One-time pad · est. 1917 · burn after decoding
Five-digit groups on a violet pad.
A numbers transmission is arriving. The top sheet of a carbon-violet pad lines up beneath it, and mod-10 subtraction — digit by digit, no borrow carried — turns noise into a courier's afternoon. Used once, this cipher is provably unbreakable. Used twice, it broke an empire's traffic.
Key groups, carbon violet. Cross off as consumed.
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|
Mnemonic A T · O N E · S I R — eight common letters cost one digit; the rest take a 2- or 6- prefix.
§ 02 — Perfect secrecy
Any message fits.
Perfect secrecy is not a slogan; it is an equation. Take the first received group. For every five-letter candidate you can propose, there exists a legal key group that turns this exact ciphertext into it — each candidate priced at exactly one key among 105 equally likely group keys. The intercept fixes the message's length and nothing else.
Claude Shannon proved it in 1949: when the key is truly random, as long as the message, and never reused, the ciphertext is statistically independent of the plaintext. This transmission's full key runs 55 digits — 1055 pads, every one of them possible.
Received group 01 — this cycle·····
Every candidate resolves. The group prefers none of them — and the pad that was actually used is the only witness.
§ 03 — The failure
The VENONA condition.
In 1942, under wartime pressure, the Soviet pad factory duplicated a run of key pages — by most accounts tens of thousands of sheets. American analysts spent the next four decades on the consequences. Subtract two ciphertexts that share a key and the key vanishes: what remains is one plaintext minus the other, and language leaks straight through the arithmetic.
Below, two archival-length cables. With pad discipline, cable B gets its own sheet and the difference stream is statistically flat. Throw the switch to reuse cable A's sheet — same arithmetic, and structure rises out of the noise.
Cable A
Cable B
Difference
digit pairs—
coincidence κ—
χ² vs uniform—
leak past21.67
No structure — sheet discipline holds
Distribution of the difference digits 0–9 across — pairs. Dashed line: uniform expectation. χ² above 21.67 (9 degrees of freedom) is a leak at the 1% level.
§ 04 — The ledger
One idea, four dates.
Gilbert Vernam, an engineer at AT&T, wires a teleprinter to mix message tape with key tape, character against character. The patent is granted in July 1919.
Joseph Mauborgne of the U.S. Army adds the condition that makes it perfect — and impractical: the key must be random, as long as the traffic, and never used twice.
Claude Shannon publishes the proof: under Mauborgne's conditions the one-time pad achieves perfect secrecy — the only cipher for which this has ever been proven.
VENONA. Duplicated Soviet pad pages let American analysts read, across thirty-seven years, roughly three thousand messages — a fraction of the traffic, and enough.