Iván Blanco-Chacón ; Raúl Durán-Díaz ; Rahinatou Yuh Njah Nchiwo ; Beatriz Barbero-Lucas
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Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the
non-split case
cm:11153 -
Communications in Mathematics,
July 19, 2023,
Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications)
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https://doi.org/10.46298/cm.11153Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the
non-split caseArticle
Authors: Iván Blanco-Chacón ; Beatriz Barbero-Lucas ; Raúl Durán-Díaz ; Rahinatou Yuh Njah
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Iván Blanco-Chacón;Beatriz Barbero-Lucas;Raúl Durán-Díaz;Rahinatou Yuh Njah
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 $\mathbb{F}_q[x]/(\Phi_{p^k}(x))$ with $k>1$ in the case where $q\equiv 1\pmod{p}$ but $\Phi_{p^k}(x)$ is not totally split over $\mathbb{F}_q$. Our attack uses the fact that the roots of $\Phi_{p^k}(x)$ over suitable extensions of $\mathbb{F}_q$ 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.
Comment: 20 pages; 1 figure; Minor updates as per referee's requests;
formatted for publication
Volume: Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications)
Published on: July 19, 2023
Accepted on: June 26, 2023
Submitted on: April 4, 2023
Keywords: Computer Science - Cryptography and Security, 94A60 (Primary), 68W20, 12-04 (Secondary)
Funding:
Source : OpenAIRE Graph- Number-theoretic well-rounded lattices; Funder: Research Council of Finland; Code: 351271