Iván Blanco-Chacón ; Raúl Durán-Díaz ; Rahinatou Yuh Njah Nchiwo ; Beatriz Barbero-Lucas - 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) - https://doi.org/10.46298/cm.11153
Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the non-split case

Authors: 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.


    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)

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