Abstract
We introduce some new variants of lattice problems: Quadrant-SVP, Quadrant-CVP and Quadrant-GapCVP'. All of them are NP-hard under deterministic reductions from subset sum problem. These new type of lattice problems have potential in construction of cryptosystems. Moreover, these new variant problems have reductions with standard SVP (shortest vector problem) and CVP (closest vector problem), this feature gives new way to study the complexity of SVP and CVP, especially for the proof of NP-hardness of SVP under deterministic reductions, which is an open problem up to now.
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