Article | REF: H5216 V1

Lattice-Based Cryptography

Authors: Corentin JEUDY, Adeline ROUX-LANGLOIS

Publication date: July 10, 2023

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ABSTRACT

The recent advances of quantum technologies are threatening the cryptographic mechanisms that are currently deployed in most cybersecurity systems. It is thence necessary to find alternatives to these mechanisms which are not subject to quantum attacks. Lattice-based cryptography is an interesting and versatile candidate that withstands quantum attacks, and it is considered the most promising option to date. This paper describes the foundations of lattice-based cryptography, as well as digital signature and encryption schemes which are on track to replace current cryptographic standards.

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AUTHORS

  • Corentin JEUDY: Cryptography research engineer at Orange Innovation

  • Adeline ROUX-LANGLOIS: CNRS Research Associate - Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, Caen, France

 INTRODUCTION

Post-quantum cryptography refers to cryptographic schemes that would not be vulnerable following the construction of a sufficiently powerful quantum computer. In this article, we focus on so-called asymmetric cryptographic constructions, enabling users to communicate or authenticate securely without first possessing a common secret. It is this branch of cryptography that will be most affected by the arrival of a quantum computer. Indeed, the security of the constructions we use today relies on two families of problems that are classically difficult, but which will become quantum easy.

Cryptography based on Euclidean lattices is one of the post-quantum solutions identified in recent years. It seems to be the most promising and has many advantages. In particular, it enables us to design a multitude of cryptographic constructions, from the simplest to the most advanced, which are increasingly efficient while basing their security on well-studied algorithmic problems. In this article, we will explain how to build an encryption scheme and two signature schemes that are secure even against quantum computers, and what are the hard problems on which the security of these constructions is based.

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KEYWORDS

cryptography   |   lattices   |   post-quantum


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Cryptography based on Euclidean lattices