The Shortest Vector Problem in Lattices with Many Cycles

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 Zn /Λ. We give a proof that the shortest vector problem is NP-complete in the max-norm for n-dimensional lattices Λ where Zn /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.

• Type: Conference
• Year: 2001
• Where: CALC
• Authors: Mårten Trolin
• Keywords: Additive Group Zn, CALC 2001, Cryptology, Shortest Vector Problem, Zn /Λ