For Post-Quantum, Don’t Dismiss Isogenies … One of the Smallest Key Sizes for PQC

We need to migrate way from ECDH, as it is based on elliptic curves and which can be cracked by quantum computers. And so NIST is now assessing a range of finalists: Kyber, SABER, NTRU and McEliece. The first three are lattice based, and one of these is likely to win the competition. When we look at key sizes we see that McEliece has a relatively large public key, but it is Supersingular Isogeny Diffie-Hellman (SIDH) that has the smallest public and private key:

Type  Public key size (B)   Secret key size (B)  Ciphertext size (B)
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SIDH                  564                 48                  564
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
McEliece6688128 1,044,992             13,892                  240
McEliece6960119 1,047,319             13,948…