Learning Objectives – after this chapter you will be able to:
- Explain how Proof-of-Work selects the miner of the next block.
- Describe nonce, difficulty target, hash rate and difficulty adjustment.
- Explain miner rewards, the longest (most-work) chain rule and the 51% attack.
- Evaluate the main criticisms of Proof-of-Work.
Proof of Work
- Cryptocurrencies have no central gatekeeper to check new transactions. Instead, a distributed network of participants validates incoming transactions and adds them to the chain as new blocks.
- Proof-of-Work (PoW) is the consensus mechanism that decides which participant – called a miner – earns the right to add the next block. Miners who produce valid blocks are rewarded with newly created coins and transaction fees.
- A block is considered valid only if producing it required a large amount of computational work. This lets anonymous participants in a decentralized network trust the chain without trusting each other.
- The “work” is a race: miners compete to be the first to solve a hash puzzle that has no shortcut. The winner broadcasts the block, and other nodes verify it instantly before accepting it. Only after acceptance is the reward really earned.
- Because miners invest heavily in hardware and electricity, cheating (e.g. including invalid transactions) would make them lose that investment – so they are economically motivated to validate honestly.
How Mining Works
- The miner collects pending transactions and builds a candidate block (header + transactions).
- It repeatedly changes the nonce in the header and computes the block hash (Bitcoin uses double SHA-256).
- It stops when the hash is below the difficulty target – in practice, when the hash begins with enough leading zeros.
- It broadcasts the block; other nodes check the hash with one computation – hard to find, easy to verify.
- Nodes add the block to their chain and miners start working on the next one.
Toy example (SHA-256, target: hash must start with “0000”)
| Nonce | SHA-256("Block 1 | Alice pays Bob 5 | nonce=…") | Valid? |
|---|---|---|
| 0 | 49502b3d2d7d912c40a1be18159f8b9b85e5f3d986f48897cf60e26f23987178 | No |
| 1 | e2359f2ededf9d1b5ade20bf4406507089b00d52a7380c22821fae05d35b27ce | No |
| 2 | 69042cede5920a902be9570257237bf0efcc362570331a1deac5bf6cc0f97640 | No |
| … | … | … |
| 47207 | 0000ecf7f65b7539e84adab917460254c3c2fb3520b97f7fc21dbaf4efdfdee3 | Yes |
It took 47,208 attempts to find a valid nonce for this simple target. Real networks use far harder targets, so miners need specialised hardware performing trillions of hashes per second.
Important Terms
| Nonce | A number in the block header that miners change to get a different hash. |
| Difficulty target | The threshold the block hash must be below. Lower target = harder puzzle. |
| Difficulty adjustment | Bitcoin re-calculates difficulty every 2,016 blocks so that blocks keep arriving about every 10 minutes, regardless of total mining power. |
| Hash rate | Number of hashes computed per second by a miner or the whole network. |
| Block reward | New coins created in the block’s coinbase transaction plus all transaction fees. Bitcoin’s subsidy halves every 210,000 blocks. |
| Mining pool | Miners combine hash power and share rewards to earn a steadier income. |
| ASIC | Application-Specific Integrated Circuit – hardware built only for mining one hash algorithm. |
Longest Chain Rule and the 51% Attack
- If two miners find a block at almost the same time, the chain temporarily forks. Nodes follow the chain with the most cumulative work (often called the “longest chain”); the losing block becomes stale (orphaned) and its transactions return to the mempool.
- That is why merchants wait for several confirmations (blocks on top) before treating a payment as final.
- A miner or group controlling more than 50% of the network’s hash rate could build a longer private chain and replace recent blocks – enabling double spending. This is the 51% attack. On large networks it is extremely expensive.
Criticism of Proof-of-Work
PoW systems attract criticism, mostly about their large appetite for electric power:
- Energy requirements: In Bitcoin’s early days, ordinary desktop computers could mine with negligible electricity. Today mining is dominated by specialised hardware, and the network’s total electricity use is comparable to that of some countries (the Cambridge Bitcoin Electricity Consumption Index tracks live estimates).
- Centralization: Decentralization is one of the main attractions of cryptocurrency, but high hardware and energy costs have concentrated mining in large pools and industrial operations. A few entities could therefore control a large share of the hash rate.
- Electronic waste: ASICs become obsolete quickly as newer, more efficient models appear.
