1. Why are the number of points mod p going to be p? I thought in the previous section we decided that there would be 3 points, sometimes including infinity? And is Hasse's Theorem just a proof that there are going to be at least p points, or is that showing that there can be less than p points? Also, is it possible for there to be less than p points? What about significantly less than p?
2. I think this chapter is going to be a bit rough for me. What I am thinking right now is still how are we going to put a message into an elliptic curve equation? I feel that it seems a bit impractical, even with a fast working computer. Although I am not very knowledgeable with how this works still, I think that it would take more time to encode, and possibly be easier to cipher then an RSA or something along those lines.
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