It’s a Lattice Bake-off and is there a Show-stopper?
As you should already know, our existing public key methods, such as RSA and ECC, are on the way out. Peter Shor showed that quantum computers will make sure they are not based on a hard problem anymore. We may be looking at five to 10 years before the computers will be built at scale, so NIST has been looking to standardize on a digital signature method and also a key exchange mechanism (KEM)/public key method. Whichever method wins these will be integrated into the core security of our digital work, as the concept of having a public key and an associated private key is fundamental in identifying identities and in protecting our secrets.
The contenders
One of the most respected companies around cryptography is Cloudfare, and who have generally invested in pushing forward good practice in the area. Overall they have been evaluating the three short-list contenders for PQC (Post Quantum Cryptography) and have found [here]:
We see that there are three finalists: Dilithium, Falcon and Rainbow, and three alternatives: SPHINCS, Picnic and GeMMS. If you are interested, I have implemented these in C code here: