Elliptic Curve Cryptography

What's Inside

This guide walks you through the complete mathematical stack that makes Bitcoin's elliptic curve cryptography work. No hand-waving. No "trust me, it's secure." Every claim is proved or derived.

You'll start with modular arithmetic — the "clock math" that underpins everything — and build up through finite fields, group theory, and the discrete logarithm problem to reach the actual curve: secp256k1.

Then you'll see how those foundations produce ECDSA (the original Bitcoin signature scheme), Schnorr signatures (the Taproot upgrade), and MuSig2 (multi-party signing). Every verification equation is derived, not just stated.

Each chapter includes exercises with full solutions so you can verify your understanding.