Build a toy blockchain with proof-of-work mining

This is the same genesis hash from the proof-of-work chapter, and the same Merkle root from the cryptographic-primitives chapter — nothing new is being invented here. Block 1 commits 4 transactions to a root, mines a nonce against that root, and block 2 repeats the process chained onto block 1's hash.

1. Commit transactions to a Merkle root — reused, not reimplemented

   $\text{merkleRoot}(\text{txs})$ is exactly the function from the cryptographic-primitives chapter. Every block runs its own transaction set through it once.

2. A block's hash folds in the previous hash and this root

   $\text{blockHash}(\text{prevHash}, \text{root}, \text{nonce}) = \text{toyHash}(\text{prevHash} \mathbin\Vert \text{root} \mathbin\Vert \text{nonce})$ — the same shape as the mining chapter's blockHash, with the Merkle root standing in for the raw data string.

3. Mining is the same brute-force nonce search

   Try $\text{nonce} = 0, 1, 2, \ldots$ until $\text{blockHash}(\ldots) < T$. Same difficulty target $T=50$, same search, same asymmetry: expensive to find, one hash to check.

4. A chain is blocks whose prevHash fields actually link up

   Block $i$'s prevHash must equal block $i-1$'s mined hash. Change anything upstream — a transaction, a root, a nonce — and every downstream prevHash reference stops matching, breaking the chain from that point forward.

• root — this block's Merkle root, committing all of its transactions to one hash.
• prevHash — the previous block's mined hash; the literal link in "blockchain."

Both blocks are exactly as mined — every hash matches, and every link points at the block before it.

Tamper with block 1's first transaction and watch the damage cascade: a different Merkle root produces a different block hash, that new hash no longer meets the difficulty target (it was only mined to work for the original root), and block 2's stored prevHash no longer points at anything real. One tampered transaction breaks two blocks.

Genesis hash 33 (mined in the proof-of-work chapter). Block 1 reuses the crypto-primitives chapter's exact 4 transactions.

1. Block 1's Merkle root

   $\text{merkleRoot}(\text{txs}) = 577$ — identical to the cryptographic-primitives chapter's worked example, because it's the same 4 transactions.

2. Mining block 1

   Searching nonces against $(\text{prevHash}=33, \text{root}=577)$: $\text{blockHash}(33,577,0)=981$, then $982, 983, 984, 985, \ldots$ for nonces $1$ through $5$ — every one of them lands in the $980$s, well past the target. Nonce $600$ is the first to succeed: $\text{blockHash}(33, 577, 600) = 43 < 50$.

3. Mining block 2

   A second batch of 4 transactions gives root $506$. Chained onto block 1's hash $43$, the same search against $(\text{prevHash}=43, \text{root}=506)$ starts at $\text{blockHash}(43,506,0)=594$, climbing through the $590$s for the first several nonces, until nonce $900$ is the first to succeed, giving hash $19$.

4. Tampering with block 1

   Change transaction 0 to "alice pays bob 9": the Merkle root becomes $301$ instead of $577$, so $\text{blockHash}(33, 301, 600) = 498$ — nowhere near under $50$. The nonce that worked for the original root doesn't work for the tampered one; block 1 is no longer validly mined, and block 2's prevHash = 43 no longer matches block 1's real (recomputed) hash.