Secrets of the Enigma machine

Science HeaderThe recent release of The Imitation Game in Irish cinemas has drawn popular attention to the Enigma machine used by the Nazis to encrypt messages. The movie is based on the biography of one of the greatest British mathematicians of the 20th century, Alan Turing, who is credited with building the first computers that decoded the messages sent by the Nazis during the Second World War. This allowed the Allies to read the Nazi military correspondence, which helped the British win the Battle of Britain and indeed had a considerable influence on the victory of the Allies over the Nazis.

The Enigma was discovered by two Dutch naval officers, who constructed the machine so that the Dutch would be able to encrypt their messages during the First World War. Holland was a neutral country during the way and they wanted to keep their messages secret from all other countries. After the war, a commercial version of the machine became available to companies which wanted to keep their correspondence secret. At the time, Germany was crushed and their army was almost non-existent so, by the mid 1920s, many Germans were seriously considering ways to seek revenge. The German military soon laid their hands on the Enigma machines and began testing and modifying them to improve their coding quality. The specialists in the field of cryptology considered Enigma unbreakable. Indeed, we are talking about hundreds of billions of combinations. The British knew that the Germans were using the Enigma for military purposes, but after some analysis they came to the conclusion that the Enigma is indeed unbreakable and they abandoned any further work on it. Meanwhile, in Poland, the Polish intelligence was putting together a team of the finest cryptologists in the country. One of the men on the team was to eventually find a solution to the problem that everyone in the world considered impossible to solve.

The Polish team included three brilliant Polish mathematicians, Marian Rejewski, Jerzy Różycki and Henryk Zygalski. They received the commercial version of the Enigma machine and some coded messages, which were obtained by tuning into the German radio frequency. People could listen to the Germans, but no one could decode the messages. After a few weeks, Marian Rejewski knew that he needed to use theory of permutations to solve the Enigma. When Hitler’s Political Party gained seats in the Reichstag, a French spy in the German cryptology office delivered schematic diagrams of the improved Enigma and a list of the keys that the Germans have already used. The keys are the essential component to decode encrypted messages. Once the key is determined, all messages could be easily deciphered. The Germans used a different key every day. This information provided by the French spy was very helpful to Rejewski. He used his mathematical genius to write down mathematical equations governing the Enigma which even in modern mathematics are considered extremely complex.

Cracking it for the first time
In late December 1932, the solving of the equations and construction of the improved Enigma, as shown in the diagrams delivered by the French spy, granted access to the German military secrets. Now Rejewski was joined by his two colleagues Różycki and Zygalski to find easier ways of decryption and build machines that could decrypt efficiently. In the meantime, the Germans kept improving the coding ability of the Enigma, so decoding messages became harder and took more time. The Poles needed to construct a machine that would find the key within minutes. Indeed, they designed and built a machine they called a “cyclometer”. The setting up of the machine took months, but then it could calculate the correct key in minutes. Zygalski came up with a method of decrypting messages using what are now called “Zygalski sheets”. These were later used by the cryptologists at Bletchley Park, where Alan Turing was working. Later the Poles built a more advanced machine called a cryptological bomb, because the ticking noise it made reminded them of a ticking time bomb. It made the decryption more efficient.

The next improvement in the Enigma allowed for an unimaginable number of combinations. The Polish cryptologists had no funds to build more advanced machines to decode the new messages and in the summer of 1939, they decided to invite the French and British cryptologists to Poland and hand over all of their work. Everyone knew that Hitler intended to start a war and so knowing what the Germans were up to was very important. The work of the Polish cryptologists got to Alan Turing at Bletchley Park and this saved Turing about nine months of work. After the meeting in Poland, each team of cryptologists was given a special identification letter; the French were X, the British were Y and the Polish were Z, hence they were the XYZ. When Poland was invaded by the Nazis, Rejewski and his colleagues moved to work in France. Later, when France was invaded, Rejewski moved to London and continued his work.

Post-war secrecy
After the war, Rejewski came back to Poland to his wife and his two children. His work on cracking the Enigma remained a secret until the late 1960s. This was because after the war, any Polish solider coming back from working in the West was constantly under surveillance. The secret government police would spy on them all of the time. If the Communists knew about what Rejewski did during the war, they would have tortured him for information. Rejewski regretted not having developed his academic career but it would have been very difficult for him to go back to University. Despite his calm and peaceful life, Rejewski, his neighbours and co-workers were constantly spied on. The letters that he and his wife wrote were read by the secret police and he was unable keep in contact with his colleagues in Poland, France or Britain. Only after he had retired, Rejewski wrote down his memoirs and gave them to the Historical Institute in Poland. In early 1970s the memoirs became public and Rejewski was visited by many journalists to tell his amazing story. However, most of the famous books already published on the history of the Enigma were mainly based on British sources. The authors of the books barely mentioned the work of the Polish cryptologists. In one book, Marian Rejewski is referred to as a woman, because the author thought that Marian was a female name.

Alan Turing did not have an easy life after the war. At the age of 39, he was involved in a relationship with a 19 year old male student and, as homosexual acts were illegal in Britain at the time, Turing was brought before court. When convicted and given an ultimatum, Turing chose to be chemically castrated instead of going to prison. He committed suicide in 1954 at the age of 41 with a poisoned apple.

Advanced and extremely complicated mathematical methods were finally implemented to solve the Enigma machine. The first ever computers were built. These would decode the Nazi messages in minutes hence giving a huge advantage to the Allies. The cryptologists did not win the Second World War, all of the soldiers fighting out on the front did. However the cryptologists made a very important contribution to the victory of the Allies and saved many lives.

Illustration: Sarah Larragy