Breaking the Enigma Code: The Allied Victory in the Secret War

How mathematics, ingenuity, and perseverance defeated the Nazis’ unbreakable cipher

Introduction: The Unbreakable Code

In the shadows of World War II, while battles raged across Europe, Africa, and the Pacific, another war was being fought in absolute secrecy. This was the secret war of codebreaking, where the ability to read an enemy’s encrypted messages could mean the difference between victory and defeat, life and death for millions.

At the heart of this secret war was Enigma, the German cipher machine that the Nazis believed was unbreakable. Used by the German military to encrypt their most sensitive communications, Enigma generated ciphers of such complexity that even the best codebreakers of the day considered them impossible to crack. Yet, through a combination of mathematical genius, engineering brilliance, and relentless perseverance, Allied codebreakers at Bletchley Park achieved the impossible.

The breaking of the Enigma code is widely regarded as one of the greatest intellectual achievements of the 20th century. It shortened the war by an estimated 2-4 years, potentially saving 14-21 million lives and changing the course of history.

The Enigma Machine: A Marvel of Engineering

The Enigma machine was not just a cipher device; it was a marvel of electromechanical engineering that represented the cutting edge of 1930s technology.

How Enigma Worked

The Enigma machine enciphered messages through a complex series of electrical pathways:

1. Keyboard: The operator typed the plaintext message
2. Plugboard (Steckerbrett): Connected letters in pairs, swapping them before encryption
3. Rotors: Three or four rotating wheels, each with 26 contacts on each side
4. Reflector (UKW): Sent the electrical signal back through the rotors via a different path
5. Lampboard: Displayed the encrypted letter

The brilliance of Enigma lay in its polyalphabetic substitution: each time a key was pressed, at least one rotor advanced, meaning that the same plaintext letter would never be encrypted as the same ciphertext letter twice in a row (unless the rotors returned to their starting position).

Enigma’s Security Features

The Germans had every reason to believe Enigma was unbreakable:

• 158,962,555,217,826,360,000 possible settings for a 3-rotor Enigma (approximately 159 quintillion)
• Daily key changes: New rotor order, ring settings, and plugboard connections every 24 hours
• Message keys: Each message used a different starting position (indicator)
• Reciprocal encryption: If A encrypted to B, then B would always encrypt back to A
• No letter could encrypt to itself: Due to the reflector design

For comparison, if someone tried to break Enigma by brute force, testing one million settings per second, it would take longer than the age of the universe to try all possibilities.

The Polish Foundation: The First Cracks

The story of breaking Enigma begins not in Britain, but in Poland, where mathematicians at the Cipher Bureau (Biuro Szyfrów) made the first crucial breakthroughs.

The Polish Cipher Bureau

In 1928, German cipher experts began working on a machine cipher. By 1932, the German military had adopted Enigma. Recognizing the threat, the Polish General Staff’s Cipher Bureau, led by Colonel Gwido Langer, began studying German radio traffic.

The Three Polish Mathematicians

Three brilliant mathematicians from Poznań University joined the effort:

1. Marian Rejewski (1905-1980): The primary codebreaker who made the first breakthrough
2. Jerzy Różycki (1909-1942): Developed methods for determining rotor order
3. Henryk Zygalski (1908-1978): Created the Zygalski sheets for finding rotor starting positions

Rejewski’s Breakthrough

In late 1932, Rejewski received documents from a French intelligence source (later identified as Hans-Thilo Schmidt, codename “Asché”) that contained sample Enigma messages and their plaintext. Using these, Rejewski deduced:

• The internal wiring of the Enigma rotors
• The structure of the plugboard connections
• The operation of the reflector

By 1933, Rejewski had built a replica of the Enigma machine without ever having seen one.

The Bomba and Zygalski Sheets

The Poles developed several tools and techniques:

• The grillage method: For determining plugboard connections
• The clock method: For finding rotor order
• The bomba (not to be confused with the British bombe): An electromechanical device for finding rotor starting positions
• Zygalski sheets: Perforated sheets that, when overlaid, revealed possible rotor settings

The 1938 Crisis: Increased Complexity

In 1938, the Germans increased Enigma’s security:

• Added two new rotors (IV and V), increasing the number from 3 to 5
• Added a fourth rotor position for the ring settings
• Increased the number of plugboard connections from 6 to 10

These changes dramatically increased the number of possible settings, making the Polish methods ineffective. With war approaching, the Poles realized they needed help.

