1) If 2P for all points is equal to infinity, then the factoring method that we learned a little bit ago would never work for computers right? Because everything is in binary? Unless we always just have different elliptic curves that are only encoded in binary mod 2? What does it mean that elliptic curves are used over fields GF(2^n) with n large? Say at least 150?
2) I am just amazed that somehow this has practical use for computers. What exactly else do they use elliptic curves for?
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