Researchers examine 5 mathematical paths that could break Bitcoin's cryptography

• —Bitcoin uses secp256k1 elliptic-curve cryptography, where key recovery needs about 2^128 operations
• —The point-decomposition approach (Semaev, 2004) failed to break the scheme due to computational cost
• —A 2021 matrix-based method was acknowledged as ineffective by co-author Ayan Mahalanobis in August 2026
• —Pollard rho and mapping the problem to other curves have not yielded an exploitable weakness