The History and Mathematics of Codes and Code Breaking

Tag: Bletchley Park (Page 1 of 2)

Factors of Victory

Singh argues that German overconfidence in their Enigma was the main reason for Allied crypt analysts cracking the German's monstrous cipher. However, if it were not for the involvement of the Polish in the cracking of early Enigma, the Allies would not have had valuable information to crack the cipher.

During the German invasion of Poland, Polish officials gave the British all the information they had on Enigma. This gave the British the head start they needed to further allowed crypt analysts at Bletchley Park to construct new Bombes and other methods to deconstruct the Enigma cipher. This eventually lead to innovations of technological breakthroughs such as the Colossus that ultimately helped end the war.

On another front of the war, the Americans started to use the Navajo language as a means of communication during WWII to help keep secure transmissions. This was a major stepping point for the Allies because the language was hard to make sense of due to conjugations, and it could be used quickly. Additionally, when plain text messages were hidden in another language and further encoded using other cryptographic methods, Navajo Coder Talk was borderline unbreakable. Because of all this, the Navajo Code Talkers were instrumental in pushing Americans to the Japanese coast in WWII.

Advancements made by the Allies in WWII echo their importance, even to this day. Without Polish involvement in the cracking of Enigma and the Navajo Code Talkers, the Axis powers would have had an overwhelming advantage in the war. Thanks to both of these key examples of cryptography, we can analyze their importance to give new perspectives to WWII.

Never Become Lazy and False Genius During War

The Germans had created one of the strongest ciphers of seen with the invention of the enigma. If they had kept standard practices and routine shifts in keys the cipher would have been impossible to decipher. The Germans originally planned on continued randomization of the day keys and plugboard settings. As the war went on, the randomness decreased and they began to use the same day keys and with more of a pattern. The Allied forces were able to build on the Polish achievements and spot these patterns, or cillies as they called them. Often times the same key would be used repeatedly just for the sake of easiness, disregarding the need for more security.

Another point of weakness in the German enigma was that methods in which they believed made their machine more secure actually made it easier to decrypt. Their idea that never making a swap between adjacent letters actually eliminated two possibilities on the plugboard. Also, never allowing a scrambler to be in the same spot two days in a row made sure that the same number was never repeated or that a scrambler was never in the same place twice. The codebook compilers reduced by half the number of possible scrambler arrangements as stated in The Code Book. This greatly reduced the combinations that codebreakers at Bletchley Park had to attempt.

The Germans had an impenetrable cipher that was flawed with human error. The Allieds Tipex and SIGABA ciphers both went unbroken throughout the entire war due to their increased complexity and diligence with sticking to proper protocol.

The Allies’ Teamwork Against the Germans’ Human Error

While the Germans’ overconfidence in the strength of Enigma was a primary factor leading to their loss in the World War II, I believe how the Allies worked in a united and coherent way also significantly influenced the outcome of the battle of cryptography. The French Secret Service first obtained the documents that suggested the wirings of the military Enigma machine, and then handed them to the Poles so that the Biuro Szyfrów could try to crack the Enigma with such a starting point. Furthermore, after the Poles successfully broke the Enigma cipher for several years but were no longer able to decipher the Germans’ messages when more scramblers and plugboard cables were added, they offered their code-breaking techniques to the British and the French, letting them continue the decipherments. Therefore there came the stories at Bletchley Park and Alan Turing’s well-known accomplishments. If any one of France, Poland and Britain was unwilling to share its information and works with others, the Allies might not break the Enigma because no one would have enough resources indispensable to cracking the codes.

In comparison to the Allies’ teamwork, the Germans, interestingly, compromised their own cipher. Germans are always acknowledged as procedural and rigid; with these characteristics they sometimes yielded advantages in the war in which the order and decisive operations mattered. However, their adherence to rules also resulted in flaws in their encryption. The repetition of message keys, and the rigidly structured weather reports were exploited by the Allies to crack the Enigma. Without the human error on the German side, it would take the Allies more time to break the code and end the war.

