Cryptography

The History and Mathematics of Codes and Code Breaking

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The Logic of Codebreakers Beat Enigma

In the novel The Code Book, Singh argues that German overconfidence in the strength of Enigma was a primary reason why the Germans did not win the war. According to the blog post, “Never Become Lazy and False Genius During War”, the author, Naiksj, suggests that the laziness of the Germans and the way that they never change routine caused them the war. I agree with the author's argument. The Germans would usually begin the day with a weather report and many of their messages would contain similar phrases. This allowed the codebreakers to notice different patterns in the code.

I believe that the Allied powers succeeded because of the logic of the codebreakers. The Germans used the Enigma machine in the same ways every day, and the codebreakers were logical enough to realize this. Any random person would most likely not be able to notice the patterns in the encoded messages. It takes a level of intelligence to figure out what different patterns can represent. When we were first asked what trait is most important on Top Hat the first time I said creativity. I recently changed my answer to logic because after reading more of the book, I decided that logical reasoning has to be involved in codebreaking. Creativity and luck are both important attributes to codebreaking; however, without logic, those two traits cannot do much. I believe that there needs to be a foundation of logic for a code to be broken.

Never Become Lazy and False Genius During War

A comment on another student's analysis of how the enigma was broken.

(http://derekbruff.org/blogs/fywscrypto/2017/10/08/an-interdisciplinary-approach/) (link to original blog post)

In his blog post titled "An Interdisciplinary Approach," Browkm10 shows how the creativity of the minds in Bletchley park heavily contributed to the success of the team. We talked about in class how breaking a cipher involved a certain degree of logic, creativity, and skill. Browkm10 discusses how all the major players like Turing brought diverse expertise to the table. He talks about how there were chess champions, bridge builders, and machine experts all congregated together working on the same problem. He ultimately argues that it was the combination of creativity and logic that made the defeat of the German enigma possible.

I do think, however, that he/she left out an important aspect that had to take place for the enigma to be broken, which was luck. The cipher was only able to be solved because of a few key mistakes that were made by the Germans. They didn't allow switchboards to have connections to adjacent letters, which lowers the total number of combinations by a huge amount. They also had rules about scambler placement that had the same effect. It was the logic and creativity that made breaking the enigma possible, but there were a good amount of mistakes made by the Germans as well that contributed to the Enigma's demise. I think overall the blogger made some very good points, but I think that this nuance's his/her argument.

 

Reasons contributed to the fallen of Enigma

In the blog post (http://derekbruff.org/blogs/fywscrypto/2017/10/08/the-allies-teamwork-against-the-germans-human-error/), the student proposed an interesting idea that the Allies’ teamwork and creativity outcome the German’s general traits of procedural and rigid. I voted for creativity in the class research on TopHat which asked what trait is more important for figuring out an encrypted message. Cryptography or figuring out encrypted messages should not be like repeating the dull routine of changing letters into encrypted ones. German’s procedure of obeying the rules is probably one of the factors besides their overconfidence that caused their failure in the war against the Allies.

Germans made mistakes when they used too much of repetitive words in their enciphered text. For example, they started every message with the same words to praise their leader. They also used the Enigma machine under some unsuitable circumstances. They even used the encrypting methods for the weather report. Doing this is completely unnecessary at all and is probably just a show-off of their skills. Too many resources are provided to the Allies to decipher the messages. Their compliance made them precise and loyal soldiers, but that’s their disadvantage in the war of ciphers.

In contrast to Germans’ rigidity, the Allies’ teamwork between countries improved their chance to succeed. They also have a born advantage of language. The usage of Navajo language in military encryption was ingenious and made the codes unbreakable. The Allies’ cryptographers can focus more on deciphering German messages rather than worrying about their own message security. Combing German’s disadvantage and the Allies’ advantage, even a machine strong as Enigma will fall.

