This was a pretty confusing section. I'm having a hard time understanding elliptic curves over finite fields. An longer explanation of the example in the section would really help.
Elliptic curves are interesting but they just seem to become less and less and intuitive the more I learn about them. It is interesting that NIST recommended 15 specific elliptic curves (mod 2) for use in elliptic curve cryptosystems. I might be wrong, but it seems that ECC is easier to implement than RSA since you choose from fewer curves, and key generation is easier than RSA. But it's still a strong system. That's just my initial thought.
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