Paper 2019/1028
Faster Sieving Algorithm for Approximate SVP with Constant Approximation Factors
Divesh Aggarwal, Bogdan Ursu, and Serge Vaudenay
Abstract
Abstract. There is a large gap between theory and practice in the complexities of sieving algorithms for solving the shortest vector problem in an arbitrary Euclidean lattice. In this paper, we work towards reducing this gap, providing theoretical refinements of the time and space complexity bounds in the context of the approximate shortest vector problem. This is achieved by relaxing the requirements on the AKS algorithm, rather than on the ListSieve, resulting in exponentially smaller bounds starting from $\mu\approx 2$, for constant values of $\mu$. We also explain why these improvements carry over to also give the fastest quantum algorithms for the approximate shortest vector problem.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- lattice techniques
- Contact author(s)
-
bogdanbear @ gmail com
divesh aggarwal @ gmail com
serge vaudenay @ epfl ch - History
- 2019-09-11: received
- Short URL
- https://ia.cr/2019/1028
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/1028,
author = {Divesh Aggarwal and Bogdan Ursu and Serge Vaudenay},
title = {Faster Sieving Algorithm for Approximate {SVP} with Constant Approximation Factors},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/1028},
year = {2019},
url = {https://eprint.iacr.org/2019/1028}
}
