The History and Mathematics of Codes and Code Breaking

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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.

Allied Success and German Error

As we know from history, the Allies were successful in cracking the Axis' encryption methods. A major part of this success, as Singh states, is German overconfidence. Another reason for their success was simply limited ability. The Enigma Machine, as impressive as it was, was restricted by possible plug board settings and scrambler combinations. The limitations of the machine combined with its extreme complexity and German laziness, led to repeated message keys, cillies, and stereotypical messages. As a result, the Allies were able to exploit cribs and this helped lead to the cracking of the Enigma. Allied success in with decryption, relied on German limitation. The Enigma was indeed limited, and this allowed the Allies the chance to break the code. German laziness also helped the Allies exploit the weaknesses in Enigma as they helped make it more predictable and pattern based.

Allied success did not only lie in German error. It also relied deeply on their own coding ability. The Allies had very strong encryption methods, such as the Typex, the SIGABA and the Navajo code talkers. Knowing that they had sound encryption methods allowed them to focus more on the decryption of Axis codes, rather than struggling to encrypt their own codes. Being able to focus their efforts on decryption played a major role on breaking the Enigma and other Axis coding methods. The difference between the Axis and the Allied forces was simply that the Allies had stronger encryption methods. In the end, Allied success was based off of the fact that the Allies won the coding 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.

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.

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One overlooked important contribution to Allied success in cracking Enigma was that the Allies had knowledge of the structure of Enigma machines; had the Germans kept Scherbius’s invention as classified as possible—including exactly how many scramblers were used and the plugboard—efforts on the Allied side would have been much more stymied by pure bafflement of how the text could have even been conceived. Without knowing that there were scramblers, how many of them were employed, and how they worked, their progress would have been much more set back. They wouldn’t even know where to start, since all previous methods of decrypting messages would render to be useless. To guess out of the blue that there are 3 scramblers in effect in addition to a plugboard would have required some great intellectual leaps itself. 

Another flaw lies in the inherent structure-oriented nature of militaries.They always fall to regimented schedules, customs, and chain of command. In a way, they are sort of formulaic. In ROTC, we often write up memorandums, which is the main way formal messages are communicated through the detachment, and they always follow a certain template: the date is always in a specific location and distance away from the edge of the paper, the first line is always “MEMORANDUM FOR…”, the line after that is always “FROM”, and the line after that is always “SUBJECT.” Knowing this, the intense structured military environment allows no room for subjectivity, which reduces individual creativity and expression. It will always follow an objective that has been laid out for someone to fill in the blanks. Its repercussions can be seen in two areas: the location and repetition of the scrambler settings for the next message and the weather report that usually came at 6am every day. 

Had the weather report not contained the German word “weather” as the second word of each message and rather been incorporated into differently structured sentences (today’s weather is…the weather for today…it appears that it will rain at 1600 today…etc.) this would have drastically reduced the amount of cribs available for the code breakers. Unfortunately, under normal circumstances, it is unfavorable to deviate from the norm. Because that’s not how militaries work. In the military, they rely on unison and synchronicity. If a soldier decided to put a potentially life saving device in a pocket that was not designated for that device and ended up in a life threatening situation, he might not make it because other soldiers count on the fact that that device will always be in a specific pocket, which in this case is not. This wastes time and reduces efficiency. These are some other important factors that led to Allied success in cracking Enigma.


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How can we make security more "secure"?

On page 99 of Little Brother by Cory Doctorow, Marcus delineates the flaws of cryptology and how ultimately cracking the Enigma led to the victory against the Nazis in WWII. One of the flaws was secrecy; after Alan Turing cracked the Enigma, any Nazi message could be deciphered because “Turning was smarter than the guy who thought up Enigma” (99). As a result, it sparked the thought that any security system is “vulnerable to someone smarter than you coming up with a way of breaking it” (99). Bruce Schneier also refers to flaws of a security system in his Afterword, explaining that it is useless for you to come up with a system entirely by yourself because there is no way for you to detect flaws in your creation. You are limited to your knowledge. Outsiders with different levels of thinking would help by suggesting different views in which people can think of in order to break the system.

