The math that lets strangers transact without trusting each other.
What you will learn
Explain public/private key pairs
Describe how mining adds blocks
Understand why a 51% attack is so expensive
Private vs public key
Private vs public key
Linking blocks by hash
Linking blocks by hash
Public vs private keys
You have two keys: a public key (like an address — share it freely) and a private key (like a password — never share it). The private key signs transactions proving you control the funds; the public key lets anyone verify that signature. You can prove ownership without revealing the secret.
💡 Signing without revealing
Signing a transaction is like stamping a wax seal only you possess. Anyone can check the seal against your public signature and confirm it's authentic — but nobody can forge it because forging requires your private key.
How mining adds a block
Miners race to solve a puzzle: find a nonce such that the block's hash falls under a difficulty target. The winner broadcasts the block, others verify it, and the winner earns a block reward + fees. The difficulty auto-adjusts to keep blocks arriving on schedule.
The 51% attack
If one party controls more than half the network's hashing power, they could theoretically rewrite recent history (double-spend). But the cost is enormous — hardware, electricity, and the collapse in value their own attack would cause. Attacking the chain destroys the asset you'd steal.
Difficulty adjustment
As more miners join, blocks would arrive too fast — so the protocol raises difficulty every ~2 weeks (Bitcoin) to keep the average block time near 10 minutes. This self-balancing is what makes the network robust to hardware improvements.
💡 Why 10 minutes?
Bitcoin's ~10-minute block time trades confirmation speed for security: the longer the interval, the harder it is for competing chains to form and the more secure each confirmation becomes. Other chains pick faster times with different tradeoffs.
❓ Quick check
Your private key should be:
A) Shared publicly
B) Kept secret — it proves ownership
C) Printed on the blockchain
D) Stored in a public database
The private key is the sole proof of control; losing it loses the funds.
(Knowledge check — full exam is next)
Key takeaways
Public key = address; private key = secret that signs
Mining = racing to solve a hash puzzle; difficulty self-adjusts
A 51% attack is economically self-defeating
📝 Weekly Exam — pass with 80% to unlock next week
10 questions. Review the Deep Dive and courses before attempting.
1. Your public key is used to:
Public key = receive + verify; private key = sign/spend.
2. Your private key should be:
Whoever holds the private key controls the funds.
3. A miner wins a block by:
The proof-of-work puzzle: hash below target.
4. Difficulty adjustment keeps:
It targets a stable average block interval.
5. A 51% attack lets an attacker potentially:
Majority hashpower could reorder recent blocks.
6. Why are 51% attacks rare in practice?
Economic self-interest: attacking devalues what you'd gain.
7. Bitcoin's ~10-minute block time is a tradeoff between:
Longer = more secure but slower confirmations.
8. The block reward + transaction fees together are called the:
Rewards align miner behavior with the network.
9. If more miners join the Bitcoin network, difficulty:
Difficulty adjusts up with more hashpower.
10. Losing your private key means:
No private key = no proof of ownership = funds lost.
Your score: —
🛠 Weekly Project
Generate a real keypair and sign a message.
1
Use the Lab or a reputable wallet to generate a new keypair.
2
Copy your public address (safe to share).
3
Sign a short message like 'AEON Week 5' with your private key.
4
Verify the signature using your public key.
5
Write one sentence explaining why the signature proves ownership without revealing the private key.