Digital signatures
A signature on paper doesn't prove much: anyone who's seen yours once can copy it. A digital signature is different. It proves the text came from you and that not a single letter has changed since — and faking it is just as impossible as counting backwards on the curve from the previous chapter. Because that's exactly what it uses.
Words you might need
- Signing
- Using your private key to make a kind of seal over a text. The seal is a number that belongs to exactly that text and exactly that key.
- Verifying
- Using the public key to check that the seal is correct. Anyone can do that, because anyone may have the public key. If it checks out: the text is genuine and unchanged. If it doesn't: something's been altered, or someone else signed it.
- ECDSA
- The name of the signature system that runs on elliptic curves. The EC stands for elliptic curve. This is what your ID card uses.
- Certificate
- A statement from a trusted authority: "this public key belongs to this person". Signed by that authority itself, too. Without a certificate you know someone signed it, but not who.
The lock in reverse
In the chapter on asymmetric keys, anyone could lock the padlock with your public key, and only you could open it with your private one. A signature flips that around: you do something with your private key, and anyone can use your public key to check that it was you. Because only whoever holds the private key can make a seal that matches the corresponding public key.
What a signature does and doesn't prove
| Does | Doesn't |
|---|---|
| That the signer held the private key. | Who that person is. You need a certificate for that. |
| That the text is letter-for-letter the same as when it was signed. | That the text is true. You can perfectly sign a lie. |
| That the signer can't deny it afterwards. | When it happened. That's what a timestamp is for. |
Try it yourself
Everything happens in your browser. Nothing is sent to the server.
- Click Make a key pair. Notice how much shorter this public key is than RSA's — that's the curve.
- Click Sign. You get a 64-byte seal.
- Click Verify. Valid.
- Now change one letter in the text — a period, a capital letter — and click Verify again, without signing again. Invalid. There's no "almost right".
- Put the text back and click Sign twice. Two different seals for the same text — and yet both valid.
From key to person
A valid signature says: "someone with that private key signed this". But who is that? That's where the certificate comes in. The Belgian State says: "this public key belongs to Koen Thomeer, born on such-and-such date" — and signs that statement itself. Want to be sure it really was the State? Then you check that signature against the State's key. This gives you a chain of trust that ends at one key you simply have to believe: the root. On your ID card, those certificates sit in the chip, next to your keys.
Two keys on your card, on purpose
| Key | What for | What it means |
|---|---|---|
auth |
Logging in: proving it's you | Not a signature under a document. Just "yes, this is me". |
sign |
Signing documents | Legally just as valid as your signature with a pen. Irrevocable. |
That's why your card sometimes asks for your PIN twice, and why the
second time matters more. Logging into a website uses auth.
Signing a contract uses sign, and that one you can never
undo. In the final chapter you'll do both with your own card.
This is math: proving you know something without saying it
Your private key is a number n. Your public key is the point n·P on the curve. A signature is a calculation in which n is hidden in such a way that anyone with n·P can check that you know n — without n ever coming out. And that randomness from step 5? Every signature uses a fresh random number; without it, n leaks out anyway. That actually happened in 2010 with the PlayStation 3, whose master key leaked because of it. One missing random number, and a multi-billion-dollar company was wide open. Math doesn't forgive sloppiness.