Finding out there is a class of weak 256-bit elliptic curves so large that they can be hit randomly with 2^30 tries would be a cryptanalytic breakthrough analogous to discovering all elliptic curve cryptography is broken.
Read section 3.1 of the Koblitz and Menezes paper. It was already implausible with 160 bits of freedom. https://eprint.iacr.org/2015/1018
If you want to believe the NSA knows ECC is broken and chose to risk moving the US government to it and somehow no one figured out the same break in 30 years, you're free to do so. But pretending the seed choice plays any role in that theory is over.
1. Only a very small number of valid seeds were discarded when compared to the number of n values. It seems we don't yet know why valid seeds were discarded but the explanation of a buggy curve validity checker doesn't seem implausible to me.
2. Directly to your point, most of the prime192 and prime239 curves required larger n values to find a valid seed and they are both smaller and used an earlier timestamp.
More precisely: not very random tries.
It is possible such a correlation could occur. but it would be much weirder than this being the result of a random search, which would already be very weird.
Oof, about that...
Well, at least now we have a way to perform that analysis! Generate a bunch of curves by varying (along any degree of freedom) the input parameters to the seed generating function and see if there's any difference between the curves that are generated.
You are entirely familiar with the precedent of the DES s boxes of course, where that is exactly what happened.
Are there non-trivial weaker and stronger seeds for this category of elliptic curves?
When they made the changes to the s boxes for differential cryptanalysis resistance the entire concept of that was essentially secret, so who knows what they know about elliptic curves.
> If that many curves are bad, then ECC was a mistake.
I mean that is the logical conclusion from the behaviour around this approach where a few good things are effectively endorsed without justification.
The fact is any application of an algorithm that involves so much "trust me bro" on the selection of what are a large number of opaque quasi random but not quite or provably so numbers only has as much trust in it as you have in the people that created it.
Ghislaine Maxwell's social security number?
And the disclosure happened now through Anthropic that is 100% not going to anger the NSA before the IPO and will have permission.