Section 3.2
What do hashes and signatures actually prove?
A cryptographic hash maps an input into a fixed-length output. Its useful properties include making it computationally difficult to find a matching input for a specified output or two different inputs with the same output. Changing the input will generally change the output unpredictably.1NIST, Blockchain Technology Overview, NISTIR 8202, especially the discussion of cryptographic primitives and consensus models.Open sourceSee in source list
Blocks use hash commitments to link information together. Bitcoin's block header commits to the previous block and to a Merkle root representing the block's transactions. A Merkle tree allows a compact proof that a particular item is included in a committed set without reproducing the entire set. These structures make changes detectable and help participants verify relationships between records.2Bitcoin Developer Guide, Block Chain.Open sourceSee in source list
A digital signature addresses a different question: whether an instruction was authorised using the relevant signing key under the specified scheme. It does not establish that the instruction was commercially sensible, that its author was legally entitled to act, or that the beneficiary will perform a separate obligation.
| Mechanism | What it helps establish | What it does not establish by itself |
|---|---|---|
| Hash commitment | Consistency with particular committed data | Truth or economic quality of that data |
| Digital signature | Authorisation under a key and verification rule | Identity, legal authority or informed consent |
| Merkle inclusion proof | Membership in a committed collection | Acceptance of that collection by the relevant network |
| Consensus evidence | Status of a history under protocol assumptions | Solvency of an issuer or performance of an external contract |
These mechanisms work together. None is a universal certificate that “the transaction is safe.”
For a small inclusion example, imagine a block committing to four transaction identifiers: A, B, C and D. A verifier checking B can receive B's sibling A and the combined commitment for C and D. It hashes B with A, then combines that result with the C-and-D commitment and compares the result with the Merkle root in the block header. A match shows that B belongs to the transaction set committed by that header, assuming the hash construction holds.
The proof does not show that the header belongs to the branch the institution accepts. The verifier must separately establish the header's place in the relevant chain and apply its confirmation or finality policy. Inclusion in a committed candidate block and acceptance of that block are distinct claims.
Distinguish integrity from provenance and availability
Suppose a platform publishes a hash of a collateral report. An auditor later obtains the report and confirms that its hash matches. This demonstrates consistency with the committed document. It does not establish that the collateral exists, that valuation inputs were appropriate or that the assets were unencumbered.
Now suppose the platform stops supplying the document. Its hash remains observable, but the observer cannot reconstruct a large missing report from the hash. A commitment to data and access to data are different services.
Finally, suppose an intermediary supplies a valid transaction inclusion proof against a block header. The institution must still establish that the header belongs to the relevant accepted chain and satisfies its settlement policy. A proof against a discarded branch is not enough.
The practical verification chain is therefore:
1. Identify the precise statement being verified.
2. Establish the authenticity and relevance of the reference commitment.
3. Obtain the data necessary to verify that statement.
4. Verify the statement using the correct rules.
5. Assess the economic or legal assumptions outside those rules.
This discipline also applies to proof-of-reserves claims, oracle reports and bridge messages. A mathematically sound proof can support a much narrower proposition than a commercial presentation suggests.