WP34
Beyond the Square-Root Barrier: Automated Discovery of Algebraic and Algorithmic Shortcuts in Bitcoin Cryptography
A hypothesis-driven, reproducible study of secp256k1, ECDSA, BIP340 Schnorr and SHA-256 with machine-checked identities and controlled negative results
Bitcoin's security rests on the elliptic-curve discrete-logarithm problem on secp256k1, on SHA-256, and on the ECDSA and BIP340 Schnorr signature schemes. The generic cost of the discrete logarithm, Θ(√n), is a theorem in the generic-group model; the curve's unusual structure, a special prime, j-invariant 0 and…