The history of
breaking Enigma

Hans-Thilo Schmidt, an employee of the German cipher office, sells Enigma documents to French intelligence. In December 1931 Captain Gustave Bertrand agrees with the Polish Cipher Bureau that France will supply intelligence and Poland will do the cryptanalysis.

The material includes documentation on the machine, training messages in both plain text and cipher text, and later the keys for September and October 1932. It does not include the rotor wiring. Rejewski receives the keys in December 1932, when his analysis cannot go further without them.

Each operator chooses a three-letter message key and types it twice, starting from the same daily position used by every operator. The first and fourth enciphered letters of every message therefore stand for the same key letter, as do the second and fifth, and the third and sixth.

With about 80 messages from one day, Rejewski links these letters into three tables and analyses them with the theory of permutations. Operators who choose keys such as AAA, or three neighbouring keys on the keyboard, help him split the tables into the machine’s individual steps.

The French keys give Rejewski the plugboard pairs for the days he is studying, leaving the right-hand rotor as the main unknown. His equations fail until he guesses that the keys are wired to the entry wheel in alphabetical order. The commercial Enigma uses keyboard order.

The keys cover two months in different quarters of the year, and the rotor order changes each quarter. A different rotor stands on the right in each month, so Rejewski can solve two rotors; the third rotor and the reflector follow.

By early 1933 the Bureau reads German Army Enigma messages. The AVA Radio Company in Warsaw builds replica machines to Rejewski’s design.

Daily keys are recovered by hand. The grill and other hand methods rely on the plugboard swapping only six pairs, which leaves 14 letters unchanged. Różycki’s clock method compares the letters of pairs of messages to identify the rotor on the right, which turns at every key press.

On 1 October 1936 the Germans begin using five to eight plugboard pairs, and the hand methods stop working. The Poles return to the three tables built from each day’s doubled message keys.

The plugboard changes which letters appear in each cycle of those tables, but not the cycle lengths. Rejewski’s cyclometer, two linked sets of rotors with lamps, measures the lengths for all 105,456 rotor orders and starting positions. The card catalogue takes more than a year to compile; with it, a daily key usually takes 10 to 20 minutes.

From 1 May 1937 naval operators no longer send a doubled message key. The indicator comes from a book and is disguised with bigram tables, so the Polish catalogue no longer applies to naval traffic.

The Poles still break the key for 8 May. A torpedo boat that has not received the new instructions is told to use the old system, which gives away the day’s starting position, and a message continuation with a predictable opening supplies a crib.

The Germans replace reflector A with reflector B. The catalogue was compiled with the old reflector, so the Poles work out the new wiring and compile the catalogue again.

From 15 September 1938 each operator picks a starting position, sends it unenciphered and enciphers the doubled message key from it. The catalogue no longer works, but the doubled key sometimes shows the same enciphered letter in the first and fourth places, the second and fifth, or the third and sixth. The Poles call these repeats females; they occur only at certain rotor positions, whatever the plugboard pairs.

Zygalski’s perforated sheets mark the positions that can produce a female, and stacking the sheets for a day’s messages leaves a hole at the likely setting. The AVA company builds six bomby in November 1938, one for each rotor order; each tests rotor positions against three females, and a search takes about two hours.

Rotors IV and V let operators choose three rotors from five, and the possible rotor orders rise from 6 to 60. The Nazi Party’s SD network still uses the old indicator procedure, so when a new rotor stands on the right, Rejewski recovers its wiring with the 1932 method.

On 1 January 1939 the plugboard rises to as many as ten pairs, so the letter in a female is less often unplugged. The sheets and bomby cover 6 rotor orders; covering 60 needs ten times as much equipment, more than the Bureau can build.

At the Cipher Bureau’s centre at Pyry, outside Warsaw, the Poles show French and British codebreakers their replicas, the Zygalski sheets and designs for the bomba and cyclometer. Alastair Denniston and Dilly Knox represent Britain. German changes have reduced Polish success in the preceding months, but the Poles have read far more traffic than either ally.

Knox’s first question is how the keys are wired to the entry wheel. France and Britain each receive a Polish-built replica; Bletchley Park has its machine in August 1939.

After Poland is invaded, Rejewski, Różycki and Zygalski reach France and resume work on 20 October 1939 at PC Bruno, near Paris, with French colleagues. At Bletchley Park, John Jeffreys’ section makes Zygalski sheets for all 60 rotor orders, and a set goes to PC Bruno.

Using the sheets, the team in France breaks a wartime key in early January 1940, and Bletchley Park makes its first wartime break the same month. Alan Turing meets the Polish codebreakers in France that January.

Victory, built by the British Tabulating Machine Company under Harold “Doc” Keen, arrives at Bletchley Park. Alan Turing designed it to work from a crib, a guessed piece of plain text, so it does not depend on the indicator procedure. In June and July, with text captured from the patrol boat VP 26, it helps Hut 8 solve six days of April naval traffic.

Because of the reflector, Enigma never enciphers a letter as itself. Codebreakers slide the crib along the cipher text and reject any position where a letter would stand above itself; the bombe then searches for rotor settings consistent with the crib.

On most Army and Air Force networks the message key is now enciphered once. The females that the Zygalski sheets and the bomba relied on disappear. Codebreakers now need cribs, operator mistakes or captured keys.