The Warsaw Meeting: Sharing Secrets

On July 25-26, 1939, just weeks before the German invasion of Poland, the Poles held a secret meeting in the Kabaty Woods near Warsaw. They shared their Enigma knowledge with French and British intelligence representatives, including:

• Replicas of the Enigma machine
• Documentation of their codebreaking methods
• Blueprints for the bomba
• Training on their techniques

This act of selfless cooperation, coming at a time when Poland itself was about to be invaded, laid the foundation for Allied Enigma-breaking efforts.

Bletchley Park: The Codebreaking Factory

With the Polish contributions and the outbreak of war, British codebreaking efforts moved to Bletchley Park, a Victorian mansion in Buckinghamshire, England. What began as a small operation would grow into a massive, secret city of codebreaking.

The Government Code and Cypher School (GC&CS)

Bletchley Park was the headquarters of GC&CS, the British codebreaking organization. Under the direction of Alastair Denniston, and later Edward Travis, it employed over 10,000 people at its peak, including:

• Mathematicians and cryptanalysts
• Linguists and classical scholars
• Engineers and electricians
• Administrative staff
• Wrens (Women’s Royal Naval Service) who operated the machines

Hut 6 and Hut 8: The Enigma Huts

Enigma breaking was primarily the responsibility of two huts:

• Hut 6: Focused on German Army and Air Force Enigma messages (led by Gordon Welchman)
• Hut 8: Focused on German Navy Enigma messages (led by Alan Turing)

The separation was necessary because the different services used Enigma differently:

• Army/Air Force: Used 3 rotors from a set of 5
• Navy: Used 3 rotors from a set of 8 (later with the M4 variant)
• Different plugboard patterns
• Different operating procedures

Alan Turing: The Father of Computer Science

Alan Mathison Turing (1912-1954) was the brilliant mathematician who became the driving force behind British Enigma-breaking efforts. Often called the “father of computer science,” Turing’s work at Bletchley Park laid the foundations for modern computing.

Turing’s Contributions

1. The Bombe: Turing’s most famous contribution was the bombe, an electromechanical device designed to find the daily Enigma settings.

   • Named after the Polish “bomba” but completely redesigned
   • Built by the British Tabulating Machine Company
   • Each bombe was about 2 meters tall, 2 meters wide, and 1 meter deep
   • Contained 36 Enigma equivalents (one for each letter of the alphabet)
   • Could test 17,576 possible settings per minute

2. Banburismus: A statistical method for determining the rotor order and ring settings

3. The Turingery: A cryptanalytic process for breaking Naval Enigma

4. Delta-kappa: A method for exploiting “cribs” (known or guessed plaintext) in messages

The Bombe in Action

The bombe worked by exploiting the fact that no letter could encrypt to itself (due to the reflector). This meant that if a message contained a “crib” - a known piece of plaintext - the bombe could eliminate impossible settings.

Process:

1. A crib was identified (e.g., weather reports often contained the word “WETTER” - weather)
2. The crib was aligned with the ciphertext
3. The bombe tested possible rotor settings
4. When a contradiction was found (a letter encrypting to itself), that setting was eliminated
5. The remaining settings were the possible solutions

At its peak, Bletchley Park operated 211 bombes, each working 24 hours a day.

The Naval Enigma Challenge

Breaking Naval Enigma was particularly crucial and particularly difficult. The German Navy used Enigma for:

• U-boat communications
• Fleet movements
• Convoy attacks

The M4 Enigma: Four Rotors

In 1942, the German Navy introduced the M4 Enigma (also known as the “Shark” cipher), which added a fourth rotor. This dramatically increased the complexity:

• 3-rotor Enigma: 159 quintillion possible settings
• 4-rotor Enigma: 456 quintillion possible settings

For ten months, from February to December 1942, the Allies were unable to read Shark traffic. This was the Blackout Period, during which Allied shipping losses soared.

The Capture of U-110

The breakthrough came on May 9, 1941, when the British captured German submarine U-110. The crew abandoned the submarine before it sank, and Royal Navy sailors boarded it, recovering:

• The current Enigma settings
• Codebooks
• The “Kurzsignalheft” (short signal book)
• Operating instructions

This material, combined with subsequent captures (notably U-559 in October 1942), provided the “cribs” and information needed to attack the 4-rotor Enigma.

The Turingery and Four-Rotor Breaking

Turing and his team in Hut 8 developed the Turingery, a method for breaking 4-rotor Enigma:

1. Banburismus was used to determine rotor order
2. Cribs were identified from known message formats
3. The bombe was adapted to handle four rotors
4. Traffic analysis helped identify when settings changed

By December 1942, Naval Enigma was being read regularly again.

