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arXiv · 2312.11533

Cryptanalysis of PLWE based on zero-trace quadratic roots

Beatriz Barbero-Lucas·Iván Blanco-Chacón·Raúl Durán-Díaz·Rodrigo Martín Sánchez-Ledesma·Rahinatou Yuh Njah Nchiwo
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Abstract

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 $x^2+\rho$ with $\rho$ 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.

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Beatriz Barbero-Lucas, Iván Blanco-Chacón, Raúl Durán-Díaz, Rodrigo Martín Sánchez-Ledesma, Rahinatou Yuh Njah Nchiwo. 2023-12-15. Cryptanalysis of PLWE based on zero-trace quadratic roots. https://arxiv.org/abs/2312.11533

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