Digital Signatures

Computer Network & Network Security System — Network Security, NEC licence examination syllabus (Nepal Engineering Council).

Digital Signatures: proving a message really came from you

Encryption hides WHAT you said. Digital signatures prove WHO said it.

A digital signature does the opposite operation from normal encryption: the sender encrypts (signs) using their OWN PRIVATE key, and anyone can verify it using the sender's PUBLIC key. If it verifies correctly, the message could only have been signed by someone holding that private key.

✍️ The Signing & Verification Process

HashingThe message is first run through a hash function, producing a short, fixed-size "fingerprint" of the message.

SigningThe sender encrypts JUST the hash (not the whole message — much faster) using their private key.

VerificationThe receiver decrypts the signature with the sender's public key, re-computes the hash of the received message themselves, and checks the two hashes match.

💡 One-liner: "What does a digital signature actually prove?" → Authenticity (it really came from that sender) AND integrity (the message wasn't altered) — but NOT confidentiality, since anyone can still read the original message unless it's separately encrypted too.

Why the hash is not just an optimisation

The chapter above gives speed as the reason for signing the hash rather than the message, and that is true. But there is a second reason that questions probe more often.

RSA can only operate on numbers smaller than n. A message longer than the modulus cannot be signed directly at all — it would have to be split into blocks, and an attacker could then reorder or remove blocks while every individual signature still verified. Hashing first produces one fixed-size value covering the entire message, so any change anywhere in it breaks verification.

💡 This is why the hash function must be collision-resistant. If an attacker can find two messages with the same hash, a signature on one is a valid signature on the other — and the signer never saw the second. That property, not speed, is what the security depends on.

The three properties, and the one that is missing

✍️ What a signature does and does not give

Authentication ✓Only the private-key holder could have produced it.

Integrity ✓Any alteration changes the hash and breaks verification.

Non-repudiation ✓The signer cannot later deny signing, since nobody else could have.

Confidentiality ✗The message is still readable by anyone. Signing is not encrypting.

To get confidentiality as well, the message must be separately encrypted with the recipient's public key. Signing and encrypting are different operations using different keys in different directions, and conflating them is the commonest error in exam answers on this topic.

💡 Keep the directions straight: sign with your own private key so anyone can verify with your public one; encrypt with the recipient's public key so only they can decrypt with their private one. Same algorithm, opposite key usage, entirely different purpose.

Syllabus points

Concept and purpose
Hashing + signing / verification process

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