Earlier this year, Cendyne published A Deep Dive into Ed25519 Signatures, which covered some of the different types of digital signature algorithms, but mostly delved into the Ed25519 algorithm. Truth in advertising.
This got me thinking, “Why isn’t there a better comparison of different elliptic curve signature algorithms available online?”
Most people just defer to SafeCurves, but it’s a little dated: We have complete addition formulas for Weierstrass curves now, but SafeCurves doesn’t reflect that.
For the purpose of simplicity, I’m not going to focus on a general treatment of Elliptic Curve Cryptography (ECC), which includes pairing-based cryptography, Elliptic-Curve Diffie-Hellman, and (arguably) isogeny cryptography.
Instead, I’m going to focus entirely on elliptic curve digital signature algorithms.