elliptic-curves

An internal Anthropic research model reportedly solved the 26-year-old mystery behind the NSA's elliptic curve seed constants in under 30 minutes, with the article showcasing the model's chain-of-thought reasoning.

Anthropic researchers cracked the 25-year-old mystery of how NIST's elliptic curve seeds were generated — they came from the POSIX drand48 RNG seeded with UNIX timestamps, not hashed sentences — claiming Filippo Valsorda's full bounty and donating it to ISRG/Let's Encrypt.

Claude, an internal Anthropic AI model, has solved the elliptic curve rank problem by finding curves of rank 30 and 31, surpassing the previous record of 29. The solution is part of the FrontierMath challenge and is credited to Claude along with researchers Levent Alpöge and Ava Howell.

An elliptic curve with rank at least 30 has been discovered, setting records in conductor, naive height, and other invariants on the Elliptic Curve Rank Leaderboard.

This paper trains a two-layer transformer encoder to classify rational elliptic curves by rank from Frobenius traces, achieving >99% accuracy. Mechanistic interpretability reveals the model learns the Mestre-Nagao heuristic and concentrates attention on prime positions, demonstrating that transformers can learn number-theoretic algorithms.