What You Will Be Able To Do

• Trace a UTXO transaction
• Describe a block and the chain
• Explain mining and proof of work
• Compute the 21 million supply
• Write a toy miner

The 2008 Whitepaper

• Published 31 October 2008 by Satoshi Nakamoto
• Nine pages, title: Bitcoin, a peer-to-peer electronic cash system
• Genesis block created on 3 January 2009
• Author's identity is unknown

Coins As Unspent Outputs

• No account balances in the protocol
• A UTXO is a chunk locked to an owner
• Balance equals the sum of UTXOs you can unlock

Anatomy Of A Transaction

• Inputs reference earlier outputs and carry signatures
• Outputs hold an amount and a lock
• Outputs total at most the inputs
• The leftover is the fee

Inputs:   UTXO(7 BTC), signed by Alice
Outputs:  5.0   -> Bob
          1.999 -> Alice (change)
Fee:      0.001 BTC

Spending An Output Once

• Full nodes track the set of unspent outputs
• Using an output marks it as spent
• A second spend of it is rejected
• Open question: which of two conflicts came first?

Anatomy Of A Block

• Header: previous hash, Merkle root, time, target, nonce
• Body: list of transactions
• First transaction is the coinbase
• Target interval is about ten minutes

Header { version, prev_hash, merkle_root,
         time, target, nonce }
Body   { coinbase, tx1, tx2, ... }

Mining: Find A Lucky Nonce

• Change the nonce, hash the header, check the result
• Valid means the hash is below the target
• Finding is slow and random
• Checking takes one hash

Demo: Toy Miner

• Difficulty equals the count of leading zeros
• Each extra zero multiplies expected work by 16

import hashlib, itertools

def mine(data, difficulty):
    prefix = '0' * difficulty
    for nonce in itertools.count():
        text = f'{data}{nonce}'.encode()
        digest = hashlib.sha256(text).hexdigest()
        if digest.startswith(prefix):
            return nonce, digest

print(mine('block 1', 4))

Why Proof Of Work Secures History

• Orders transactions by choosing who writes the next block
• Editing an old block needs redoing its work
• Every later block must be redone as well
• Nodes follow the chain with the most work

Difficulty Adjusts Itself

• Every 2,016 blocks nodes compare actual time with two weeks
• Blocks too fast: puzzle gets harder
• Blocks too slow: puzzle gets easier
• Result: one block about every ten minutes

Block Reward And Halving

• Reward started at 50 BTC per block
• Halves every 210,000 blocks, about four years
• Rewards so far: 50, 25, 12.5, 6.25, 3.125
• Last halving shown here: April 2024

Why 21 Million

• Sum the rewards: a geometric series
• Total approaches 21 million and stays below it
• Smallest unit: one satoshi, a hundred millionth
• Final coins arrive around the year 2140

reward, total = 50, 0
while reward >= 1e-8:
    total += 210000 * reward
    reward = int(reward * 1e8 / 2) / 1e8
print(total)

Nodes, Miners And Wallets

• Miners propose blocks
• Full nodes validate every rule and accept or reject
• Wallets store keys and sign transactions
• The supply cap is enforced by nodes

Recap

• UTXOs are coins as unspent outputs
• Blocks link by hashes and hold a Merkle root
• Proof of work picks the next block
• Difficulty keeps blocks near ten minutes
• Halvings lead to a cap of 21 million

Next Week: Consensus

• Proof of work versus proof of stake
• Finality, forks and orphaned blocks
• 51 percent attacks and validators
• How Ethereum agrees today

Questions And Exercise

• Write and time mine() at difficulties 1 to 5
• Verify a nonce with one hash
• Build a three-block chain and break it