The Shortest Vector Problem in Lattices with Many Cycles
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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.
KeywordsLattices LLL algorithm shortest vector problem
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