Signatures and Trust

Encryption can keep a message secret on its way to Olivia. But secrecy answers only one question. When a message arrives, Olivia still wants to know two more things: did it really come from the person it claims to be from, and did anyone change it along the way?

A digital signature answers both. It is a small piece of proof attached to a message that shows the message genuinely came from a particular person and arrived unchanged. From here on we will just say signature.

Think of an old wax seal. Someone presses a unique signet ring into warm wax to close a letter. Anyone can recognize the stamp, but only the owner of that ring can make it — and if the seal is cracked when the letter arrives, you know it was opened or meddled with. A digital signature does the same job with math instead of wax.

What Encryption Leaves Out

Imagine Olivia gets a message that is perfectly encrypted — no one in the middle could read it. That feels safe, but two worries remain. The message could have been written by an impostor pretending to be her bank. Or a genuine message could have been quietly altered before it reached her.

Secrecy does nothing about either one. Keeping a letter sealed in an envelope does not prove who wrote it, and it does not prove the words inside were not swapped. Those are two separate guarantees: authenticity — who really sent it — and integrity — that it was not changed. A signature is the tool that delivers both.

Signing With the Private Key

Back in public-key encryption you met the idea of a key pair: a private key that one person keeps secret, and a matching public key that anyone can have. To send Olivia a secret, people encrypt with her public key, and only her private key can open it.

A signature uses the same pair, but the other way around. The sender signs the message using their own private key — the half only they hold. Anyone who has the matching public key can then check that signature. If the check passes, it could only have been made by the holder of that private key.

That is the wax seal in math form. Making the stamp needs the one ring nobody else has (the private key); recognizing the stamp needs only knowledge anyone can hold (the public key). So a passing check is proof the message came from whoever owns that private key.

How a Signature Catches Tampering

A signature is not a fixed badge stuck on the end. It is calculated from the contents of the message itself. So the signature and the message are tied together: change even one character of the message, and the signature no longer matches.

That is what makes integrity automatic. When the receiver's check passes, it confirms two things at once — the message came from the right private key, and the message is exactly what was signed. If an attacker altered a single word in transit, the check fails, and the receiver knows not to trust it. One move, both guarantees.

Where Does Trust Come From?

Here is the careful part. A signature proves which key signed the message. It does not, on its own, prove who owns that key. Those are different claims, and mixing them up is the main trap.

Suppose an attacker makes their own key pair, signs a message, and labels it "from Olivia's bank." The signature is perfectly valid — it really was made by that private key. But the key is the attacker's, not the bank's. The signature is genuine; the identity behind it is a lie.

So a signature is only as meaningful as your confidence that the key belongs to the real sender. Bridging that last gap — tying a key to a real-world identity you can rely on — needs something extra called a certificate, which is exactly how the web proves a website is the real one. That is where the next chapter picks up.