The algorithm is completely analogous to Diffie-Hellman key exchange in that you efficiently raise a number to a power times and send the result over while keeping as private key.
The only difference is that a different group is used: instead of using the cyclic group, we use the elliptic curve group of an elliptic curve over a finite field.
Elliptic curves by Computerphile (2018)
Source. youtu.be/NF1pwjL9-DE?t=143 shows the continuous group well, but then fails to explain the discrete part.Variant of Diffie-Hellman key exchange based on elliptic curve cryptography.
ECDH has smaller keys. youtu.be/gAtBM06xwaw?t=634 mentions some interesting downsides:
- bad curves exist, while in modular, any number seems to work well. TODO why?
- TODO can't find this mentioned anywher else: Diffie-Hellman key exchange has a proof that there is no algorithm, ECDH doesn't. Which proof?
