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arXiv · 2209.11962

Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the non-split case

Iván Blanco-Chacón·Raúl Durán-Díaz·Rahinatou Yuh Njah Nchiwo·Beatriz Barbero-Lucas
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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 $\mathbb{F}_q[x]/(\Phi_{p^k}(x))$ 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.

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Iván Blanco-Chacón, Raúl Durán-Díaz, Rahinatou Yuh Njah Nchiwo, Beatriz Barbero-Lucas. 2022-09-24. Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the non-split case. https://doi.org/10.46298/cm.11153

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