A note on BDD problems with λ2-gap

In CRYPTO 2009, Lyubashevsky and Micciancio presented reductions BDD1/2γ (Bounded Distance Decoding Problem) ⩽ uSVPγ (Unique Shortest Vector Problem) ⩽ BDD1/γ, and posed an open problem whether the reduction gap can be closed. This paper concerns bounded distance decoding (BDD) problems for lattices with large λ2-gap. In the presence of larger λ2-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.