Some Complexity Results and Bit Unpredictable for Short Vector Problem

Kuan Cheng

Paper 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 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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Not published yet
Keywords: Lattice SVP uSVP GapSVP
Contact author(s): ckkcdh @ hotmail com
History: 2013-03-09: last of 3 revisions; 2013-02-06: received; See all versions
Short URL: https://ia.cr/2013/052
License: CC BY

BibTeX

@misc{cryptoeprint:2013/052,
      author = {Kuan Cheng},
      title = {Some Complexity Results and Bit Unpredictable for Short Vector Problem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/052},
      year = {2013},
      url = {https://eprint.iacr.org/2013/052}
}