Anthropic says Claude solved the 25-year mystery of the NIST elliptic-curve seeds
In under half an hour, an internal Claude research model found that the seeds behind NIST’s P-256 and other standard curves came from a 1990s lrand48 random-number generator seeded with Unix timestamps, not a hashed secret phrase.
Anthropic said on October 16 that Claude has explained a puzzle that had stood in cryptography for more than 25 years: where the “seed” values behind the elliptic curves in NIST’s ECDSA digital-signature standard, adopted in 2000, came from.
Why it mattered
The seeds were supplied by the US National Security Agency with no explanation, fuelling long-running suspicion that the curves could have been chosen to contain deliberate weaknesses. Former NSA employee Jerry Solinas recalled in 2015 that they were hashes of a humorous phrase, but no one could reproduce them, and a public bounty was offered for the answer.
What Claude found
According to Anthropic, an employee asked an internal research model, without pointing it to that clue, whether it could work out how the seeds were generated. In under half an hour, Claude traced the seeds for P-192, P-224, P-256, P-384 and P-521. None came from a hash: they were output from the C library’s lrand48 random-number generator, initialised with Unix timestamps between May 1997 and April 1998. P-256’s published seed, for example, was candidate 1842 from a run seeded on August 16, 1997.
Claude wrote a scanner to recognise the output of 1990s-era generators, spotted that the top bits of some seeds were all zero (a signature of lrand48), and then used a lattice-reduction method to recover the generator’s internal state, regenerating all 160 bits of each seed. It also explained, for the first time, how the base points of several curves were chosen.
What it means
Anthropic stressed that this is not a cryptographic break or a new attack. Because the seeds came from a simple clock-seeded generator that anyone can now reproduce, the company said, the idea of a deliberate backdoor becomes much less plausible. The seed for the B-163 binary curve and the base points of P-224, P-256, P-384 and P-521 remain unexplained. The $36,864 bounty will be donated to the Internet Security Research Group.
The write-up drew more than 400 points on the Hacker News front page and has become a widely discussed example of AI tackling a long-standing open problem.
Sources: Anthropic, Yahoo Tech. Image: Anthropic.
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