Program Description
In under half an hour, Claude discovered the origins of the NIST P-192, P-224, P-256, P-384, and P-521 seeds. None of them were the results of any hash algorithm at all, but rather the output of the C library's Irand48 random-number generator, seeded with a Unix timestamp!
The algorithm used would sample bytes from the random number generator (RNG) initialized by a Unix timestamp (t) for some number of iterations (n). Each iteration would draw 20 bytes as a candidate seed. So, the first 20 bytes are candidate 1, the next 20 bytes are candidate 2, and so on. For example, P-256 required 1,842 iterations to output the standardized seed.
This is not a cryptographic break, new attack, or weakness in the ECDSA curves. In fact, this makes us more confident the curves were chosen without any backdoors or intentional weaknesses. For many years, people have been suspicious of the origins of the NIST curve parameters. They were presented to NIST without any mention of how they were chosen, leaving people wondering if they may have been chosen to have deliberate backdoors in them.
These findings make that much less plausible. The seeds were generated in a very simple way: a common pseudorandom number generator initialized from the clock, which anyone can now reproduce. That leaves much less room for subversion and that we can be confident the parameters are secure.