Lattices with Many Cycles Are Dense

Abstract We give a method for approximating any n-dimensional lattice with a lattice Λ whose factor group Zn /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.

• Type: Conference
• Year: 2004
• Where: STACS
• Authors: Mårten Trolin
• Keywords: Closest Vector Problem, Shortest Vector Problem, STACS 2004, Theoretical Computer Science, Vector Problem