The History and Mathematics of Codes and Code Breaking

Tag: Bletchley Park

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.

There's No "I" in "Team"

Photo credit: "Share" by AJ Cann via Flickr CC

Photo credit: "Share" by AJ Cann via Flickr CC

A key factor to Bletchley Park's success was the collaborative efforts that were used in order to crack Enigma time and time again. After reading Singh's chapter in The Code Book that discussed Bletchley Park, one might get the idea that Alan Turing was the key to the Allied success. Alan Turing was, no doubt, a key player in the cryptanalysis that led to the Allied success. However, there were thousands of other men and women that aided in the breaking of Enigma and deciphering German messages.

One image that stands out to me that Singh wrote of were the huts in Bletchley Park. Singh illustrates these huts as hubs of collaboration between some of the brightest minds in their given field. If a cryptanalyst was working on a cipher or encrypted message and was stumped, he would pass it to another cryptanalyst. A single message could make its way around the hut numerous times, with each cryptanalyst getting one step closer to the solution until it was solved.

Within each hut there was a clear sense of teamwork, but from hut to hut there was a similar sense as well. Each hut had a specific purpose, so once one hut had done its job with a message, it would be handed over to the next hut for the next step. This ensured that each member of Bletchley Park was doing what he or she thrived at, leading to maximized efficiency as well as an overwhelming necessity and use of communication and teamwork.

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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