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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I’m not an expert in cryptography, but I believe the idea is that using any old curve for EC you have a chance of generating a predicable value. Using a recommended curve you get something that is at least somewhat proven to produce good values.
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