1. The thing I don't quite understand is why we would want to mod an elliptic curve. It seems to me that gives us less points on the curve to work with. In cryptography, don't we want as many options as possible, leaving more room for error on the part of the attacker? In short, how does mod-ing an elliptic curve increase advantages? Perhaps this won't be made clear til we start examining the cryptography applications of elliptic curves.
2. I'm starting to guess that as far as cryptography applications go, elliptic curves may be useful once we DO mod a point because then it will be harder to undo the mod, thus increasing the security. One other thing, I got lost on why they used 2773 as an example when it isn't prime. How important is it for p to be prime when modding? What goes wrong when p is not prime?
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