Ring learning with errors: a crossroads between post-quantum cryptography, machine learning and number theory

Abstract

The present survey is intended to serve as a comprehensive account of the main areas of the cryptography based on the Ring Learning With Errors Problem. We cover the major topics, from their mathematical foundations to the main primitives, as well as several open ends and recent progress with an emphasis in the connections with algebraic number theory. This work is based to a certain extent on an invited course and a seminar given by the author at the Basque Center for Applied Mathematics in 2018 and at the ICIAM 2019.Agencia Estatal de Investigació