Group-based Cryptography in the Quantum Era
This is an expository overview for researchers in cryptography, addressing the incremental compilation of existing knowledge without new results.
The article provides an overview of post-quantum group-based cryptography, describing families of groups like polycyclic and graph groups as platforms, along with their algorithmic properties and applications in cryptography, including fully homomorphic encryption, and discusses open problems in the field.
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.