Types of Post-Quantum Cryptography

Post-quantum cryptography (PQC) research is currently mostly focused on these 6 approaches listed below.

Hash-based cryptography #

Leslie Lamport invented hash-based signatures in 1979. The XMSS (eXtended Merkle Signature Scheme) and SPHINCS hash-based signature schemes were introduced in 2011 and 2015, respectively¹.

Hash-based cryptography has been thoroughly studied. It has been around for a long time.

Popular Scheme: The Merkle signature scheme, XMSS.

Lattice-based cryptography #

First introduced by Miklos Ajtai in the year 1996, whose security was based on lattice problems.

Popular Scheme: NTRU, CRYSTALS-Dilithium (digital signature algorithm) and CRYSTALS-KYBER (public key encryption and key establishment algorithm).

TODOs below

Multivariate cryptography #

Code-based cryptography #

Isogeny-based cryptography #

Symmetric key quantum resistance #