Paper 2014/545
Solving closest vector instances using an approximate shortest independent vectors oracle
Chengliang Tian, Wei Wei, and Dongdai Lin
Abstract
Given a lattice $L\subset\R^n$ and some target vector, this paper studies the algorithms for approximate closest vector problem (CVP$_\gamma$) by using an approximate shortest independent vectors problem oracle (SIVP$_\gamma$). More precisely, if the distance between the target vector and the lattice is no larger than $\frac{c}{\gamma n}\lambda_1(L)$ for any constant $c>0$, we give randomized and deterministic polynomial time algorithms to find a closest vector, which improves the known result by a factor of $2c$. Moreover, if the distance between the target vector and the lattice is larger than some quantity with respect to $\lambda_n(L)$, using $\SIVP_\gamma$ oracle and Babai's nearest plane algorithm, we can solve $\CVP_{\gamma\sqrt{n}}$ in deterministic polynomial time. Specially, if the approximate factor $\gamma\in(1,2)$ in the $\SIVP_\gamma$ oracle, we obtain a better reduction factor for CVP.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- lattice-based cryptography
- Contact author(s)
- tcl0815 @ gmail com
- History
- 2014-07-18: received
- Short URL
- https://ia.cr/2014/545
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2014/545, author = {Chengliang Tian and Wei Wei and Dongdai Lin}, title = {Solving closest vector instances using an approximate shortest independent vectors oracle}, howpublished = {Cryptology {ePrint} Archive, Paper 2014/545}, year = {2014}, url = {https://eprint.iacr.org/2014/545} }