Comment by fidotron
2 days ago
It doesn't prove anything about the core part of the suspicion, which is they were selected using some undisclosed criteria, which may make them weaker or stronger than some other random numbers.
You are entirely familiar with the precedent of the DES s boxes of course, where that is exactly what happened.
> which may make them weaker or stronger than some other random numbers
Are there non-trivial weaker and stronger seeds for this category of elliptic curves?
Exactly.
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.
The number of weak classes of elliptic curve would have to be gargantuan for this specific search to produce some. If that many curves are bad, then ECC was a mistake.
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Again, Koblitz and Menezes take this idea on directly in their paper. But I mean, at this point, nobody serious is going to take the P-curve seed conspiracy theory seriously ever again.