Group-based Cryptography in the Quantum Era

TL;DR

This paper provides an overview of post-quantum group-based cryptography, focusing on polycyclic and graph groups, their algorithmic properties, and applications in fully homomorphic encryption, highlighting open research problems.

Contribution

It surveys current group-based cryptographic platforms and explores their algorithmic features and cryptographic uses in the quantum era.

Findings

Polycyclic and graph groups are promising platforms for post-quantum cryptography.

Combinatorial algebra plays a role in fully homomorphic encryption.

Several open problems remain in the development of quantum-resistant group-based cryptography.

Abstract

In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic groups and graph groups, dealing in particular with their algorithmic properties and cryptographic applications. We then, describe some applications of combinatorial algebra in fully homomorphic encryption. In the end we discussing several open problems in this direction.