Isogenies? The End Game for Public Key Encryption?
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.
So it is likely that a lattice-based method will win, and become a standard. But what about the future? What if lattice methods are cracked? Well, NIST has a plan for this, and have defined a competition for alternative candidates. These candidates will be the backup route against the likely lattice method. And one area which shows the most promise as an alternative is isogenies. So let’s look at one of the most promising methods: SIKE. It has such potential that AWS has defined a standard for its integration into TLS 1.2 [here]:
