### 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

Available format(s)
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
See all versions
Short URL
https://ia.cr/2017/1228

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}
}

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