How Alan Turing broke the Enigma Code and the Polish contribution

Alan Turing the British mathematician, logician and cryptanalyst was born on 23rd of July 1912 in London, his talent in mathematics and his high ability in solving advanced problems was recognized in a very early age. He later completed his undergraduate studies in 1934 in King’s College in Cambridge with honours in mathematics and in 1936 he published his paper "On Computable Numbers, with an Application to the Entscheidungsproblem", putting the foundations of computer science. In 1938 he obtained his PhD degree from Princeton University.

The very same year, Turing had jointed the British Government Code and Cypher School (GC&CS), part of the British intelligence organization and specifically the Foreign Office's codebreaking section. When the war was declared in 1939 its headquarters were moved at Bletchley Park, Britain’s main decryption establishment. At Bletchley Park approximately 10.000 persons were working all day long at the time, with one main goal, to break the German Enigma code! Tuning was leading a team consisted of scientists and mathematicians that was trying to break the Enigma code.

The Polish Contribution

In fact, the Polish had already broke the Enigma Code in 1932. A team consisted of young mathematicians, with most notable Marian Rejewski, Henryk Zygalski and Jerzy Rózyki had already found a way to figure out how the machine worked. While the English that same period used linguistic experts to decrypt the code the Polish understood much earlier that the key factor for finding the solution were mathematics.

This team worked at the Polish Cipher Bureau (Biuro Szyfrów) trying to resolve the Enigma code. The things that they needed to know to decipher it was firstly to know how the machine operated, secondly to know the rotors wiring and finally to know the daily machine settings (The Germans switched the settings almost every day). Rejewski’s thinking was brilliant, as he managed through techniques such as group theory, linguistic patterns and by exploiting the fact the Nazi used to send the daily chosen message key components (in simple words the daily machine settings) at the start of every transmission or they repeated it on the same message to come close to a solution. Figuring all those things out, the only problem left to actually make them able to read the messages the Nazi send was the internal enigma wiring. In this critical point luck helped them. A spy named Hans-Thilo Schmidt sold secrets of the Enigma to the French, those secrets contained German operating instructions of the enigma, two sheets of the monthly key settings and the plugboard settings. The French unable to make good use of the information, forwarded it to the British which in turn didn’t succeed to break the code either so the information was passed to the Polish.

The Polish having gathered all this information and with the knowledge they had, bought an commercial enigma machine and rearranged it according to the data they had gathered, the machine produced was called the Enigma Double. Later in 1938, Rejewski managed to build the so called “Bomba” (Bomba Kryptologiczna) or Polish Bomba a device that could reconstruct enigma daily keys by simulating the work of an Enigma machine. This way the Polish could read between 1933 to 1938 about 75% of the intercepted messages from the German communications. All “Bomby” were destroyed by the Polish in 1939, when the Germany invaded Poland. Although, the same year in a meeting in Pyry near Warsaw, the Polish gave to the French and British information regarding their decryption techniques and equipment. Meanwhile, one year earlier the Germans had increased the machine security and made the machine more complicated. The Polish had no resources to cope with that and everything was back to square one.

How does the Enigma machine work

At this point it is really important to be more explicit about what the Enigma machine was and how it worked. The Enigma machine is an electro-mechanical device invented by the German engineer Arthur Scherbius. This machine is in fact a scrambler-machine that was usually used in military services, more widely in WWII by the Nazi to protect their military communications. It was consisted of a keyboard, a plugboard, rotors, a reflector and a lampboard. But how does it works? Well, to put it simply this cipher device could substitute a letter with another so the person that was using it could encrypt messages, it transcribed information.

The image below can help you see the “journey” a single letter does passing thought the machine’s complex installation.

The operator just typed a letter which was scrambled through the rotors and another different letter was displayed in the lampboard. The person that received the encrypted message could decrypt it by knowing the exact settings of the machine.

How did Turing broke the Enigma Code

Now let’s go back to Turing and see how he managed to break the Enigma Code. Using the intelligence acquired by the Polish, Turing made the assumption that each German message contained a crib, which means plaintext, a known and familiar or guessed piece of text the German would use in every message. For example, the Nazi used to transmit every day the weather forecast so the word “wettervorhersage” (in English weather forecast) would appear in the same position in most messages. Also, a word that was used in every message was the phrase “Heil Hitler”, which the Germans would put in the end of every message.

These crucial components were really helpful in decreasing dramatically the number of the possible Enigma settings. But all these flaws came from human errors, so one can think did the machine itself have any flaws? The answer is yes the device did had a single flaw, that flaw was that a single letter could turn to any letter other than itself. For example, the letter A could become any other letter but never A. Since it was almost impossible for humans to go through all the possible combinations and of course there was not enough time, Turing designed in 1939, along with colleague Gordon Welchman, a machine similar to the Polish “Bomba” the British “Bombe”.

(Replica of British "Bombe")

The first “Bombe” was called “Victory”. “Victory”, better and faster from the “Bomba”, weighted a ton and had the exact internal wiring of the Enigma, could check approximately 17,500 possible positions until it finds a match when the letters obtained from the crib were allocate in it. The machine would stopped working when it found the correct pair of letter, so in a way the “Bombe” used logic to dismiss possibilities. When the correct answer was revealed part of the Enigma key was known, so they could figure out the other part and use the key for every message that was intercepted. About 200 “Bombe” devices were built and worked all day. Until the end of the war about 2 million messages were decrypted and it is said that breaking the Enigma code shortened WWII by 2 years.

It is needless to say how important Turing’s contribution to humanity was. His legacy is huge! His contribution, as the father of modern computer science, in this particular field was huge. Also he contributed in others fields such as artificial intelligence, mathematics and cryptanalysis.

The died on the 7th of June 1954 from cyanide poisoning. When his body was found a half-eaten apple was laying in his bedside. It is said the apple he consumed contained the fatal dose. His death was determined to be a suicide, but it is unclear until today whether it was a suicide or an accident, some talk even about murder.

The urban legend says that the half-eaten apple had inspired the Apple logo, it was a way to honor Turing’s contribution to computer science.

Well maybe that is just a tale, but one thing is sure Alan Turing was a genius!

Sources:
https://en.wikipedia.org/wiki/Alan_Turing
https://www.britannica.com/biography/Alan-Turing
http://www.bbc.co.uk/timelines/z8bgr82
https://en.wikipedia.org/wiki/Enigma_machine
http://enigma.louisedade.co.uk/howitworks.html
https://en.wikipedia.org/wiki/Cryptanalysis_of_the_Enigma

Photos Source:
1 2 3 4 5