Examples#
Runnable experiments for every subpackage, built from the scripts under
examples/<name>/. Each one includes assertions, a figure, a “What to look
for” guide, and an exercise. Download any of them as a Python script or a
Jupyter notebook, or run it in the browser with JupyterLite. The guided
A guided course: from fingerprints to shared history gives a learning order across subpackages.
Cryptography
Hashing and commitments, Diffie-Hellman and RSA, blind signatures, secret sharing, elliptic curves, and Schnorr proofs and signatures.
Zero-knowledge and succinct proofs: sum-check and PCPs, KZG, Groth16 and PLONK with their trusted setups, Zerocash, and transparent Bulletproofs, FRI, STARKs and Halo.
Anonymity on public ledgers: mix-nets and Tor, ring signatures and stealth addresses, address clustering, CoinJoin and mixers, and hidden amounts from confidential transactions to Mimblewimble.
Ledgers
Merkle trees and proofs, signed transfers, blocks, ledger state, and cumulative-work fork selection.
Keys as users hold them: check digits, Base58Check and Bech32 addresses, PBKDF2 and scrypt, brain wallets, HD keys and seed phrases, multisig and threshold ECDSA, social recovery, and ERC-4337 accounts.
Agreement
Proof-of-work search and its expected cost, catch-up probabilities, and stake-weighted proposer selection.
Peer graphs, logical clocks, gossip and reliable broadcast, Kademlia and its attacks, block relay, forks, and transaction privacy.
Execution
A deterministic 256-bit stack machine with gas and atomic failure, Turing machines, Bitcoin Script, and smart contracts and their attacks.
A world-state model of contracts calling contracts: token standards, wallets, proxies and their famous failures, with Hoare logic, symbolic execution and fuzzing.
Economics
Incentives, fees and markets: auctions, block rewards and mining games, EIP-1559, stablecoins and market makers, and the value of transaction ordering.
Ponzi schemes, Benford’s law, proofs of reserves and solvency, honeypots and rug pulls, pump-and-dumps, wash trading, and phishing.
Scaling
Layer 2 and interoperability: payment channels from Spilman to Lightning and eltoo, atomic swaps and bridges, Plasma, sharding, rollups, and data-availability sampling.