Colossus: The World’s First Electronic Computer

While the bombe was electromechanical, the Allies also developed the world’s first electronic, programmable computer to help with codebreaking.

The Need for Speed

The Lorenz cipher, used by the German High Command for strategic communications, was even more complex than Enigma. It used:

• 12 rotor wheels (compared to Enigma’s 3-4)
• A teleprinter code (Baudot code) instead of letters
• More complex encryption

Breaking Lorenz required faster computation than the bombes could provide.

Tommy Flowers and Colossus

Thomas Harold Flowers (1905-1998), a Post Office engineer, designed Colossus, the world’s first electronic computer. Key features:

• Used 1,800 vacuum tubes (thermionic valves)
• Operated at 5,000 characters per second
• Was programmable using patch panels and switches
• Could perform logical operations (AND, OR, NOT)
• Used a clock speed of 5 MHz

Colossus Mark 1 became operational in December 1943, and Colossus Mark 2 (with 2,400 tubes) followed in June 1944. By the end of the war, 10 Colossus computers were in operation at Bletchley Park.

Colossus’s Achievements

Colossus was used primarily to break the Lorenz SZ42 cipher, used for:

• Hitler’s personal messages
• High Command communications
• Strategic plans and orders

Colossus’s work provided intelligence that:

• Confirmed the success of the D-Day deception (Operation Fortitude)
• Revealed German troop movements and intentions
• Aided in the planning of Allied offensives

The Secrets of Colossus

Due to its importance, Colossus was kept top secret even after the war. Its existence was only revealed to the public in the 1970s, and full details were not declassified until the 2000s.

Ultra Intelligence: The Impact of Codebreaking

The intelligence obtained from breaking Enigma and other ciphers was given the codename Ultra. Ultra intelligence provided the Allies with:

• German military plans and orders
• U-boat positions and hunting patterns
• Supply and troop movements
• Diplomatic communications
• Technical developments

Ultra and the Battle of the Atlantic

Ultra intelligence was particularly crucial in the Battle of the Atlantic:

• Revealed U-boat patrol lines
• Identified U-boat “wolf pack” tactics
• Allowed convoys to be rerouted away from U-boat concentrations
• Enabled the targeting of U-boat supply vessels

Result: The tide of the Battle of the Atlantic turned in mid-1943, with U-boat losses becoming unsustainable.

Ultra and D-Day

Ultra played a vital role in the success of Operation Overlord (D-Day):

• Confirmed that the Germans had been deceived by Operation Fortitude (the Allied deception plan that convinced the Germans the invasion would come at Calais)
• Revealed German troop dispositions in Normandy
• Identified which German units would respond to the invasion
• Allowed the Allies to anticipate German counterattacks

Ultra and the Eastern Front

While Ultra primarily benefited the Western Allies, it also provided valuable intelligence about:

• German plans for the Eastern Front
• Soviet capabilities and intentions (through German intercepts)
• The development of new German weapons and technologies

The Cost of Secrecy

The success of Enigma breaking required absolute secrecy. Even the existence of Bletchley Park and Ultra was known only to a select few.

Need-to-Know Basis

• Only those directly involved in codebreaking knew the full extent of the operation
• Intelligence from Ultra was carefully controlled to avoid revealing the source
• “Gardening” operations (mining) were sometimes conducted to create plausible explanations for Allied knowledge

The Double Agent Game

The Double-Cross System (XX System) managed German spies in Britain. remarkably:

• Every German spy in Britain was either captured or turned
• The Germans were fed false information through these double agents
• This reinforced the deception that Enigma was still secure

The Sacrifice

To maintain the secret, the Allies sometimes had to make painful sacrifices:

• Coventry, November 14, 1940: The Allies knew Coventry would be bombed but chose not to act on the intelligence, fearing it would reveal that Enigma had been broken. (This story, while widely told, is debated by historians)
• Convoy PQ-17, July 1942: A convoy to Russia was dispersed based on false intelligence, leading to heavy losses, to protect the Ultra secret
• Individual losses: Some operations were allowed to proceed despite known risks

The principle was: The long-term advantage of reading Enigma outweighed the short-term cost of any single operation.

