Elliptic Curve Cryptography: From Theory to Bitcoin

Interactive Jupyter notebooks covering the mathematical foundations of elliptic curve cryptography and its applications in Bitcoin — from abstract algebra through ECDSA, Schnorr signatures, and onion routing.

Course Modules

Work through these in order. Each notebook is self-contained (shared code is included as a preamble cell).

#	File	What it covers
0	00-intro.ipynb	Motivation, the two problems ECC solves, roadmap
1	01-algebraic-foundations.ipynb	Groups, rings, fields, finite fields, projective space
2	02-elliptic-curves.ipynb	Weierstrass equation, secp256k1 parameters, curves over F_p
3	03-point-operations.ipynb	Point addition, doubling, scalar multiplication, compression
4	04-key-exchange.ipynb	ECDH, ElGamal encryption/decryption on curves
5	05-ecdsa.ipynb	Signing, verification, nonce catastrophe, DER encoding
6	06-bitcoin-applications.ipynb	Schnorr signatures (BIP 340), ECDH in Lightning onion routing
7	07-exercises.ipynb	Self-assessment, exercises, knowledge map, further reading

Appendix Notebooks

File	What it covers
A1-wright-trick.ipynb	How Craig Wright faked a Satoshi signature in 2016
A2-nonsense-signature.ipynb	The "nonsense signature" algebraic forgery trick
A3-original-paper.ipynb	Original research paper companion notebook

Teaching

See SPEAKER-NOTES.md for bullet-point talking points, live demo callouts, and timing estimates per module (~93 min total).

Setup

Prerequisites: Python 3.11+

python3 -m venv .venv
source .venv/bin/activate
pip install jupyterlab matplotlib numpy plotly

Run

source .venv/bin/activate
jupyter lab

Then open 00-intro.ipynb and work through the modules in order.