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(nā1)/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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Ā© 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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