Towards Larger Public Keys For Key Exchange
As RSA key sizes have increased to over 2,048 bits, we have been lucky that elliptic curve methods came along and gave us much smaller keys [here]:
In this case, we see a 32-byte secret (private) key size for P256, and 64 bytes for the public key (as it has an x- and y-co-ordinate value) and then another byte added to identify the type of point. This gives a 65 byte public key. For X22519, we only require a single co-ordinate value, and thus only need 32 bytes for the public key (and which is the same size as the secret key). The ciphertext is the payload send between two parties in order to exchange keys.
Unfortunately ECC has a core weakness and that the method can be cracked by quantum computers. To overcome this we need new methods which are quantum robust. These include Kyber, SABER, NTRU, McEliece and SIKE [here]:
With ths we see that the isogeny-based SIKE method has the smallest key sizes, followed by the lattice methods (Kyber, SABER and NTRU), and with McEliece with the…
