Why do there need to be “recommended” elliptic curves? If “recommended” ones are just ones that someone has found a shortcut for, why isn’t it better to just choose a new random one each time? Is it that decrypting or validating different curves requires different specific code?
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Not just any random curve has the desirable properties, so you need to pick one that does. So you have two choices:
1. Ask for a recommendation (“*hey pal, do you you have an edge to get me a good curve?*”)
2. Pick one at will and prove it can be used in a cryptographically secure way (“*good luck*”).
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