Everything so far replaces hard math with different hard math. Quantum key distribution does something else entirely: it makes eavesdropping leave fingerprints.
Not because the eavesdropper is not clever enough. Because the laws of physics will not let them do it quietly.
The original scheme is called BB84, after Bennett and Brassard, who published it in 1984.
| Alice bit | Alice basis | Sent | Bob basis | Keep? | Key bit |
|---|---|---|---|---|---|
| 1 | + | |1⟩ | + | keep | 1 |
| 0 | × | |+⟩ | + | drop | — |
| 1 | × | |−⟩ | × | keep | 1 |
| 0 | + | |0⟩ | × | drop | — |
+ = rectilinear basis {|0⟩, |1⟩} · × = diagonal basis {|+⟩, |−⟩}
How it goes
Alice sends. For each bit she flips two coins: one for the bit itself, one for how to send it — upright, or diagonal. Then she sends a single particle of light set up that way.
Bob measures. He does not know which way she chose, so he guesses. Guess right and he gets her bit perfectly. Guess wrong and he gets a coin flip.
They compare notes, out loud. Over an ordinary phone line they say which way they each chose — never the bits themselves. They throw away every round where they disagreed. About half survive.
They test. They pick some of the surviving bits at random and read them out loud. If those match, nobody interfered.
They tidy up. A bit of processing turns the rest into a shorter key that an eavesdropper knows nothing about.
Why an eavesdropper cannot hide
Eve has two problems, and they are both laws rather than inconveniences.
She cannot copy it. You cannot photocopy a quantum state. That was proved in 1982 and it is a theorem, not an engineering gap.
Looking changes it. So she has to measure — but she does not know which way to measure either. Half her guesses are wrong, and a wrong guess wrecks the state. She then has to send Bob something, and what she sends is not what Alice sent.
A full intercept-and-resend attack introduces about a 25% error rate on the sifted key.
The damage shows up as errors in that comparison step — about one in four of the test bits comes out wrong. Alice and Bob see it immediately and start again.
Notice what the security does not depend on: how much computing power Eve has. It could be infinite. It would not help.
Worth remembering
- Alice sends random bits in random ways; Bob guesses how to measure.
- They compare methods in public, never bits, and keep about half the rounds.
- An eavesdropper cannot copy the particles and cannot avoid disturbing them.
- Listening in shows up as roughly one in four test bits going wrong.
- Security rests on physics, not on the attacker being short of computing power.