# On Bounded Distance Decoding, Unique Shortest Vectors, and the Minimum Distance Problem

@inproceedings{Lyubashevsky2009OnBD, title={On Bounded Distance Decoding, Unique Shortest Vectors, and the Minimum Distance Problem}, author={Vadim Lyubashevsky and Daniele Micciancio}, booktitle={CRYPTO}, year={2009} }

- Published 2009 in CRYPTO
DOI:10.1007/978-3-642-03356-8_34

We prove the equivalence, up to a small polynomial approximation factor √ n/ log n, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and GapSVP (the decision version of the Shortest Vector Problem). This resolves a long-standing open problem about the relationship between uSVP and the more standard GapSVP, as well the BDD problem commonly used in coding theory. The main cryptographic application of our work is the proof that the Ajtai-Dwork ([AD97… CONTINUE READING

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