In February 1940 John Herivel suggests that hurried operators may choose a first message setting close to the day’s ring settings, so the first indicators from many operators would cluster around them. In late May such a cluster lets David Rees break Red, a Luftwaffe key that the Polish methods could no longer break.

Codebreakers also look for cillies: message keys such as three consecutive keyboard letters, a word or a set of initials, or a key reused from the previous message.

A plugboard cable swaps two letters both ways: if A is plugged to E, E is plugged to A. Gordon Welchman’s diagonal board wires this rule into the bombe, so a deduction about one letter pair also tests its reverse.

The board removes most false stops. Agnus Dei, the first bombe fitted with it, is installed in August 1940.

The Italian Navy uses a commercial-type Enigma with no plugboard. Knox’s rodding method, devised in 1937, tests a crib against each position of the right-hand rotor using prepared tables.

In March 1941 Mavis Lever sees that an operator’s test message contains no L. Because Enigma never enciphers a letter as itself, she concludes that the operator typed only L, and the key is recovered. Intelligence from Italian naval Enigma helps the Royal Navy at Cape Matapan on 28 March.

The methods used on Army and Air Force keys do not work on naval Enigma. Message settings come from a book, eight rotors allow 336 rotor orders, and cribs are scarce. Captured rotors give Bletchley Park all eight wirings in 1940, but the keys remain unknown.

In May 1941 the weather ship München yields a weather codebook, and U-110, captured on 9 May, yields indicator books. Keys from München and the weather ship Lauenburg let Bletchley Park read Dolphin, the main naval key, with little delay in June and July.

Every naval message setting of a day is enciphered from one starting position. Once the bigram tables are known, Hut 8 can line up pairs of messages whose settings overlap; at the right offset, letters repeat between the two cipher texts about as often as in German text, and more often than at random.

Turing’s Banburismus scores these repeats with Bayesian statistics to identify the likely right-hand and middle rotors. It can cut the rotor orders to test from 336 to about 18, saving bombe time; from August 1941 Hut 8 breaks Dolphin without captured keys.

Many messages follow fixed forms, such as weather reports, and bombe menus are built from these guessed texts. When the same text is sent in Enigma and in a hand cipher that has already been broken, the decrypt gives the Enigma message’s plain text.

The RAF sometimes lays mines in chosen places, an operation called gardening. German signals about the cleared channels are then sent in both naval Enigma and the dockyard cipher, which Bletchley Park can read.

The Atlantic and Mediterranean U-boats move their key, Triton (Shark at Bletchley Park), to the four-wheel M4. A new edition of the weather short signal book removes Hut 8’s main cribs at the same time.

The thin fourth wheel does not step during a message, so it works like a choice of 26 reflectors rather than a full fourth rotor. Bletchley Park already knows its wiring from a December 1941 message sent on four wheels and repeated on three, but without cribs the bombes cannot be used against Shark.

Before U-559 sinks, sailors from HMS Petard recover its weather short signal book and short signal book; Anthony Fasson and Colin Grazier die in the attempt. Hut 8 finds that U-boats encipher weather reports with the fourth wheel in its neutral position, so the M4 works like a three-wheel machine, and weather broadcasts read by Hut 10 supply the plain text.

On 13 December 1942 Bletchley Park sends the Admiralty the positions of more than 12 U-boats. When a new weather book starts on 10 March 1943, Hut 8 uses sighting reports, also sent in three-wheel mode, and reads Shark again from 19 March.

British four-rotor bombes enter service in June 1943 and US Navy bombes in August. Joseph Desch’s team at NCR in Dayton, Ohio, completes the prototypes Adam and Eve in spring 1943. WAVES, members of the US Navy’s women’s reserve, wire the rotors and operate the machines in Washington.

From September 1943 Shark is usually broken within 24 hours, and at the end of the year the US Navy’s OP-20-G takes over the work. By spring 1944, 96 US bombes are in routine use, spending about 45 percent of their time on non-naval keys under British direction.

The Luftwaffe introduces UKW-D, a reflector whose wiring operators can change, called Uncle Dick or Uncle D at Bletchley Park. It is issued for selected traffic only; most messages still use reflector B.

Networks use the same rotor order, ring settings and plugboard with both reflectors. Once the reflector B key is broken, the UKW-D messages can be attacked with it, and in Norway Bletchley Park finds the D wiring within 24 hours.

The Luftwaffe’s Uhr is a box that replaces the plugboard cables and changes their connections in 40 positions. Bletchley Park receives the first Uhr messages on 10 July 1944.

Some operators who do not know the new procedure resend messages with the ordinary key, which gives the first break. The Uhr changes only the 20 plugged letters, and once one setting is known the effect of all 40 can be predicted.

By the end of the war Britain has 211 bombes, worked by about 1,676 Wrens and 263 RAF personnel at Bletchley Park and outstations such as Eastcote and Stanmore. About 50 are kept for a time; the rest are dismantled. One US Navy bombe survives, at the National Cryptologic Museum.

Veterans keep the work secret for decades. Gustave Bertrand describes the Polish and French work in 1973, and F. W. Winterbotham’s The Ultra Secret brings the British work to a wide audience in 1974.