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by nullc 1206 days ago
The choice of the identity element, if one can be encoded at all, gives you one point with known key by design. Choice of the generator, if it isn't NUMS, can give you a second arbitrary value with a known key-- this latter one could even be a no-one-but-us backdoor but a somewhat contrived one.

Like if you want to secretly know the private key of 0xDEADBEEF, set your generator to lift(0xDEADBEEF) x (1/$secret). Now the deadbeef pubkey has a DL relative to your generator of $secret.