The Shortest Vector Problem in Lattices with Many Cycles

  • Mårten Trolin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2146)


In this paper we investigate how the complexity of the shortest vector problem in a lattice A depends on the cycle structure of the additive group ℤn/A. We give a proof that the shortest vector problem is NP-complete in the max-norm for n-dimensional lattices A where ℤn/A has n — 1 cycles. We also give experimental data that show that the LLL algorithm does not perform significantly better on lattices with a high number of cycles.


Lattices LLL algorithm shortest vector problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Mårten Trolin
    • 1
  1. 1.Department of Numerical Analysis and Computer ScienceRoyal Institute of TechnologyStockholmSweden

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