## Cryptology ePrint Archive: Report 2013/052

Some Complexity Results and Bit Unpredictable for Short Vector Problem

Kuan Cheng

Abstract: In this paper, we prove that finding the approximate shortest vector with length in $[\lambda_{1},\gamma \lambda_{1} ]$ could be reduced to GapSVP. We also prove that shortest vector problem could also be reduced to GapSVP with a small gap. As the complexity of uSVP is not very clear, we improve crurrent complexity results\cite{AD2011} of uSVP, proving uSVP could be reduced from SVP deterministically. What's more, we prove that the search version of uSVP could be reduced to decisional version of uSVP with almost the same gap.

At last, based on the results above, we prove a bit-unpredictable property of SVP.

Category / Keywords: foundations / Lattice, SVP, uSVP, GapSVP

Publication Info: Not published yet

Date: received 2 Feb 2013, last revised 9 Mar 2013

Contact author: ckkcdh at hotmail com

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