(2026-03) Cryptanalysis of Polynomial Learning With Errors (PLWE); A Survey
2026-03-02
Lattice-based cryptography (LBC) has emerged as one of the most promising fields supporting post-quantum cryptography (PQC). The Learning With Errors (LWE) problem \cite{Regev}, due to its strong security guarantees, plays a fundamental role in LBC, although it is not very efficient for cryptographic applications. To address this limitation, several variants of LWE have been developed, such as Ring-LWE (RLWE) \cite{LPR2010}, which is suitable for theoretical purposes, and Polynomial-LWE (PLWE) \cite{BV}, which is more practical. This survey provides a systematic review of vulnerable instances of PLWE. These attacks may extend to RLWE in instances where the two problems are equivalent.. This paper serves as a resource for those seeking a structured overview of the state-of-the-art attacks on PLWE.