I think that this concept is interesting; you are limited by what you know. And everyone around us knows something that we don’t. Recently I read a passage in Harvard Business Review on how companies and organizations should welcome people in different kinds of fields to evaluate an idea because they won’t think the same way that people in a particular company does; a mathematician thinks differently than a historian does, and the distance between their thinking has the potential to bolster ideas, limit flaws, and suggest new ideas that haven’t been thought of yet. Could this be the way to strengthen our current security systems? What kind of people do we need to evaluate them? How many people do we need (until we pass the point to where the security measure is too widely known and therefore ironically more vulnerable)?

I believe this is one of the fundamental qualities of Cryptology and all security measures: how do we know a system is safe to use? Truth is, we really don’t know, but we can always come closer by cross referencing and past experiences, allowing security to get better and better with each step of the way.


There's Always Someone Smarter

A passage from Cory Doctorow's Little Brother that caught my attention was "[t]he problem had been that Turing was smarter than the guy who thought up Enigma.  Any time you had a cipher, you were vulnerable to someone smarter than you coming up with a way of breaking it (99)."  It first caught my attention because we just recently discussed World War II and Bletchley Park, where Alan Turing broke Enigma.  Second, when Marcus, the main character of the novel, said "you were vulnerable to someone smarter than you coming up with a way of breaking it," I was reminded of the several in-class discussions about always assuming your cipher is breakable.

Throughout history, there have been several instances where cipher makers have been overconfident in the security of their ciphers.  For example, in the 16th century, Mary Queen of Scots employed a substitution cipher, using numbers and symbols.  Unfortunately for her, she placed too much confidence in both her cipher and her contacts, and by the use of frequency analysis, her cipher was broken, and her plot to escape imprisonment and murder Queen Elizabeth I was unveiled.  In 1587, Mary Queen of Scots was executed.

Another example of cipher overconfidence came from the Germans during WWII.  Their Enigma was incredibly secure, so naturally the Germans assumed that it was unbreakable.  However, the British had a team of highly intelligent mathematicians on their side, including Alan Turing, who discovered a flaw in Enigma, and was therefore able to break it.  He created a machine called a "bombe" that was able to break the daily German Enigma key.  The Germans were unknowingly sending intercepted and decipherable messages.  Their overconfidence in their cipher led to their ultimate downfall.

Overconfidence in one's security plays a large role in Little Brother.  With the Department of Homeland Security monitoring nearly everything from transportation routes to Internet usage, Marcus and his friends were in serious need of ciphers and codes to protect their privacy.  Marcus learns early on that with every bright idea, there exists another that is better.  Most likely, there is always someone who's smarter.

The Allies Work Better Under Pressure

It is no secret that Allied code breakers bested German code makers during World War II which contributed enormously to an Allied victory in the war. Germany's overconfidence in the strength of its Enigma cipher definitely contributed to the Allies' code breaking success, but another main contribution was the pressure that Germany forced against the Allies. The Allies were on their heels trying to defend against Germany, which led countries to band together and individual cryptographers to band together to fight a common enemy. The necessity for the Allies to break Enigma in order to thwart the Axis' attacks brought Poland, England, France, and America together which gave them the resources to crack Enigma and Purple (Japan's encryption method).

Without the pressure the Axis powers were putting the Allies under, they would not have felt the urgency to break Enigma and Purple. The Allies won this war on intelligence because they were on the defense and needed to break Enigma and Purple in order to turn the tables against the Axis, while the Axis got complacent and confident about their machines because they were able to advance through Europe and the Pacific without their code being decrypted. Since the Allies were under such pressure, they had to find a way to gain the advantage. Therefore, countries such as Poland and England teamed up and individuals such as the mathematicians at Bletchley Park teamed up to crack the Enigma and Purple ciphers. Without the pressure that the Axis' exerted on the Allies, the Allies would not have been so desperate to find any way possible to crack Germany and Japan's seemingly unbreakable ciphers.

1 Comment

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.


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