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My err - rubbish wording as I was thinking primes and talking curves.

Still, while I'm punching here a wee bit above my weight - I should read the 186-4 again - there are some tests to verify the strength of the prime. Is it enough for a similar classification? - I don't know...

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The prime field is part of the definition of the curve. Everyone interoperating on that curve shares it. It may have been generated weirdly --- the Curve25519 prime sure was! --- but all that tells you is what curve they're using.

It's true that the particular curves a system supports could be a kind of fingerprint, but that's a banal observation, equally true of the ciphers they support, or the compression algorithms.

My last comment was towards key generation, not curves. Bug as I said, I am not in a position to say what the impact is.

Sorry, I don't follow. Are you talking about key generation in ECC systems? There's no prime involved there.

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