

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Abstract

We prove that to find a nontrivial integer linear relation between vectors of a lattice L ⊂ℝn, whose euclidean length is at most M, one needs O (n 5+ε(ln Mn/λ)1+ε) binary operations for any ε > O, where λ is the first successive minimum of L.

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Authors and Affiliations

  1. 43-2 Profsoyusnaya ul. Apt. 723, 117420, Moscow, Russia

    I. A. Semaev

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  1. I. A. Semaev
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Semaev, I.A. (1998). Evaluation of linear relations between vectors of a lattice in euclidean space. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054871

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  • DOI: https://doi.org/10.1007/BFb0054871

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

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