A chain of hashes

Wonder

1. How does a sequence of digital records resist tampering more effectively than a physical ledger?
2. Why does adding a single new block make every previous transaction harder to alter?
3. What is the computational cost for an attacker who attempts to change a past entry?

Explore

1. In 1991, Stuart Haber and W. Scott Stornetta published ‘How to Time-Stamp a Digital Document.’ They proposed linking documents in a chain where each new record contained the cryptographic hash of the previous one. This structure created an immutable history: altering any past document would change its hash, breaking the link to every subsequent record. Satoshi Nakamoto cited this 1991 paper in the Bitcoin whitepaper as a foundational inspiration for the blockchain’s structural integrity.
2. Each Bitcoin block header includes a 32-byte field called ‘previous block hash.’ This value is the double SHA-256 hash of the entire preceding block header. A miner places this hash in the new header before mining begins, because it is part of the data being hashed. The result is a chain where every block cryptographically commits to its parent. Without this specific link, blocks would be independent islands; with it, they form a continuous sequence anchored at the genesis block from January 3, 2009.
3. The Merkle root in the header binds all transactions within that block to the hash. If an attacker modifies even one transaction in a historical block, the Merkle root changes. Consequently, the block’s own hash changes. Because the next block stores the old hash of this modified block as its ‘previous block hash,’ the link breaks. The chain is now invalid from that point forward. To repair it, the attacker must re-mine the proof-of-work for that specific block.
4. Re-mining one block is insufficient because all subsequent blocks also contain hashes that no longer match. The attacker must redo the proof-of-work for every block after the modified one to create a valid chain. This requires enormous computational power. While the honest network continues to add new blocks, the attacker races against them. If the attacker’s hash rate exceeds that of the rest of the network combined, they can overtake the chain and replace history.
5. Nodes do not follow the longest chain by block count; they follow the chain with the most cumulative proof-of-work, known as ‘chainwork.’ This metric accounts for the difficulty adjustments that make later blocks harder to mine. A branch with more blocks but less total work is not followed, even though its blocks may be valid. The deeper a transaction is buried in the chain, the more work an attacker must replicate to move it. Each confirmation adds layers of computational effort required to reverse the history.
6. Open any block explorer and select a recent block. Note its ‘previous hash’ field. Click that hash to navigate to the parent block. Verify that the parent’s own header hash matches the value stored in the child. Repeat this process three times, tracing the chain back through the links. This manual verification confirms that each block cryptographically commits to its predecessor, forming an unbroken sequence of work-validated records extending back to genesis.

Key facts

Exercise nine, six, three, one

Fact check

Dates, figures and claims checked against the published sources listed below.

• S. Haber and W. Scott Stornetta, 'How to Time-Stamp a Digital Document' (1991)
• Satoshi Nakamoto, 'Bitcoin: A Peer-to-Peer Electronic Cash System' (2008), sections 3-4
• A. M. Antonopoulos & D. A. Harding, Mastering Bitcoin, 3rd ed. (2023), ch. 11