Paper 2014/907 Original: eprint.iacr.org/2014/907 ↗
Finding shortest lattice vectors faster using quantum search
Abstract
By applying a quantum search algorithm to various heuristic and provable sieve algorithms from the literature, we obtain improved asymptotic quantum results for solving the shortest vector problem on lattices. With quantum computers we can provably find a shortest vector in time $2^{1.799n + o(n)}$, improving upon the classical time complexities of $2^{2.465n + o(n)}$ of Pujol and Stehlé and the $2^{2n + o(n)}$ of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time $2^{0.286n + o(n)}$, improving upon the classical time complexity of $2^{0.337n + o(n)}$ of Laarhoven. These quantum complexities will be an important guide for the selection of parameters for post-quantum cryptosystems based on the hardness of the shortest vector problem.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2015-04-17: last updated
- 2014-11-04: published
- Short URL
- https://ia.cr/2014/907
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2014/907,
author = {Thijs Laarhoven and Michele Mosca and Joop van de Pol},
title = {Finding shortest lattice vectors faster using quantum search},
howpublished = {Cryptology {ePrint} Archive, Paper 2014/907},
year = {2014},
url = {https://eprint.iacr.org/2014/907}
}