The idea
A MAC proves a message came from someone who holds the shared key. That is good enough between two parties who trust each other. If they later disagree, it settles nothing, because Bob holds the same key and could have made the code himself.
A digital signature fixes this by using a key pair. Only Alice has her private key, so only Alice can produce a signature that her public key verifies. The second half of the topic is a different question: not whether a message is genuine, but whether the party at the other end is who it claims to be.
How it works
From MAC to digital signature
A MAC provides integrity and authentication, but it does so through a shared symmetric key. A digital signature uses a pair of asymmetric keys, one public and one private, to prove the authenticity of the message.
The lecture gives two ways to achieve it, signing a document and signing a digest of a document. The services offered are integrity, authentication and message nonrepudiation, the last by using a trusted third party.
How it works
Signing the document
In a cryptosystem the keys used are the private and public keys of the receiver. In a digital signature the keys used are the private and public keys of the sender.
| Cryptosystem | Digital signature | |
|---|---|---|
| Whose keys | The receiver's | The sender's |
| Purpose | Confidentiality | Authenticity of the sender |
The figure on this slide shows the pair (M, S), the message and its signature, travelling together. The signing and verifying boxes did not extract, so only that pair label survives. This is why the commutative property from the RSA topic matters: the sender applies the private key first, and the receiver applies the public key to check it.
How it works
Signing the digest
Signing a whole long document with a public-key algorithm is slow, for the reason the hash topic gave. The lecture’s second method signs a digest of the document instead. The slide is a figure with the labels private and public. Its text did not extract beyond those two labels, so the steps are not reproduced beyond what the lecture states in words: the signature is made on the digest, and the services offered are the same as for signing the document.
How it works
Using a trusted third party for nonrepudiation
The lecture’s figure shows Alice sending (M, S_A) and a trusted centre passing on (M, S_T). Its caption reads that the trusted centre confirms Alice’s identity. So Bob receives a message vouched for by a third party both sides trust, and Alice cannot later deny sending it. The lecture states only that nonrepudiation is obtained by using this third party. It does not give the internal steps of the centre.
How it works
Entity authentication
Entity authentication is used when one party, the claimant, proves its identity to another party, the verifier. The entity can be a person, a process, a client or a server.
| Message authentication | Entity authentication | |
|---|---|---|
| Timing | Applied to a message | Real-time |
| Coverage | Message by message | The claimant for the entire duration of the session |
The claimant is identified with three kinds of witnesses.
- Something known: a password, PIN number, secret key or private key.
- Something possessed: a passport, driver’s licence, ID card, credit card or smart card.
- Something inherent: handwriting, a conventional signature or biometrics.
Where marks get lost
The keys flip between confidentiality and signing
For confidentiality, Alice encrypts with Bob’s public key. For a signature, Alice signs with her own private key. If an answer says the sender signs with the receiver’s key, it is describing a cryptosystem, not a signature.
In the exam
- A digital signature gives integrity, authentication and nonrepudiation. A MAC gives integrity and authentication only.
- Know the two methods, signing the document and signing the digest, and that both use the sender’s key pair.
- Nonrepudiation relies on a trusted third party.
- Entity authentication is real-time and per session. The three witnesses are known, possessed and inherent, each with the lecture’s examples.
Aside
What the slides do not say
The signing and verifying steps in both signature figures are drawings, and the extracted text does not give them. The description here is limited to what the lecture states in words. Check the lecture slides directly before relying on a step-by-step account of the signing process.
Check yourself
- A MAC shares a symmetric key. A signature uses the sender’s key pair.
- Signature services are integrity, authentication and nonrepudiation via a trusted third party.
- Cryptosystem uses the receiver’s keys. Signature uses the sender’s keys.
- Entity authentication is real-time and covers the whole session.
- Witnesses: something known, possessed or inherent.