Cryptanalysis of PLWE based on zero-trace quadratic roots
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911315818184704 |
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| author | Barbero-Lucas, Beatriz Blanco-Chacón, Iván Durán-Díaz, Raúl Sánchez-Ledesma, Rodrigo Martín Nchiwo, Rahinatou Yuh Njah |
| author_facet | Barbero-Lucas, Beatriz Blanco-Chacón, Iván Durán-Díaz, Raúl Sánchez-Ledesma, Rodrigo Martín Nchiwo, Rahinatou Yuh Njah |
| contents | We extend two of the attacks on the PLWE problem presented in (Y. Elias, K. E. Lauter, E. Ozman, and K. E. Stange, Ring-LWE Cryptography for the Number Theorist, in Directions in Number Theory, E. E. Eischen, L. Long, R. Pries, and K. E. Stange, eds., vol. 3 of Association for Women in Mathematics Series, Cham, 2016, Springer International Publishing, pp. 271-290) to a ring $R_q=\mathbb{F}_q[x]/(f(x))$ where the irreducible monic polynomial $f(x)\in\mathbb{Z}[x]$ has an irreducible quadratic factor over $\mathbb{F}_q[x]$ of the form $x^2+ρ$ with $ρ$ of suitable multiplicative order in $\mathbb{F}_q$. Our attack exploits the fact that the trace of the root is zero, and has overwhelming success probability as a function of the number of samples taken as input. An implementation in Maple and some examples of our attack are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11533 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cryptanalysis of PLWE based on zero-trace quadratic roots Barbero-Lucas, Beatriz Blanco-Chacón, Iván Durán-Díaz, Raúl Sánchez-Ledesma, Rodrigo Martín Nchiwo, Rahinatou Yuh Njah Cryptography and Security 11T71 (Primary), 94A60, 12-04 (Secondary) We extend two of the attacks on the PLWE problem presented in (Y. Elias, K. E. Lauter, E. Ozman, and K. E. Stange, Ring-LWE Cryptography for the Number Theorist, in Directions in Number Theory, E. E. Eischen, L. Long, R. Pries, and K. E. Stange, eds., vol. 3 of Association for Women in Mathematics Series, Cham, 2016, Springer International Publishing, pp. 271-290) to a ring $R_q=\mathbb{F}_q[x]/(f(x))$ where the irreducible monic polynomial $f(x)\in\mathbb{Z}[x]$ has an irreducible quadratic factor over $\mathbb{F}_q[x]$ of the form $x^2+ρ$ with $ρ$ of suitable multiplicative order in $\mathbb{F}_q$. Our attack exploits the fact that the trace of the root is zero, and has overwhelming success probability as a function of the number of samples taken as input. An implementation in Maple and some examples of our attack are also provided. |
| title | Cryptanalysis of PLWE based on zero-trace quadratic roots |
| topic | Cryptography and Security 11T71 (Primary), 94A60, 12-04 (Secondary) |
| url | https://arxiv.org/abs/2312.11533 |