- Limited throughput: PoW chains such as Bitcoin process relatively few transactions per second.
These concerns were a major reason Ethereum moved to Proof-of-Stake in 2022 (Chapters 16–17).
Key Takeaways
- PoW miners repeatedly hash the block header with different nonces until the hash is below the target.
- Puzzles are hard to solve but easy to verify; difficulty adjusts to keep block time stable.
- Security comes from cost: rewriting history needs a majority of hash power (51% attack).
Question / Answer (15 questions)
Answer : Proof-of-Work is a consensus mechanism in which miners compete to solve a computationally expensive hash puzzle. The first miner to find a valid solution earns the right to add the next block and receive a reward, and other nodes can verify the solution easily.
Answer : Miners must find a block header whose double SHA-256 hash is numerically below the current difficulty target. Because hash outputs are unpredictable, the only method is to try many nonce values until one works.
Answer : The nonce is a field in the block header that miners change on each attempt. Each different nonce produces a completely different block hash, allowing the miner to search for a hash below the target.
Answer : Finding a valid hash may require trillions of attempts, but any node can check a proposed block by computing its hash once and comparing it with the target.
Answer : Every 2,016 blocks, Bitcoin recalculates the difficulty target based on how long those blocks took. If blocks came too fast the puzzle becomes harder, and if too slow it becomes easier, keeping the average block time around 10 minutes.
Answer : The block subsidy (newly created coins in the coinbase transaction) plus all the transaction fees from the transactions included in the block.
Answer : Mining requires large investments in hardware and electricity. A block containing invalid transactions would be rejected by other nodes, so the miner would lose the reward and the cost of the work.
Answer : When competing versions of the chain exist, nodes follow the chain with the most cumulative proof-of-work, commonly called the longest chain. This resolves temporary forks.
Answer : A valid block that is not part of the main chain because another block at the same height ended up on the chain with more work. Its transactions return to the mempool if not already confirmed.
Answer : Recent blocks can still be replaced during a temporary fork or an attack. Each additional block built on top makes reversal less likely, so waiting for confirmations reduces the risk of double spending.
Answer : If an attacker controls more than half of the network’s hash rate, they can secretly build a chain faster than everyone else and then publish it to replace recent blocks. This can reverse their own transactions and enable double spending.
Answer : Mining pools are groups of miners who combine their hash power and share rewards according to contribution. They reduce the variance of income for individual miners, but they also concentrate influence.
Answer : Very high energy consumption, centralization of mining in large pools and industrial facilities, electronic waste from obsolete ASIC hardware and limited transaction throughput.
Answer : An Application-Specific Integrated Circuit is hardware designed only for one task, such as computing SHA-256. ASICs are far more efficient than general computers, which raises the barrier to entry for individual miners.
Answer : Ethereum stopped using Proof-of-Work at The Merge on 15 September 2022 and now uses Proof-of-Stake.
MCQ Test : Check Your Understanding (5 questions)
Select an option and press Check Answer, or answer all questions and press Submit Test to see your score. Each answer comes with an explanation.
Bibliography/References
The notes, questions and MCQs on this page are original explanations written for this course. The works listed below were consulted and are cited for attribution and further reading. Product names, logos and trademarks belong to their respective owners. Short quotations, where used, are marked and attributed.
- Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System. https://bitcoin.org/bitcoin.pdf
- ethereum.org. (n.d.). Proof-of-work (PoW). Ethereum Developer Documentation. https://ethereum.org/en/developers/docs/consensus-mechanisms/pow/
- Investopedia. (n.d.). What Is Proof of Work (PoW) in Blockchain? https://www.investopedia.com/terms/p/proof-work.asp
- Bitcoin Project. (n.d.). Bitcoin Developer Guide. developer.bitcoin.org. https://developer.bitcoin.org/devguide/
- Cambridge Centre for Alternative Finance. (n.d.). Cambridge Bitcoin Electricity Consumption Index. https://ccaf.io/cbnsi/cbeci
- Narayanan, A., Bonneau, J., Felten, E., Miller, A., & Goldfeder, S. (2016). Bitcoin and Cryptocurrency Technologies: A Comprehensive Introduction. Princeton University Press. ISBN 978-0-691-17169-2.
- Antonopoulos, A. M. (2017). Mastering Bitcoin: Programming the Open Blockchain (2nd ed.). O’Reilly Media.