On the shortness of vectors to be found by the Ideal-SVP quantum algorithm

AK Lenstra; Alice Pellet-Mary; C Pomerance; D Micciancio; D Stehlé; D Stehlé; DJ Bernstein; E Landau; Emmanouil Doulgerakis; HW Lenstra Jr; J Hoffstein; L Babai; L Ducas; LC Washington; M Ajtai; Martin R. Albrecht; Martin R. Albrecht; NC Ankeny; NP Smart; O Regev; PQ Nguyen; R Cramer; R Cramer; R Schoof; R Schoof; R Schoof; S Halevi; T Lepistö; V Lyubashevsky; V Lyubashevsky; W Sinnott; Y Chen

On the shortness of vectors to be found by the Ideal-SVP quantum algorithm

Authors: AK Lenstra
Alice Pellet-Mary
C Pomerance
D Micciancio
D Stehlé
D Stehlé
DJ Bernstein
E Landau
Emmanouil Doulgerakis
HW Lenstra Jr
J Hoffstein
L Babai
L Ducas
LC Washington
M Ajtai
Martin R. Albrecht
Martin R. Albrecht
NC Ankeny
NP Smart
O Regev
PQ Nguyen
R Cramer
R Cramer
R Schoof
R Schoof
R Schoof
S Halevi
T Lepistö
V Lyubashevsky
V Lyubashevsky
W Sinnott
Y Chen
Publication date: 14 May 2019
Publisher: 'Springer Science and Business Media LLC'
Doi

Abstract

The hardness of finding short vectors in ideals of cyclotomic number fields (hereafter, Ideal-SVP) can serve as a worst-case assumption for numerous efficient cryptosystems, via the average-case problems Ring-SIS and Ring-LWE. For a while, it could be assumed the Ideal-SVP problem was as hard a