The Human Cost

The work at Bletchley Park took a tremendous toll on those involved:

• Long hours: Shift work around the clock, 7 days a week
• Pressure: The knowledge that lives depended on their work
• Secrecy: Inability to share their achievements or even acknowledge their service
• Conditions: Initially poor working conditions (Hut 8 was described as “a beastly, draughty, smelly, noisy place”)

Notable Figures

Beyond Turing, many other remarkable individuals contributed:

• Gordon Welchman: Head of Hut 6, developed the diagonal board for Enigma breaking
• Hugh Alexander: Chess champion who became a leading cryptanalyst
• Stuart Milner-Barry: Chess player and codebreaker in Hut 6
• Joan Clarke: Turing’s colleague and one of the few women in a senior cryptanalysis role
• Dilly Knox: Veteran codebreaker who worked on early Enigma and later the Abwehr Enigma
• Mavis Batey: Codebreaker who broke the Italian Naval Enigma and later worked on German ciphers

The Wrens of Bletchley Park

The Women’s Royal Naval Service (WRNS or “Wrens”) played a crucial role:

• Operated the bombes and Colossus machines
• Performed clerical and administrative work
• Conducted traffic analysis
• Managed the flow of intelligence

At its peak, 75% of Bletchley Park’s workforce were women.

The End of the War and Beyond

As the war drew to a close, the impact of Enigma breaking became clear:

• Estimated war shortening: 2-4 years
• Lives saved: 14-21 million
• Shipping saved: Millions of tons of Allied shipping
• Battle outcomes: Decisive Allied victories in the Atlantic, North Africa, and Normandy

Post-War Secrecy

After the war, the secrecy continued:

• Bletchley Park was quickly abandoned and fell into disrepair
• Staff were sworn to secrecy under the Official Secrets Act
• Many never spoke of their work, even to family members
• The existence of Ultra was not publicly acknowledged until the 1970s

The Legacy of Bletchley Park

The legacy of Enigma breaking extends far beyond World War II:

1. Computer Science: Turing’s work laid the foundation for modern computing
2. Artificial Intelligence: Turing’s later work on the Turing Test influenced AI development
3. Cryptography: Modern cryptographic techniques build on World War II advances
4. Signals Intelligence (SIGINT): The collection and analysis of signals intelligence became a permanent feature of modern warfare and diplomacy
5. GCHQ: The Government Communications Headquarters, Britain’s signals intelligence agency, traces its origins to Bletchley Park

The Turing Machine and Modern Computing

Turing’s theoretical work on the Turing Machine (1936) provided the conceptual foundation for:

• Stored-program computers
• The von Neumann architecture
• The concept of algorithms and computation
• Modern computer science

Many consider Turing’s work at Bletchley Park to be the birth of practical computing.

Breaking Enigma: Quick Facts

Timeline: Key Enigma Breaking Milestones

• 1918: Arthur Scherbius patents the Enigma machine
• 1926: Enigma adopted by German Navy
• 1928: German military begins using Enigma
• 1932: Marian Rejewski begins work on Enigma at Polish Cipher Bureau
• 1933: Rejewski reconstructs Enigma machine
• 1938: Germans add rotors IV and V
• July 1939: Poles share Enigma knowledge with Britain and France
• September 1939: Bletchley Park begins operations
• 1940: Alan Turing joins Bletchley Park, designs the bombe
• May 1941: Capture of U-110 provides Enigma materials
• 1941: First bombe becomes operational
• February 1942: Germans introduce M4 (4-rotor) Enigma for U-boats
• October 1942: Capture of U-559 provides M4 materials
• December 1942: Naval Enigma (M4) broken regularly
• December 1943: Colossus Mark 1 becomes operational
• June 1944: Colossus Mark 2 becomes operational
• June 1944: Ultra intelligence crucial for D-Day success
• 1945: War ends; Bletchley Park’s role remains secret

Sources and Further Reading

• “The Code Book” by Simon Singh
• “Enigma: The Battle for the Code” by Hugh Sebag-Montefiore
• “The Hut Six Story” by Gordon Welchman
• “Alan Turing: The Enigma” by Andrew Hodges
• “Codebreakers: The Inside Story of Bletchley Park” by F.H. Hinsley and Alan Stripp
• “The Ultra Secret” by F.W. Winterbotham
• “Colossus: The Secrets of Bletchley Park’s Codebreaking Computers” by B. Jack Copeland
• Bletchley Park National Museum
• The National Archives: World War II Codebreaking
• “Seizing the Enigma” by David Kahn

Visiting Bletchley Park Today

Today, Bletchley Park is a vibrant museum and educational center where visitors can:

• See the original huts where codebreaking took place
• View reconstructed Enigma machines and bombes
• Learn about the Colossus computer
• Explore interactive exhibits on cryptography
• Visit the Alan Turing exhibition
• Walk through the restored mansion and grounds

Bletchley Park stands as a testament to the power of human ingenuity, the importance of mathematical thinking, and the profound impact that a small group of dedicated individuals can have on the course of history.