ECDSA

Anthropic Model Reconstructs NSA Seeds for NIST Elliptic Curves in Under 30 Minutes

An internal Anthropic research model traced the origins of the five seeds used by the NSA to generate the NIST elliptic curves P-192, P-224, P-256, P-384, and P-521. The discovery resolves a 25-year-old question that arose when the curves were standardized in FIPS 186-2 for ECDSA in 2000. Researchers combined analysis of 1990s random number generators, 34 generator-output combinations, and lattice reduction techniques to identify lrand48 initialized with Unix timestamps from May 1997 to April 1998. The P-256 seed corresponds to the 1842nd candidate from a run started on 16 August 1997, and example seeds from ANSI X9.62 follow the same pattern. The work does not demonstrate any cryptographic break or backdoor in the curves and does not recommend changes to production systems. Several questions remain open, including the seed for curve B-163 and the reason certain candidate values were discarded.

25-Year Mystery Solved: NIST Elliptic Curve Seeds Came from lrand48 and Unix Timestamps

Researchers at Anthropic used the Claude model to trace the origins of the mysterious seed values embedded in NIST elliptic curves standardized in FIPS 186-2. The seeds for curves including NIST P-192, P-224, P-256, P-384 and P-521 were not derived from hashed humorous phrases as previously rumored but instead generated by the non-cryptographic lrand48 linear congruential generator seeded with Unix timestamps from 1997 and 1998. The discovery also explains the base points of several curves using the FreeLIP library's random number generator. The findings reduce long-standing suspicions of deliberate backdoors inserted by the NSA. Several candidate curves that met the criteria were skipped during selection, leaving open questions about the exact filtering process. The work was performed by a team including Nicholas Carlini and others, with the reproduction code released into the public domain.