The Math Behind PQC: Learning With Errors

Introduction

Some of the winning cryptographic schemes in the NIST standardization process belonging to the latex-based cryptography family are constructed from a problem called Learning With Errors (LWE).

Given a system of random linear equations describing a secret, the problem of Learning With Errors is based on the idea of hiding the value of the secret by adding noise (or error) to the system.

Introduced in 2005 by Israeli-American computer scientist and theoretical mathematician Oded Regev, LWE had a significant impact on postquantum cryptography from the very beginning
which earned Regev in 2018 the Gödel Prize, a prestigious award in the field of theoretical computer science.

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The authors

Veronica Cristiano, a bachelor’s degree in Mathematics from the University of Pisa and a master’s degree in Mathematics with a specialization in Cryptography at the University of Trento, joined the Telsy Cryptography research group in mid-2021.

Francesco Stocco, a master’s degree in Mathematics at the University of Padua and the Université de Bordeaux attending the course of study “Algebra Geometry And Number Theory” (ALGANT), joined the Telsy research group in Cryptography at end of 2020 focusing in particular on issues related to quantum technologies.