Diving into Alternate Elliptic Curves for Bitcoin: A Security Analysis

Abstract

Bitcoin uses the elliptic curve Secp256k1 for its security operations. This article analyzes and compares various elliptic curves to identify the most secure curve for implementation. Our comparison examines the resistance of these curves to several attacks: Brute force, Anomalous, Baby-step Giant-step, Pollard rho, Pohlig-Hellman, and field discriminant in complex multiplication. Our findings indicate that the curves Ed22519, Ed448-Goldilocks, and E-521 offer superior security compared to the other evaluated curves, thus providing clear guidance for their adoption in Bitcoin cryptography.