Hash chains
Each block in a blockchain includes the cryptographic hash of the previous block's header. Changing anything in an earlier block changes its hash, which no longer matches what the next block recorded, which cascades forward through every subsequent block — making tampering with history computationally evident, not just inconvenient.
Each block's header embeds the hash of the block before it. Edit Block 2 after the fact, and its hash changes — so Block 3's stored pointer to it no longer matches, and the mismatch cascades all the way to the newest block.
Merkle trees
Rather than hashing an entire block's transaction list as one blob, transactions are organized into a Merkle tree: pairs of transaction hashes are hashed together, then pairs of those results, repeatedly, up to a single root hash stored in the block header. This lets a client prove a specific transaction is included in a block by presenting only a small path of hashes (a Merkle proof) rather than downloading every transaction in the block.
Merkle tree of four transactions
Proving Tx2 is included needs only H1, H34, and the root — not the other transactions.
ECDSA and self-custody
Bitcoin and Ethereum both use ECDSA (over the secp256k1 curve) to sign transactions, directly applying the signature module covered earlier: whoever holds the private key can produce a valid signature authorizing a transaction, and there's no third party who can reset or recover it. Losing the private key means losing access to the funds permanently — there's no password-reset flow, because there's no central authority to appeal to.
secp256k1, the curve Bitcoin and Ethereum use — a specific instance of the general curve equation from the ECC module, with a = 0, b = 7.
The specific PQC angle for blockchains
Blockchains have an unusual quantum-risk profile worth noting: an ECDSA public key is only revealed on-chain the moment its owner first spends from that address. Coins that have never been spent from expose only a hash of the public key, adding a layer of protection — but any address that has ever sent a transaction has its full public key permanently on the public ledger, available today to be attacked by a future quantum computer running Shor's algorithm.