A note on BDD problems with lambda 2 lambda 2-gap

In CRYPTO 2009, Lyubashevsky and Micciancio presented reductions BDD1/2 gamma BDD1/2 gamma (Bounded Distance Decoding Problem) [el] uSVP gamma uSVP gamma (Unique Shortest Vector Problem) [el] BDD1/ gamma BDD1/ gamma , and posed an open problem whether the reduction gap can be closed. This paper concerns bounded distance decoding (BDD) problems for lattices with large lambda 2 lambda 2-gap. In the presence of larger lambda 2 lambda 2-gap, better reductions from BDD to uSVP and exact SVP are obtained. Some result can be regarded as a partial solution to the open problem.