A Secret Shouted Across a Room

The board shows a public tin of yellow paint, two people each stirring in their own hidden colour, two muddy mixtures shouted openly across a crowded room, and one identical brown that both sides end up holding. This is the story behind that board: who found the trick, who was made to keep it secret, the numbers that make it checkable by hand, and the one thing the trick does not do for you - which turns out to be the reason certificates and browser padlocks exist at all.

Before you start. You need nothing more than a calculator’s four buttons - add, multiply, and the idea that some sums “wrap around” once they pass a limit, the way a clock hand wraps from 12 back to 1. Everything past that gets built up as the story needs it.

The idea in 30 seconds

Two strangers, using only messages anyone can overhear, can end up holding an identical secret number that a listener cannot work out.
The trick rests on a step that is cheap to do and, as far as anyone has ever found, impossible to undo: a one-way function.
Running it backward at the sizes real computers use would take longer than the universe has existed - a wall of 617 digits, not a lock you can pick.
The idea was found twice: in secret at GCHQ in 1974, and openly by Diffie and Hellman in 1976, who got the credit for over twenty years because the first discovery was classified.
A shared secret says nothing about who you shared it with, which is why a man in the middle who runs the exchange twice, once with each side, can sit there undetected.

Read the story · Skip to the numbers