Part 1 · Cryptographic Foundations

Bitcoin is not “encryption” (it barely encrypts anything). It’s an application of a few specific cryptographic primitives. Master these four and the rest of Bitcoin is just clever arrangements of them.

The four primitives and the job each does

Primitive	The job it does in Bitcoin	Answers our question by…
Hash functions (SHA-256)	Fingerprint data; create the “work” in Proof of Work; link blocks	making history tamper-evident and making influence costly
Public-key cryptography	Give each user a keypair — a public identity and a secret	letting anyone verify ownership without a central registry
Digital signatures (ECDSA)	Prove you authorized a transaction without revealing your secret	letting strangers trust a spend without trusting the spender
Merkle trees	Summarize all transactions in a block into one hash	letting nodes verify membership cheaply

Keep asking the course’s recurring question for each one: how does this help untrusting strangers agree on one ledger?

What this part covers

1. Hash functions (SHA-256) — ✅ written. The single most-used primitive in Bitcoin. Determinism, the resistance properties, the avalanche effect, and a hands-on exercise.
2. Public-key cryptography — coming next. Private keys, public keys, and why you can share one but never the other (one-way trapdoor functions, the secp256k1 curve).
3. Digital signatures (ECDSA) — coming next. How a signature proves authorization, how it’s verified, and what gets signed in a Bitcoin transaction.
4. Merkle trees — coming next. Hash trees, the Merkle root in a block header, and Merkle proofs that power lightweight (SPV) clients.

Order matters

We start with hashing because everything else leans on it — signatures hash the message before signing, Merkle trees are made of hashes, and addresses are hashes of public keys. Build this floor first.

Begin with Hash functions (SHA-256) →