The History and Mathematics of Codes and Code Breaking

Tag: Allies

Why did the Allies succeed in cracking the Enigma?

While most people only credit Alan Turing for cracking of the Enigma, it is important to recognize the critical role that Marian Rejewski in paving the way for the Allies’ success.

In the early days of the war, Rejewski along with the Polish Cipher Bureau were able to identify that each letter in the ciphertext was linked to a chain of letters, thus allowing them to deduce that a relationship lied between the letters. This discovery removed the mystery surrounding the aptly named Enigma as they could now discern a pattern. If a pattern is present, then it can be concluded that there was a process taken to produce that which also means that, armed with logic and a lot of hard work, the steps in that process can be deduced. Had Rejewski not made this discovery, it can be argued that Turing would never have been able to crack the Enigma as it gave him a direction to pursue and a starting position of where to do that from.

In addition to this, Rejewski’s creation of the first bomba allowed Turing to understand the importance of mechanizing the cryptanalysis of the Enigma. By using a computer to solve the Enigma, it allowed the Allies to be more efficient. And so, when Turing was finally able to crack the Enigma, due to the time saved, the information deciphered was still useful and so they were able to anticipate and prepare for Germany’s attacks.

Although Singh argues that German overconfidence is the primary reason that the Allies were able to crack the Enigma, the principal reason for the Allies success was because of Rejewski. His creativity and innovative thinking was the breakthrough that allowed the Allies to ultimately break the Enigma.

Not a Single Factor is Responsible for the Allied Success

Although Singh argues that the primary reason that the Allies had success over the Germans in the cryptographic war, I believe that this simplifies the argument way too much. While undoubtedly the Germans were overconfident in the security of the Enigma machine, this was only a problem when they became lazy and began to repeat messages, giving the Allied cryptanalysts a chance to  break their codes.

Perhaps one of the most overlooked parts of the Allied codebreaking success was the determination and resilience of the code-breakers, and on top of that how diverse they were. As a group consisting of people from so many different backgrounds, their different ways of approaching the deciphering were no doubt crucial in the Allies breaking the German codes. Furthermore, it can not be overstated how impressive the resilience of the codebreakers was. Most days they worked fruitlessly for hours upon hours in an attempt to crack the codes and got absolutely nowhere. And then as soon as the clock struck midnight all of their work from the day before was rendered useless and they had to start all over again. While this would drive most people mad, the Allied cryptanalysts continued to decipher day after day.

Finally, the Allied codes were so strong because of the rarity of the Navajo language. Trying to understand a language without any indication of what any words mean is nearly impossible and the Germans were certainly among those who discovered this. Furthermore, when they combined the language with code words it became impossible for the Germans to break it without capturing an actual Navajo who would be able to decipher the messages for them. This brilliant way to securely transmit messages for the Allies proved to be a crucial part in them winning the war.

Too Much to Lose

Although German overconfidence played a major role in the success of Allied cryptanalysts, there were many other factors at play. One of the most significant reasons for Allied success was that the Allies had much more to lose. Initially, Marian Rejewski cracked Enigma because the threat of a German invasion of Poland was extremely high. Whereas other countries such as France had given up on breaking the Enigma, the Polish had too much to lose should they fail. Rejewski and his team spent a full year creating a book full of all of the potential keys for the Enigma. When it became clear that a German invasion of Poland was inevitable, Rejewski and his team handed over their work to the British, in hopes that they might be able to use it as well.

As the Germans added features to the Enigma to strengthen its encryption, such as additional plug board options, the Allies had to step up their game. Once again, the Allies had too much to lose for them not to invest the time and resources into cryptography. For each message the British failed to decipher in time, thousands of lives could be lost. The message could be about the location of the next air raid, or where the German troops were planning to move. Should the Allies have been able to know this information in advance, they might have been able to evacuate areas or adjust their strategies. Therefore, it was incredibly important to them that they be able to break Enigma. As a result, despite some reluctance on their commanding officer’s part, cryptologists at Bletchley Park were eventually given enough resources for Alan Turing to create his Turing Machine; a machine that was reliably able to crack the daily settings for Enigma.

When the stakes are higher, people work harder. German overconfidence certainly helped the Allies to be more successful with their cryptography, however, without the imminent German threat it is unlikely that people like Marian Rejewski and Alan Turing would have had the dedication or the resources, respectively, to break Enigma. Without cracking Enigma, the war could have turned out very differently.

Two Steps Forward and One Step Back

While German overconfidence in the strength of the enigma machine was partially responsible for the downfall of the cipher, many other reasons also influenced this ultimate collapse of German enciphering. I think that another main reason that the enigma was able to be broken lies in the fact that the enigma itself was simply a machine. The industrial mechanization of the early-mid 1900’s transitioned the world from simple methods to more efficient and technologically advanced means of production and thinking. These new technologies greatly impacted the way that war was waged; planes and radios and bombs all allowed for higher casualty rates while new cryptographic methods allowed for more methodical enciphering.

