Digital signatures: Schnorr, ECDSA and how PS3 was hacked

This is part two. If you haven't read it yet, start with Private keys and elliptic curves: a deep-dive for people who don't like math . What is a digital signature? You know how a handwritten signature works. You scribble something on a document and everyone agrees it proves you authorized it. Digital signatures do the same thing, except they're actually secure. A digital signature has three properties: Authentication - it proves the signer has the private key Integrity - it proves the message hasn't been tampered with Non-repudiation - the signer can't later deny signing it In blockchain, every transaction you send is signed with your private key. The network verifies that signature using your public key - without ever learning the key itself. No trust needed. Just math. There are two signature schemes that matter here: Schnorr and ECDSA . Schnorr is more "classic" math and easier to understand, so we'll start with it. ECDSA is the one everyone actually uses - for historical reasons w