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On the complexity of finding short vectors in integer lattices

  • Alsorithms 4 — Factorization
  • Conference paper
  • First Online:
Computer Algebra (EUROCAL 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 162))

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Abstract

In [Lenstra, A., et al. 82] an algorithm is presented which, given n linearly independent n-dimensional integer vectors, calculates a vector in the integer lattice spanned by these vectors whose Euclidean length is within a factor of 2(n−1)/2 of the length of the shortest vector in this lattice. If B denotes the maximum length of the basis vectors, the algorithm is shown to run in O(n 6(log B)3) binary steps. We prove that this algorithm can actually be executed in O(n 6(log B)2+n 5(log B)3) binary steps by analyzing a modified version of the algorithm which also performs better in practice.

The research for this paper has been partially supported by the Connaught Fund, Grant # 3-370-126-80.

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References

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    Erich Kaltofen

Authors
  1. Erich Kaltofen
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J. A. van Hulzen

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© 1983 Springer-Verlag

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Kaltofen, E. (1983). On the complexity of finding short vectors in integer lattices. In: van Hulzen, J.A. (eds) Computer Algebra. EUROCAL 1983. Lecture Notes in Computer Science, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12868-9_107

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  • DOI: https://doi.org/10.1007/3-540-12868-9_107

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12868-7

  • Online ISBN: 978-3-540-38756-5

  • eBook Packages: Springer Book Archive

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