The History and Mathematics of Codes and Code Breaking

Tag: enigma machine

Great Mind Games, Britain

As discussed in the book, initially, the British were quiet and low-key when it came to the fact that they could decode Germany's messages during the first world war. But then, Winston Churchill and the British Royal Navy decided to let it be known that they knew how to break the codes all along. Upon learning that their codes could be broken, the Germans began to invest their smarts into the Enigma machine technology. So should the British just have stayed quiet about their decoding abilities? Personally, I say no.

By letting Germany know that they could decode their messages after the fact, I believe it could have made the British feel as if they established some type of superiority over Germany. Such as a taller person dangling an item over the head of a shorter person, knowing that the shorter individual cannot reach it. It's like a "Na-na-na-boo-boo," moment for the British. They were so proud of their achievement, of course they were not going to stay quiet about it for too long.

And even then, it is not as simple as to say that they were just proud. They knew that it would give Germany this kind of doomed feeling even though everything was revealed after the fact. Germany must have been so secure with themselves, so secure with their encrypting strategy only for them to find out that their messages could be decoding the entire time. It is like a punch in the gut, believing something of yours was great all along only to be proven that it is not really all that good. Maybe I am reading too deep into this, but I believe there could have been some type of psychological aspect to this, and if this was done just to play mind games with Germany, it was smart.

But then it led to the creating of the Enigma machine, which was maybe not particularly great, but great mind tricks, Britain.

Britain's Fallacy

The conclusion of World War I brought a sense of elation and confidence for Allies, as they brought upon the defeat of the Central Powers. Utterly convinced that the reparations burdened upon Germany would be sufficient from ever causing such blatant militarism again, the Allies embraced peace. A common phrase that was uttered to describe World War I was that it was the “war to end all wars.” The world was still reeling from the conflict but many truly believed that it was the end of large scale conflict. Publishing a full history, revealing the inner workings of the British military was an embodiment of that idea, the idealistic view that the world had indeed changed. In reality this was not the case and a blatant disregard for the rapidly militarizing Nazi Empire was one of the primary factors which led to the Second World War. The idealistic perspectives following World War 2, imagined cooperation among countries to create a peaceful era. The League of Nations is further evidence to that idea. Though idealistic, one could argue that the released knowledge spurned on the Enigma machine which led to Alan Turing’s machine which eventually became the modern computer. Additionally, it could be argued that with Hitler so paranoid of repeating the mistakes of his predecessors, a new code would have been created regardless. The release constitutes a sharp break from common cryptography practices, as the ability to break a code becomes infinitely more powerful if that ability is secret. The hope was that ciphers would never be needed again. 

The Allies' Resource Allocation

In his blog post, the student argued that besides the overconfidence of the German, the strength of the Allies' code itself contributed to the breaking of the Enigma code. I thought this was a very interesting viewpoint and never considered this before. The surprising usage of the Navajo language as military encryption proved to be unbreakable, thus allowing the Allies more time and resources allocated solely on cryptography.

The importance of resource usage and allocation is certainly important in the cryptography war. German's sloppy and careless usage of the machine played a role in the Allies' success. The machine workers made a few mistakes that wouldn't have been made if they had a certain level of understanding on the working mechanisms behind the Enigma machine. For instance, by never repeating letters in the daily scrambler settings, they actually eliminated repetitions for the Allies' cryptanalysists. On the other hand, Allies were especially protective of their codes, with only Navajo speakers controlling the content of the messages.

In addition, as the Allies had more time and resource available to focus on code-breaking, they were able to allocate the accurate resources. As they dealt with the Enigma machine, the former strategy of recruiting linguists was abandoned. They were able to focus their resources on scientists and mathematicians, and thus eventually beating the machine with another machine.

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.

Not Quite Like the Movies

For as long as I can remember, there's always been one thing about action movies that has bothered me above all else: while the bad guys can do whatever they want, without worrying about who they hurt, the good guys have to catch up to the bad guys while also attempting to contain collateral damage. It seemed so unfair to me, but the good guys wouldn't be good if they hurt everyone in their wake (which is one of the reasons why the new Superman movie was so disappointing, but I digress).

In the case of German and Allied forces in World War II, we can assume, for argument's sake, that the Germans would be the "bad guys", and the Allied forces would be the "good guys." If the pattern which caused so much of my childhood angst was being followed, it should happen that fighting the good fight would be a hinderance for the Allies. However it had the exact opposite effect. The cause that the Allies were fighting for, and the conviction that they held to complete their cause, was a major factor in their success with cracking the Enigma machine.

Singh mentions himself that motivation is a driving force in cryptography: in periods of peace, cryptographic breakthroughs are so few and far between simply because there is no need for them. In the case of Allied efforts, there was much need to break the Enigma machine. Lives were being lost at an astonishingly fast rate, and without knowledge of German plans, there was little chance for the Allied troops to make any gains. Both the higher ups and the cryptanalysts themselves understood that the stakes were incredibly high, which proved to be an incredibly motivating factor.

The need for information proved to be a very beneficial asset not only motivationally but also resourcefully. Because the Enigma machine was so complex, it required not only a lot of manpower to solve, but also a lot of machinery. Though previously in history there was some hesitation to fund cryptographic efforts, the creation of Bletchley Park is proof that Allied officials saw the need for cryptanalysis as part of their war effort. It's hard to tell how much priority cryptography would have gotten had the situation not been as dire.

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.

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.

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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