The Shortest Vector Problem in Lattices with Many Cycles
نویسنده
چکیده
In this paper we investigate how the complexity of the shortest vector problem in a lattice Λ depends on the cycle structure of the additive group Z/Λ. We give a proof that the shortest vector problem is NP-complete in the max-norm for n-dimensional lattices Λ where Z/Λ 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.
منابع مشابه
Lattices with Many Cycles Are Dense
We give a method for approximating any n-dimensional lattice with a lattice Λ whose factor group Z/Λ has n− 1 cycles of equal length with arbitrary precision. We also show that a direct consequence of this is that the Shortest Vector Problem and the Closest Vector Problem cannot be easier for this type of lattices than for general lattices.
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