On the complexity of finding short vectors in integer lattices

  • Erich Kaltofen
Alsorithms 4 — Factorization
Part of the Lecture Notes in Computer Science book series (LNCS, volume 162)


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(n6(log B)3) binary steps. We prove that this algorithm can actually be executed in O(n6(log B)2+n5(log B)3) binary steps by analyzing a modified version of the algorithm which also performs better in practice.


Binary Complexity Integer Lattice Integer Multiplication Euclidean Length Short Vector 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Erich Kaltofen
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada

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