An Interdisciplinary Approach

While German overconfidence in the enigma did eventually contribute to the cracking of the code and their subsequent downfall,  the use of mathematicians and scientist as opposed to linguists and classicist ultimately made the most difference. Many mathematicians and scientists are interdisciplinary. For example, Alan Turing was both experienced in math and building machines. Being interdisciplinary helped the breaking of the Enigma to be approached in both a creative and a logical sense. As opposed to the linguist and classists, that may just look for the patterns within the code, mathematicians and scientists will find the algorithm within the code and  the applicability behind the code and then find a method to apply it broadly. But while there were many mathematicians and scientists, Bletchley park was also made up of "an authority on porcelain, a curator from Prague Museum, the British chess champion and numerous bridge experts" (Singh, 178). This gives breaking the code many different ways of thinking and approaches. I think this mixture of knowledge filled the need to balance both creativity and logic. This is a balance that is needed to break any code. I also think that their motivations behind breaking the codes also had a huge impact. For the British it was a matter of breaking this codes in order to save more lives and keep their country safe. On the other hand, the original way of finding out more about the Enigma was through Hans-Thilo Schmidt's want for revenge on his brother and damage of his country's security. So while the Bletchley park codebreakers were compelled to figure out Enigma for their own countries' sake, Schmidt was driven by hate for his country and his own brother.

Let's Go De-fense! *clap, clap, clap-clap-clap*

Certainly the Germans' overconfidence in the power of Enigma led to their loss in the battle of cryptography in World War II, and my classmates have brought up many other great reasons: how the Allies worked together, a few genius individuals working for the Allies, the American use of Navajo code talkers, human error on Germany's part, and Poland's (specifically Marian Rejewski) contributions to cracking Enigma. But stepping back from that, I think in the grand scheme of things it comes down to who was playing offense and who was playing defense. In general, Germany was on the offensive: the Blitzkrieg bombing of Britain, the invasions into France, and their U-boats in the Atlantic. This made the Allies often on defense, not entirely sure where and when Germany would attack next. Because of this, I think they found it more imperative to crack Enigma; if the Allies knew when the next bomb would fall, or where German troops were camped, or where the U-boats were headed, they wouldn't be caught by surprise and could be far better prepared to fight back. Therefore they were willing to hire thousands of codebreakers to work at places like Bletchley Park, and invest money in a seemingly crazy machine to break Enigma. Until Enigma was completely broken, Germany did have the upper hand, and they weren't as worried about deciphering Allied messages as long as they kept winning battles and advancing.

When the Allies (thanks to Alan Turing and his machine) were finally able to decipher any Enigma message everyday, British officers recognized the advantage they now had, one that would only be kept if Germany continued to think they were still on offense. So the Allies were very careful to not let Germany know of their success, and only here does Germany's overconfidence in Enigma come into play. Up until this point they had every right to be confident in the secrecy of many of their communications, and it showed as they swept across Europe. But England could never do a perfect job covering up what they knew, and Germany's overconfidence in Enigma led them to ignore that. In the football game of World War II, the Allies defense had intercepted the football and were running for the touchdown, while Germany's offense still thought they were advancing towards their field-goal range and their cryptographic defense was off taking a water break in the locker room.

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Fear: a powerful motivator

German’s overconfidence in their “unbreakable” enigma machine surely contributed to the Allied cryptanalysts’ victorious over German cryptographers. At the same time, other key driving forces that might have enormously contributed to the success of the Allied cryptanalysts were their consistent sense of insecurity and fear of being defeated in the war.

While the allied first laid back and lost their cryptanalytic zeal believing that Germany was no longer a threat, Poland, as a newly formed independent state, realized the danger of being in between Russia and Germany and therefore, at the time, any information regarding the two enemies was highly valued by the Poland cryptographers. The Poles tried everything they could to attempt to make a progress, including forming a new cipher bureau, employing a clairvoyant and paying to make Schmidt turn traitor to German to provide the information for the Allied to create a replica of the Enigma machine.

Similarly, after Poland shared Rejewski’s bombes with the Allied, the Bletchley Park was formed and the continuous evolvement of the enigma machine motivated this group of talented people to keep taking risks, being creative, pushing and exploring the boundaries in order to break this seemingly unbreakable enigma machine. They tried to figure out any weakness not only of the enigma machine but also of those who used enigma. With German’s overconfidence and the Allied enormous effort driven by the fear and threat of being kept in the dark from German, eventually Allied cryptanalysts victorious over the German cryptographers and ended the war earlier than it could be.

