# Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory

## TL;DR

This survey explores the ring learning with errors problem, highlighting its significance in post-quantum cryptography, machine learning, and number theory, and discusses its connections with classical algebraic problems.

## Contribution

It provides a comprehensive overview of the current state of cryptographic functionalities based on the ring learning with errors problem and their relation to algebraic number theory.

## Key findings

- RLWE-based cryptography is a promising post-quantum candidate
- Connections between RLWE and classical algebraic problems are significant
- The survey summarizes recent advances and open problems in the field

## Abstract

The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is based to a certain extent on an invited course given by the author at the Basque Center for Applied Mathematics in September 2018.