Trace-based cryptanalysis of cyclotomic Rq,0 × Rq-PLWE for the non-split case

Loading...
Thumbnail Image
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023
Major/Subject
Mcode
Degree programme
Language
en
Pages
21
115-135
Series
Communications in Mathematics, Volume 31, issue 2
Abstract
We describe a decisional attack against a version of the PLWE problem in which the samples are taken from a certain proper subring of large dimension of the cyclotomic ring Fq [x]/(Φpk (x)) with k > 1 in the case where q ≡ 1 (mod p) but Φpk (x) is not totally split over Fq. Our attack uses the fact that the roots of Φpk (x) over suitable extensions of Fq have zero-trace and has overwhelming success probability as a function of the number of input samples. An implementation in Maple and some examples of our attack are also provided.
Description
Funding Information: I. Blanco-Chacón is partially supported by the Spanish National Research Plan, grant no MTM2016-79400-P, by grant PID2019-104855RBI00, funded by MCIN / AEI / 10.13039 / 501100011033 and by the University of Alcalá grant CCG20/IA-057. R. Durán-Díaz is partially supported by grant P2QProMeTe (PID2020-112586RB-I00), funded by MCIN / AEI / 10.13039 / 501100011033. R.Y. Njah Nchiwo is supported by a PhD scholarship from the Magnus Ehrnrooth Foundation, Finland, in part by Academy of Finland, grant 351271 (PI: C. Hollanti) and in part by MATINE Finnish Ministry of Defence, grant #2500M-0147 (PI: C. Hollanti). B. Barbero-Lucas is partially supported by the University of Alcalá grant CCG20/IA-057. Publisher Copyright: © 2023 Iván Blanco-Chacón, Raúl Durán-Díaz, Rahinatou Yuh Njah Nchiwo and Beatriz Barbero-Lucas.
Keywords
Lattice-based, Polynomial Learning With Errors, Ring Learning With Errors
Other note
Citation
Blanco-Chacón , I , Durán-Díaz , R , Nchiwo , R Y N & Barbero-Lucas , B 2023 , ' Trace-based cryptanalysis of cyclotomic R q,0 × R q -PLWE for the non-split case ' , Communications in Mathematics , vol. 31 , no. 2 , pp. 115-135 . https://doi.org/10.46298/cm.11153