Cryptanalysis of the Enigma

The Cryptanalysis of the Enigma was a very important part of World War II. It helped the western Allies read secret messages sent by the Axis powers. These messages were coded using special machines called Enigma, which made them very hard to understand.

Enigma machines were used by Germany and other Axis countries for their secret communications. In 1932, a mathematician named Marian Rejewski in Poland figured out how to break the Enigma code. He used math and some secret information from a German spy, Hans-Thilo Schmidt. By 1939, Poland shared their methods with Britain and France just before the war started.

When Germany invaded Poland, Polish experts moved to France and kept working with the British. Later, Britain built a big team at Bletchley Park to break these codes. A mathematician named Alan Turing helped create better tools to solve the Enigma puzzles. Breaking these codes gave the Allies important information that helped them win the war.

General principles

Main article: Cryptanalysis

Enigma machines used special parts called rotors and cables to create very tricky secret codes, called polyalphabetic substitution ciphers. During World War I, inventors found that random codes without patterns could be almost impossible to break. This idea led to machines that change each letter of a message using rotors, making the code very hard to understand.

Breaking these secret codes has three steps. First, you need to figure out which machine was used. Second, you must discover exactly how the machine changes the letters. Third, you need to find the special setting used for each message. Because Enigma machines had so many possible setups, figuring them out was very challenging.

The Enigma machine

Main articles: Enigma machine and Enigma rotor details

The Enigma machine was a clever way to hide messages. It used a special method to change letters into other letters, making it very hard to read the original message.

Structure

The Enigma machine had a keyboard that you pressed to type messages. Inside, it had parts that changed each letter as you typed. These parts moved each time you pressed a key, so the same letter could change into different letters in different places of the message.

There were many ways to set up the machine, which made it very hard to break. But there were also some secrets about how it worked that helped people try to read the hidden messages.

Security properties

The Enigma machine could be set up in many different ways, which made it very safe for hiding messages. But there were some rules about how it worked that made it easier for experts to try to read the messages.

Key setting

When sending secret messages, the people using the Enigma machine had special ways to make sure both the sender and receiver had the same settings. They used sheets with settings for each day and changed them often to keep messages safe.

British efforts

In 1927, the United Kingdom bought a commercial Enigma machine to study how it worked. A skilled codebreaker named Dilly Knox, who had experience from World War I and the Room 40 team, tried to break the codes but only had his own messages to practice with. When Germany started using changed versions of these machines during the Spanish Civil War and the Italian Navy used a simpler version, Britain began to catch some of these radio messages. By April 1937, Knox successfully broke some Enigma codes using clever methods and needed help from word puzzles and knowledge of the Italian language. However, Britain still could not read the more advanced military Enigma messages used by Germany.

Polish breakthroughs

Main article: Cipher Bureau (Poland)

In the 1920s, German forces began using a special code-making machine called the Enigma. Poland wanted to understand these codes because Germany was a threat to them. A group of smart students and teachers from Poznań University helped Poland's code-breaking team.

One of these students, Marian Rejewski, found clever ways to understand the Enigma codes without knowing all the secret parts of the machine. He noticed that German code workers sometimes made mistakes, like using simple starting points for their codes. These mistakes helped Rejewski and his team figure out some of the codes.

Before Rejewski started, a person in Germany who worked with secret codes gave some information to France. France then shared this with Poland. This information helped Rejewski understand how the Enigma machine worked inside.

Rejewski and his team made copies of the Enigma machine to practice their code-breaking. They used many different methods to keep solving the codes, even as Germany changed how they used the Enigma.

World War II

Polish disclosures

As war became more likely in 1939, Britain and France promised to support Poland if its independence was threatened. In April, Germany ended a pact with Poland from 1934. Poland decided to share its work on breaking the Enigma code with its allies because of the growing threat.

At a meeting near Warsaw in July 1939, Poland told France and Britain that they had broken the Enigma code. They gave each ally a copy of the Enigma machine and details of their methods for solving it. In return, Britain agreed to make special tools for solving the code. A British expert thought the Polish method might become useless if Germany changed its rules, which happened later in August.

After this, two Polish-made Enigmas were sent to Paris. One was taken to London and given to a British intelligence officer.

A British expert wrote that without Poland’s help, their success in breaking Enigma would have taken much longer.

PC Bruno

In September 1939, Poland began moving its code-breaking team and equipment out of Warsaw. By September 17, they had crossed into Romania and destroyed sensitive materials. The team managed to reach Britain with help from French and British embassies and continued their work near Paris, collaborating with British code-breakers.

Operating shortcomings

The Enigma machine had some weaknesses that made it easier to break. These included:

• Using repeated letters at the start of messages, like “AAA” or “BBB”.
• Reusing the same letter patterns in messages.
• Having only a few different parts that could be swapped around.
• Sometimes using simple or predictable settings for the machine.

These mistakes helped the Allies break the code more easily.

Crib-based decryption

Code-breakers used known pieces of plaintext — called “cribs” — to help solve the encrypted messages. They kept detailed records of common phrases, names, and locations to identify these pieces in the encrypted messages.

British bombe

The British built a machine called the “bombe” to help break Enigma codes faster. It tested many possible settings of the Enigma machine to find the right one. This machine was crucial in speeding up the process of decoding messages.

Luftwaffe Enigma

The German Air Force was the first to have its Enigma codes broken regularly. The messages were decoded quickly, helping the Allies plan their strategies.

Abwehr Enigma

In 1941, British experts broke the code used by the German intelligence service. This allowed the Allies to control German spies in Britain, turning them into double agents who worked for the Allies instead.

German Army Enigma

Breaking the German Army’s Enigma codes took longer. It wasn’t until early 1941 that progress was made, and it became reliable only in the spring of 1942.

German Naval Enigma

The German Navy used a more complex version of Enigma starting in 1937. This version included extra parts that made it harder to break. However, the British still managed to decode many messages by using captured materials and clever methods.

Italian naval Enigma

In 1940, British experts confirmed that the Italian Navy was using the same Enigma system they had broken before. Breaking these codes helped the Allies win important battles, like the Battle of Cape Matapan in 1941.

American bombes

The United States also built its own versions of the bombe machines. These American machines were faster and helped break Enigma codes more efficiently, supporting the British efforts.

After World War II

The success in breaking the Enigma code was kept secret until 1974. Even after that, some countries continued to use Enigma machines into the 1960s.

In 1995, a method was found that could figure out the settings for many Enigma messages, though it still had some limits. Today, computers can help solve Enigma puzzles, and some projects work together to decode old messages.

On May 8, 2020, to remember the 75th anniversary of VE Day, GCHQ shared the final Enigma message decoded by experts at Bletchley Park. The message, sent by a German radio operator in Cuxhaven on May 7, 1945, said that British troops had entered Cuxhaven and that radio broadcasts would stop. The next message said goodbye forever.