1. Why are elliptic curves not used more if the traditional attacks, such as the Pohlig Hellman and the Baby Step-Giant Step, don't break them?
It seems like for a large enough K, there could be many potential values for j to test until you find a square. Is there an easier way to do this? Do people actually use elliptic curves for cryptography even though it seems complex and technical?
2. I think it's interesting that there's a way to estimate how many points an elliptic curve will have. I'm not sure I understand Hasse's theorem, but the application of it is very useful and neat. Finding individual points for an elliptic curve that has many points could take too long to be feasible.
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