Cryptanalysis of PLWE based on zero-trace quadratic roots
2023
Online
report
Zugriff:
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.
Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:2209.11962
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Cryptanalysis of PLWE based on zero-trace quadratic roots
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Autor/in / Beteiligte Person: | Barbero-Lucas, Beatriz ; Blanco-Chacón, Iván ; Durán-Díaz, Raúl ; Nchiwo, Rahinatou Yuh Njah |
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Veröffentlichung: | 2023 |
Medientyp: | report |
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