Researchers at Anthropic have identified the origin of the seed values used in NIST elliptic curves, a mystery that has persisted for 25 years. Using an internal AI model, the team determined that the seeds were generated using the lrand48 random number generator from a C library, initialized with Unix timestamps.
The investigation revealed that the seeds for NIST curves P-192, P-224, P-256, P-384, and P-521 were not derived from hash functions, as previously speculated. Instead, they were produced by iterating the lrand48 generator, with initialization dates ranging from May 1997 to April 1998.
The team also traced the origin of base points for six curves created in May 1997 to the FreeLIP library, a package for arbitrary-precision arithmetic. The researchers noted that while some candidates were skipped during the generation process, there is no evidence of intentional backdoors or weaknesses in the curves.
The discovery effectively resolves long-standing concerns regarding the security of NIST ECDSA parameters. The findings suggest that the curves were generated through a simple, reproducible process, significantly reducing the likelihood of hidden vulnerabilities.
A reward of $36 864 previously offered for solving the seed mystery will be donated to the Internet Security Research Group. The source code used for the analysis has been released under the CC0 1.0 public domain license.
