What is a cryptographic signature: digital signatures explained
A cryptographic signature is a value computed from a document and a private key that anyone holding the matching public key can check, establishing that the holder of that key signed exactly this content and that the content has not changed since it was signed.
The terms cryptographic signature and digital signature are used interchangeably for this mechanism. NIST standardises it in FIPS 186-5, the Digital Signature Standard, effective 3 February 2023, which specifies three approved techniques: RSA, the Elliptic Curve Digital Signature Algorithm (ECDSA), and the Edwards Curve Digital Signature Algorithm (EdDSA). The older DSA algorithm from earlier editions is retained only for verifying signatures that already exist.
How does a cryptographic signature work?
The mechanism rests on an asymmetry: two mathematically linked keys, where one cannot be derived from the other in any practical amount of time.
- The private key signs. It stays with the signer, is never shared, and is the only thing that can produce a signature the matching public key will accept.
- The public key verifies. It is published freely. Anyone can check a signature with it, and nobody can create one with it.
In practice the document is hashed first, and the signature is computed over the digest rather than the file. That is why a signature and a hash function are always discussed together: the hash pins the content, the signature pins who committed to that content. Signing a two-hour video costs the same as signing a sentence, because both are reduced to a fixed-length digest before the key is involved.
Verification returns one of two answers, valid or invalid, with nothing in between. Change one byte of the signed content and verification fails. Present a signature made with a different private key and verification fails.
What a valid signature actually attests to
Three statements, and it is worth being able to recite them in order.
- Integrity. The content is bit for bit what was signed. Any modification since signing breaks verification.
- Authentication of the key. The signature was produced using the private key paired with this public key. Whether that key belongs to a named person or organisation is a separate question, answered by the certificate and the trust framework around it, not by the mathematics.
- Non-repudiation. Given sound key management, the key holder cannot credibly claim the signature came from somewhere else, since no one else could have produced it.
That middle point is where most misreadings start. A signature binds an act to a key. It binds that key to a human being only through everything wrapped around it: how the certificate was issued, how identity was checked at issuance, how the key is stored, and who has access to the device holding it.
What a signature does not prove
- It does not prove the content is true. A correctly signed statement can be entirely false. The signature attests to authorship and integrity, never to accuracy.
- It does not prove who was at the keyboard. It proves the key was used. A borrowed device, a shared credential, or a stolen key all produce valid signatures.
- It does not prove when. Signatures carry no inherent time. A claimed signing time from the signer's own machine is worth what any device clock is worth, which is why a timestamp from an independent authority is normally applied alongside.
Cryptographic signature vs electronic signature
These are not synonyms, and confusing them causes real trouble in procurement and in evidence.
An electronic signature is a legal concept: any electronic data attached to or logically associated with other data, used by the signatory to sign. A typed name at the foot of an email qualifies. A cryptographic signature is a technical mechanism. Some electronic signatures are built on it and inherit its properties, and many are not built on anything of the kind.
When a specification says "electronic signature", ask what sits underneath. If the answer is a stored image of a handwritten name, the document has a signature in the legal sense and no integrity protection whatsoever.
Signature example: the sealed submission opened a year later
A submission of photographs, answers and a session record is bound into one manifest and signed with the receiving platform's private key at the moment of receipt. Fourteen months later the file is disclosed to a third party, who verifies the signature with the published public key.
Verification succeeding tells them the package they are holding is exactly the package that was sealed. It tells them nothing about whether the photographs show what the claimant said they show, which is still a matter for an assessor. Getting that boundary right is what makes the sealed submission useful rather than oversold.
Where signature schemes fail in practice
The mathematics almost never fails. The operations around it do.
- Key compromise. A private key on a shared drive or in a source repository invalidates every property above, retrospectively and silently.
- Weak identity binding. A certificate issued without meaningful identity checks makes the key holder unknown, however sound the cryptography.
- Verification nobody performs. A signature that is never checked is decoration. Build the check into the review step rather than leaving it to whoever thinks to run it.
- Expiry and revocation. Verifying an old signature means knowing whether the certificate was valid when it was applied, which is exactly the gap a trusted timestamp closes.
Signing is one layer in a set. On its own it attributes and protects one artefact. Combined with evidence integrity controls at capture, a receipt time, and a chain of custody after arrival, it becomes something an assessor can walk a hearing through line by line.