Even though this mechanization of enciphering sped up the process, the complexity of the machine was almost outweighed by the simplicity of its engineering. Because it was ‘just’ a machine, the enigma machine was able to be almost reverse engineered by Alan Turing. The industrial shift in society was not just reflected in product manufacturing, but also in the ways that people thought. In one of his many papers, Turing proposed the idea of an automated calculator. While this was well ahead of the technologies available to him at the time, this shows the logical thought process which was now being used to approach breaking ciphers.

In addition, new technologies made it easier for messages to be intercepted. From the telegraph to the radio to modern communication over the internet, lines of communication are becoming increasingly more accessible to spectators. By no means am I saying that technological advances have hindered enciphering, I just think that it is important to consider how the mechanization of society influenced the thought processes and methods of decoding in and the ease with which these encoded messages could be accessed by outside forces.


A Boost of Motivation

The mindset for the Allies had changed between the First World War and the Second World War. After their success in cracking Germany’s ciphers in the First World War, the Allies felt like that could crack anything Germany tries to encipher. However, once the Germans started using the Enigma machines, the Allies were stumped. This change in attitude might be attributed to the fact that they were not in direct threat at that time so they didn’t have the motivation to try to decipher the messages. That along with the hopelessness that might come with failed attempts would make them lose motivation. Poland, however, was threatened so they had to do everything they could to decipher those messages. Therefore, with the help of Schmidt and Rejewski, they reached a breakthrough in cracking the enigma. If it wasn’t for their breakthroughs, the Allies may not have been able to crack it. Gaining that knowledge may have been the motivation they needed to fully uncover how the Enigma machine works. The Allies were also able to pick up on some keys that Germany’s operators would send. The operators would sometimes pick three consecutive letters from the keyboard which the Allies started picking up on.

Photo credit: "Enigma Machine (Bletchley Park)" by Tim Gage via Flickr CC

Photo credit: "Enigma Machine (Bletchley Park)" by Tim Gage via Flickr CC

Sometimes they would repeat the same keys and therefore the cryptanalysts would be able to predict them. Overall, cracking the Enigma took the efforts and collaboration of many individuals working as a team.

Fatal Flaws

Photo Credit: david.nikonvscanon via Compfight cc


Although the Enigma machine at first seemed nearly impossible to decode, eventually the Allies successfully were able to get breakthroughs in the machine and finally solve the Enigma machine.

A major reason for the eventual success was although the Germans used different key words each day to further stifle the Allies, the Germans sent a huge amount of these messages which gave thousands of words the ability to be analyzed. Because of the vast amount of messages sent, it gave the Allies a great number of chances to solve the Enigma machine. Perhaps if the Germans had taken a step further and alternated using the Enigma machine with a different type of encoding device, it would have given the Allies almost no chance at deciphering their messages. However, the change of key words was a brilliant idea to make the Enigma machine more difficult to solve.

Another reason for the Allies solving the Enigma machine was as a result of the Germans sending messages concerning positions of their U-boats and where others needed to be. The Allies knew where the U-boats were when attacking their boats because the Allies boats were able to be tracked. As a result, when the Germans were communicating where to go, the Allies knew what the code represented which helped them figure out the key to the Enigma machine. Had the Germans used a wider variety of codes, not sent the great number of messages encoded by the Enigma machine, and not committed this fatal flaw, the Allies possibly could have never been able to solve the machine during World War II which could have greatly affected the final outcome of the war.

Variation of Disciplines

Cryptography is an ever evolving field, and this held especially true around the time of World War II. Up until this point, most cryptanalysis had been performed by linguists and people trained in language. However, as cryptography evolved and became increasingly mathematical and technological, the personnel involved in cryptanalysis needed to evolve as well. One of the primary reasons the Allies had success over the German cryptographers was the Allies use of cryptanalysists from across many disciplines.

As discussed in class, there are many factors which go into solving a code. To break the German code required some each of creativity, logic and luck. One of the best ways to solve an abstract problem, such as breaking an enciphered message, is to think about it from many different angles and have different people each with their own different way of thinking attempting to solve the problem. As Singh noted, there were a great variety of cryptanalysists working on the German codes from mathematicians and linguists to artists and chess players. Having such varied ways of thinking ensured that if one person couldn't come up with an idea, someone else down the line would most likely be able to. Also, British cryptanalysits were specialized into various "huts" on the lawn of Bletchley park. Each of these huts had a specific directive, from working on the German Naval enigma to intelligence gathering and translation. With many different types of thinkers working on them simultaneously, each of the various tasks were able to be completed with the utmost efficiency, saving lives and ultimately helping the Allies gain a pivotal upper hand in the war.

"Hut 6, Army/Airforce Enigma codebreaking" Photo by Matt Crypto-Licensed under Public Domain by Wikimedia Commons

"Hut 6, Army/Airforce Enigma codebreaking" Photo by Matt Crypto-Licensed under Public Domain by Wikimedia Commons

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