Abstract
We show a 2^{n+o(n)}time (and space) algorithm for the Shortest Vector Problem on lattices (SVP) that works by repeatedly running an embarrassingly simple "pair and average" sievinglike procedure on a list of lattice vectors. This matches the running time (and space) of the current fastest known algorithm, due to Aggarwal, Dadush, Regev, and StephensDavidowitz (ADRS, in STOC, 2015), with a far simpler algorithm. Our algorithm is in fact a modification of the ADRS algorithm, with a certain careful rejection sampling step removed.
The correctness of our algorithm follows from a more general "metatheorem," showing that such rejection sampling steps are unnecessary for a certain class of algorithms and use cases. In particular, this also applies to the related 2^{n + o(n)}time algorithm for the Closest Vector Problem (CVP), due to Aggarwal, Dadush, and StephensDavidowitz (ADS, in FOCS, 2015), yielding a similar embarrassingly simple algorithm for gammaapproximate CVP for any gamma = 1+2^{o(n/log n)}. (We can also remove the rejection sampling procedure from the 2^{n+o(n)}time ADS algorithm for exact CVP, but the resulting algorithm is still quite complicated.)
BibTeX  Entry
@InProceedings{aggarwal_et_al:OASIcs:2018:8306,
author = {Divesh Aggarwal and Noah StephensDavidowitz},
title = {{Just Take the Average! An Embarrassingly Simple 2^nTime Algorithm for SVP (and CVP)}},
booktitle = {1st Symposium on Simplicity in Algorithms (SOSA 2018)},
pages = {12:112:19},
series = {OpenAccess Series in Informatics (OASIcs)},
ISBN = {9783959770644},
ISSN = {21906807},
year = {2018},
volume = {61},
editor = {Raimund Seidel},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8306},
URN = {urn:nbn:de:0030drops83062},
doi = {10.4230/OASIcs.SOSA.2018.12},
annote = {Keywords: Lattices, SVP, CVP}
}
Keywords: 

Lattices, SVP, CVP 
Collection: 

1st Symposium on Simplicity in Algorithms (SOSA 2018) 
Issue Date: 

2018 
Date of publication: 

05.01.2018 