Goodbye to Elliptic Curves? … Not, Quite … Here Come Isogenies
The most interesting thing I have learn in the last few years is the theory of elliptic curves. How can something so beautiful as an elliptic curve be able to create unique encryption keys for Bob and Alice, and allow Alice to digitally sign messages? It is just pure cryptography magic! But, they have a fundamental problem, and it’s a big one … they can be cracked by quantum computers. So will we see the end of elliptic curves? Well, perhaps, but isogenies could see elliptic curves scale into a post quantum era. Let’s see if elliptic curves will live on in key exchange … with SIKE.
NIST PQC
Well, we are now at the final stage of NIST’s post-quantum cryptography standardization, and which started in 2016:
The finalists mainly include lattice-based methods. For key exchange/public key encryption we have: CRYSTALS-KYBER; NTRU; and SABER, and for digital signatures: CRYSTALS-DILITHIUM and FALCON. Only McEliece (for key exchange) and Rainbow (for digital signatures) make an appearance for non-lattice-based methods. Unfortunately, Rainbow has been cracked, so it will not win.
