Isogenies Are Still Cool?

You are likely to be using an elliptic curve method — ECDH — to access this message. But in a few years, it is unlikely that we will still be using it. Why? Well, quantum computers can crack elliptic curve techniques, along with all other existing public key methods that are used in production. For this, NIST has been assessing a range of methods, including lattice techniques to perform key exchange (such as with Kyber). But as part of this, the isogeny method — SIKE — was cracked. So should we dismiss isogenies?

And, so, isogenies looked to be the next great thing in cybersecurity in replacing ECDH for key exchange, and for us to move towards a post quantum world. For key sizes, it all looked great:

Type      Public key size (B)   Secret key size (B)  Ciphertext size (B)
------------------------------------------------------------------------
Kyber512              800              1,632                  768
Kyber738            1,184              2,400                1,088
Kyber1024           1,568              3,168                1,568
LightSABER            672              1,568                  736
SABER                 992              2,304                1,088
FireSABER           1,312              3,040                1,472
McEliece348864    261,120              6,452                  128
McEliece460896    524,160             13,568                  188…