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Enigmatic Ingenuity

     While there are many reasons for the Allied cryptanalysts’ hard-won victory over the German cryptographers, the human factor—and German underestimation of its impact—stands foremost in my mind. Enigma machines, radios, weapons—these are all well and good, as long as people know how to use them. Clearly, the Germans were overconfident in the security of Enigma, but this overconfidence goes hand in hand with underestimation of the potential impact of human ingenuity and error.
     For the Germans, the Enigma machine initially provided an entirely secure method of communication. However, as time went on, the Enigma operators grew sloppy. They began using repetitive words, formed habits that allowed the Bletchley Park to break the Enigma. While the Germans could have placed less confidence in the security of the Enigma machine, they also could have recognized the potential for human error. Blinded as they were by the shininess of the Enigma machine, the Germans somewhat forgot about the people who were operating the machines. Humans, as it is said, are creatures of habit, and the German Enigma operators were no exception.
    For the British, German underestimation of the human factor proved critical in their path to victory. The Germans' mistakes did not just provide Bletchley Park with sufficient data to get a grip on the encryption. The underestimation of human ingenuity on the British side also resulted in the successful cryptanalysis of the Enigma code. The Germans seemingly did not predict the formation of an organization like Bletchley Park, where the best and brightest in every field related to cryptography, and many entirely unrelated. The British pulled in crossword addicts, scientists, bridge players, world class mathematicians, and history buffs. This ingenious mixture of people all thrown into the high pressure situations of worldwide war, working together, came up with many brilliant solutions to the Enigma problem. The Germans appear to not have thought of this possibility, or of the potential ingenuity of the people pulled together, and their subsequent capitalization on the errors of German cryptologists. The situation can really be viewed as one German Enigma operator and a machine against a diverse team of the brightest in the world. In the end, the human factor on both sides--error on one, and ingenuity on the other--resulted in British victory.
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The Importance of Logic

A confidence boost from winning the First World War led many Allied countries to lose their motivation for solving Enigma as they lacked the driving factors of fear and hardship that had provoked their initial incentive to win the war. This quickly caused German overconfidence in the security of Enigma, instigated by both the lacking effort of the Allied forces and the strength of the code itself. The Germans’ unshakable faith in their coding system would ultimately lead to their defeat as they mistakenly viewed Enigma as unbreakable.

While many other Allied countries initially gave up in most of their attempts to solve the code, Poland luckily realized the importance of having skilled cryptanalysts. Poland’s decision to hire mathematicians to solve the mechanical cipher of Enigma was one of the most crucial factors in the Allied success. By taking this mathematical approach, the cryptanalysts studied the machine’s operations and were thus able to analyze the scramblers’ and plugboard cablings’ effects.

Though creativity is an essential part of cryptanalysis, the Allied cryptanalysts used mathematics to focus more on the logical aspect of code breaking. By attacking Enigma through the discovery of repetition within the codes, the Allies were able to find patterns that uncovered the plaintext of the German code. In order to break Enigma, having a well-trained team of mathematicians was critical. Solving this highly advanced technology required a similar scientific approach in cracking its message.

Without Poland’s mathematical approach to solving Enigma, the Allied cryptanalysts would arguably never have cracked the code, as logic was the key factor in exposing the messages created by Germany’s cryptographers.

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The Cyrillic Projector: Forums by the People for the People

In addition to the intriguing Kryptos sculpture, Sanborn has produced numerous other sculptures that have fans and amateur cryptanalysts from around the world working together. Elonka has created an entire webpage dedicated to a transcript and discussion of the Cyrillic Projector.  With the help of a series of pictures taken by Randall Bollig, she was able to type up a transcript of the codes on the projector in order for people to have easier access to the information. This has allowed many people to put their heads together so that they can hopefully solve the previously intact cipher.

Much like the combined powers of the great minds in Room 40 and Bletchley park, Elonka’s online forum allows cryptanalysts from across the globe to work together to break through these ciphers. Obviously these people are working to crack the codes because they enjoy doing so—and not because there are lives and national intelligence at stake. If this type of forum existed during the wars, would it have benefited or hindered attempts to encode and decode messages? It would certainly increase the size of think tanks by enabling them to communicate without being physically present, but the easy access to information on the internet would have made it much easier for other powers to catch on to what exactly cryptanalysts were doing. If the technology existed back then, would forums like Elonka’s have been useful in cryptanalyst efforts?

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Brawn over brains


It cannot be denied that the brilliant minds at Bletchley park were necessary to the success of the code breaking. However, all of their work would've been null if they didn't have the money and resources to build or run the machines they needed. For this reason, the "brute force" was one of the most important factors to Allied success.

The Polish were the first to figure out a way to crack the enigma cipher. They were able to build the machines they needed to use brute force to decipher the messages. Everything was going great for them until the Germans added more elements to the Enigma Machine, meaning the Polish would've needed more machines to continue their processes. They simply didn't have the resources to make that happen. That's when they shared their findings with larger Allied forces. Bletchley Park was able to create all the machines necessary to continue cracking the codes, and had the manpower to run the machines as well.

Later on in Bletchley Park the intelligence was key to continuing to crack the codes, once the Germans fixed some of their "human error" mistakes, like repeating the day code. At this point, pure brute force was not enough to read the messages. Prior to this, though, brute force was the key element to deciphering the German messages.

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