RLWE/PLWE equivalence for totally real cyclotomic subextensions via quasi-Vandermonde matrices

TL;DR

This paper establishes the equivalence between RLWE and PLWE problems for certain totally real cyclotomic fields, using quasi-Vandermonde matrices to generalize the reduction approach.

Contribution

It introduces a generalized method to prove RLWE/PLWE equivalence for monogenic number fields, specifically for maximal totally real subextensions of 4p-th cyclotomic fields.

Findings

Proves RLWE/PLWE equivalence for maximal totally real subextensions of 4p-th cyclotomic fields.

Utilizes quasi-Vandermonde matrices to facilitate the reduction.

Extends previous results to a broader class of number fields.

Abstract

We propose and justify a generalised approach to prove the polynomial reduction of the RLWE to the PLWE problem attached to the ring of integers of a monogenic number field. We prove such equivalence in the case of the maximal totally real subextension of the 4p-th cyclotomic field, with p arbitrary prime.