Raúl Durán Díaz | Searcharxiv

arXiv2026

Extensions of root-based attacks against PLWE via isomorphisms of rings

In the present work we address some key questions regarding the generalization of root-based attacks presented in [2]. In particular, we analyze potential root-based attacks extensions via the construction of explicit isomorphisms from vulnerable instances, and provide a formal proof that this approach will not yield any new vulnerabilities. To do so, we first construct an explicit isomorphism between fully-split polynomial rings and polynomial rings where previous attacks apply and show that the application of such an isomorphism will always distort the samples in a way that the resulting samples cannot be used to distinguish. Then, we prove that any isomorphism between fully-split polynomial rings must be of the form of the constructed isomorphism. Lastly, we study the generalization beyond fully split settings and show that the same distortion happens, regardless of the degree of the field extension.

cs.CR↗

arXiv2025

A Generalized Approach to Root-based Attacks against PLWE

The Polynomial Learning With Errors problem (PLWE) serves as the background of two of the three cryptosystems standardized in August 2024 by the National Institute of Standards and Technology to replace non-quantum resistant current primitives like those based on RSA, Diffie-Hellman or its elliptic curve analogue. Although PLWE is highly believed to be quantum resistant, this fact has not yet been established, contrariwise to other post-quantum proposals like multivariate and some code based ones. Moreover, several vulnerabilities have been encountered for a number of specific instances. In a search for more flexibility, it becomes fully relevant to study the robustness of PLWE based on other polynomials, not necessarily cyclotomic. In 2015, Elias et al found a good number of attacks based on different features of the roots of the polynomial. In the present work we present an overview of the approximations made against PLWE derived from this and subsequent works, along with several new attacks which refine those by Elias et al. exploiting the order of the trace of roots over finite extensions of the finite field under the three scenarios laid out by Elias et al., allowing to generalize the setting in which the attacks can be carried out.

cs.CR↗