For each of the binary fields, one elliptic curve and one Koblitz curve was selected.
The NIST recommendation thus contains a total of five prime curves and ten binary curves. The curves were ostensibly chosen curba eliptica btc optimal security and implementation efficiency.
Elliptic curve cryptography is used by the cryptocurrency Bitcoin. Consequently, it is important to counteract side-channel attacks e.
Alternatively one can use an Edwards curve ; this is a special family of elliptic curves for which doubling and addition can be done with the same operation. The latest quantum resource estimates for breaking a curve with a bit modulus bit security level are qubits and billion Toffoli gates.
All of these figures vastly exceed any quantum computer that has ever been built, and estimates place the creation of such computers as a decade or more away.
This key exchange uses much of the same field arithmetic as existing elliptic curve cryptography and requires computational and transmission overhead similar to many currently used public key systems.