Enigma and Turing — The Codebreaking That Shortened the War by Two Years

Discovery

Technical Explanation

1. How Enigma worked. Enigma was an electromechanical polyalphabetic substitution machine. Each letter passed through a plugboard (Steckerbrett, 10 pairs connected in practice), then through 3 (or 4 for the Navy) rotors permuting the 26 letters, and finally a reflector that sent the signal back through the rotors. After each keystroke, the rightmost rotor advanced one position; the middle rotor advanced every 26 keystrokes, creating a different permutation for every character. Daily keyspace: choice of 3 rotors from 5 (60) × initial positions (26³ = 17,576) × Steckerbrett connections (≈1.5 × 10¹⁴) ≈ 158 × 10¹⁸.

2. The reflector flaw. The reflector guaranteed that no letter could ever encrypt to itself (if A goes in, A never comes out). This was a mathematically exploitable property: if a hypothetical plaintext (crib) produced a contradiction — a letter encrypting to itself — that hypothesis could be eliminated.

3. The Turing-Welchman Bombe. This electromechanical machine simulated 36 interconnected Enigma machines. It tested rotor positions by searching for logical consistency between the crib and the ciphertext via a network of contradictions (the "menu" technique). Gordon Welchman added the "diagonal board," exploiting the symmetry of the Steckerbrett, which reduced the search time by a factor of ~26. Cracking time: approximately 20 minutes per tested configuration.

4. Industrial-scale organisation. At its peak in 1944, Bletchley Park operated 211 Bombes running 24/7 in rotation. Cribs were obtained through intelligence work (weather bulletins broadcast at fixed hours, protocol formulas, captured codebooks). The Ultra system distributed decrypted intelligence to Allied commands via SLUs (Special Liaison Units) to protect the secret.

Why It Worked

The Germans believed Enigma was unbreakable because the sheer number of combinations (10¹⁸) made brute force impossible. But Turing understood that every incorrect hypothesis produces a logically detectable contradiction — there was no need to test all combinations, only to propagate constraints. This was an ancestor of "constraint propagation" in computer science. Human errors by operators — predictable messages, key reuse, known cribs — provided the entry points.

The sophistication lay not in raw computing power, but in the logical architecture: each Bombe run eliminated vast swaths of the keyspace simultaneously. The marriage of mathematical insight and mechanical engineering created a system that turned an astronomical problem into a tractable one.

Causal Chain

Commercial Enigma (Scherbius, 1918) → German military adoption (1930s) → Polish work (Rejewski, 1932–38) → Transfer to the British (July 1939) → Turing designs the Bombe (1940) → Welchman adds the diagonal board → U-boat decryption → Victory in the Battle of the Atlantic (1943) → Ultra intelligence for D-Day (1944) → Colossus (Flowers, 1943–44, first programmable calculator) → Turing's universal machine → Birth of computer science

Anecdote

The Bletchley Park secret remained classified for 30 years. All 10,000 people who worked there kept the secret — including married couples who discovered after declassification that their spouse had also been working at Bletchley. Turing himself received no public recognition. Persecuted for homosexuality in 1952 and sentenced to chemical castration, he took his own life in 1954. He was posthumously pardoned in 2013 and has appeared on the £50 note since 2021.

Sources

References verified during the August 2026 fact-checking audit: these are the pages
against which this bulletin's claims were checked.

1. The Cryptographic Mathematics of Enigma (10 fiches au Steckerbrett) — NSA
2. El Capitan retains title of world's fastest supercomputer — LLNL