Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the non-split case
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866929241326616576 |
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| author | Blanco-Chacón, Iván Durán-Díaz, Raúl Nchiwo, Rahinatou Yuh Njah Barbero-Lucas, Beatriz |
| author_facet | Blanco-Chacón, Iván Durán-Díaz, Raúl Nchiwo, Rahinatou Yuh Njah Barbero-Lucas, Beatriz |
| contents | 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 $\mathbb{F}_q[x]/(Φ_{p^k}(x))$ with $k>1$ in the case where $q\equiv 1\pmod{p}$ but $Φ_{p^k}(x)$ is not totally split over $\mathbb{F}_q$. Our attack uses the fact that the roots of $Φ_{p^k}(x)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_11962 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the non-split case Blanco-Chacón, Iván Durán-Díaz, Raúl Nchiwo, Rahinatou Yuh Njah Barbero-Lucas, Beatriz Cryptography and Security 94A60 (Primary), 68W20, 12-04 (Secondary) 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 $\mathbb{F}_q[x]/(Φ_{p^k}(x))$ with $k>1$ in the case where $q\equiv 1\pmod{p}$ but $Φ_{p^k}(x)$ is not totally split over $\mathbb{F}_q$. Our attack uses the fact that the roots of $Φ_{p^k}(x)$ 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. |
| title | Trace-based cryptanalysis of cyclotomic $R_{q,0}\times R_q$-PLWE for the non-split case |
| topic | Cryptography and Security 94A60 (Primary), 68W20, 12-04 (Secondary) |
| url | https://arxiv.org/abs/2209.11962 |