Paper 2017/1228
Speed-ups and time-memory trade-offs for tuple lattice sieving
Gottfried Herold, Elena Kirshanova, and Thijs Laarhoven
Abstract
In this work we study speed-ups and time-space trade-offs for solving the shortest vector problem (SVP) on Euclidean lattices based on tuple lattice sieving. Our results extend and improve upon previous work of Bai-Laarhoven-Stehlë [ANTS'16] and Herold-Kirshanova [PKC'17], with better complexities for arbitrary tuple sizes and offering tunable time-memory trade-offs.The trade-offs we obtain stem from the generalization and combination of two algorithmic techniques: the configuration framework introduced by Herold-Kirshanova, and the spherical locality-sensitive filters of Becker-Ducas-Gama-Laarhoven [SODA'16]. When the available memory scales quasi-linearly with the list size, we show that with triple sieving we can solve SVP in dimension $n$ in time $2^{0.3588n + o(n)}$ and space $2^{0.1887n + o(n)}$, improving upon the previous best triple sieve time complexity of $2^{0.3717n + o(n)}$ of Herold-Kirshanova. Using more memory we obtain better asymptotic time complexities. For instance, we obtain a triple sieve requiring only $2^{0.3300n + o(n)}$ time and $2^{0.2075n + o(n)}$ memory to solve SVP in dimension $n$. This improves upon the best double Gauss sieve of Becker-Ducas-Gama-Laarhoven, which runs in $2^{0.3685n + o(n)}$ time when using the same amount of space.
Note: Fixed a typo in the title
Metadata
- Available format(s)
-
PDF
- Publication info
- A major revision of an IACR publication in PKC 2018
- Keywords
- lattice-based cryptographyshortest vector problem (SVP)nearest neighbor algorithmslattice sieving
- Contact author(s)
- elena kirshanova @ ens-lyon fr
- History
- 2017-12-22: revised
- 2017-12-22: received
- See all versions
- Short URL
- https://ia.cr/2017/1228
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/1228,
author = {Gottfried Herold and Elena Kirshanova and Thijs Laarhoven},
title = {Speed-ups and time-memory trade-offs for tuple lattice sieving},
howpublished = {Cryptology ePrint Archive, Paper 2017/1228},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/1228}},
url = {https://eprint.iacr.org/2017/1228}
}