Why Some Intel Should Remain Secret

Prior to the publication of Winston Churchill's The World Crisis and the British Royal Navy's official history of the First World War in 1923, the Germans were completely oblivious to the fact that their encryption system had been compromised.  Since Admiral Hall managed to make it seem as though the unencrypted version of the Zimmermann Telegram had been intercepted in Mexico, they didn't know that it had actually been deciphered by British cryptanalysts.  As we discussed in class, cryptographers tend to be overly confident in the security of their codes. Most will not assume they have been broken unless there is clear evidence that they have.  Because of this, the Germans had no reason to believe that their messages weren't secure, so they initially displayed no interest in investing in the Enigma machine after the war.

However, when the British publicly announced that their knowledge of German codes had given them a major advantage in the war, the Germans realized they needed a stronger encryption system.  This realization is what led them to adopt the Enigma machine for use in military communication encryption during the Second World War.  The formidable strength of Enigma posed a major challenge to the Allies' cryptanalysts, appearing to be unbreakable.  Although it was eventually cracked, Enigma allowed the Nazis to communicate in secrecy for a large portion of the war, giving them a significant advantage.

There are a few reasons that could explain why the British announced their knowledge of Germany's codes after World War I.  For one, they were likely motivated by pride.  They wanted to show what their cryptanalysts were capable of, possibly with the intention of intimidating other countries.  Furthermore, they probably figured that since the war was over, there was no harm in revealing the strategies they used.  However, after seeing the consequences that arose later on, it is clear that the British should have stayed quiet.  Had they kept their knowledge a secret, the Nazis might have continued to use the same methods of encryption into the second World War.  If so, the Allies would have been able to know their plans ahead of time, resulting in a much shorter and less bloody World War II.

Ethical? Necessary.

In the movie “The Imitation Game,” there is a scene that Alan Turing and his team deciphered a message indicating that there is going to be an attack on the British Navy. After celebrating for finally able to beat the Enigma Machine made by Germany, they calmed down quickly and decided not to present the message to the British Navy. It's confusing for me at first of why they chose to keep the attack as a secret, but I then understood the importance of keeping some of the messages private for the good of the big picture. It took unimaginable great effort for Turing’s team to figure out how to defeat the Enigma Machine. They can’t risk the chance to let the German Intelligence find out that they cracked the code. If they changed the Enigma Machine into other types of encrypting methods, more damage than a team of warships would be made and the war might have gone in another direction. In special times, some small sacrifices need to be made to win the war.

      It’s just like what Admiral Hall did to President Wilson. If they can’t find a source of retrieving the information that they can explain, the Germans will change the encrypting methods, and the British cryptanalysts will lose the advantage. Is it ethical? It’s probably not. However, it’s the war situation; so it needs to be treated differently. Admiral Hall did this so that the American, the most powerful country in the world, can join the Allies and fight German. It’s the war strategy and leads to an acceptable result. When the messages were spread out later, the damage made can be accepted for the privilege of the great world war.

On the other hand, after the Americans joined the Allies, it’s also helping the Americans if they have access to decipher the German messages. Therefore, it’s necessary for Admiral Hall to keep some messages secret. It’s too much to risk as they will lose all of their achievements the fact that they broke the German Code was known.

Necessity and Usability

The primary factor favouring the advancement of military cryptography is when a country realizes their war efforts have been compromised due to the lack of strong encryption. For example, Arthur Scherbius’ Enigma machine was unpopular with the German military prior to the publishing of the histories of the First World War as written by Winston Churchill and the British Royal Navy. The Germans’ had yet to discover their war efforts were been manipulated by the British and saw no need to improve their current cryptography methods. Once the Germans were made aware of their cryptographic fiasco during World War I by the two British documents, they were forced to advanced their military cryptography. The Germans saw the need for the Enigma in their war efforts and thus began mass production. It is important to note that Scherbius first saw the need to replace the ineffective cryptographic methods used in World War I while the German government did not. One person realizing the inadequacy of a country’s cryptographic methods was not enough to advance military cryptography. For example, Alexander Koch, Arvid Damm and Edward Hebern all failed to find a market for their cryptographic advancements because the need for stronger encryption was not recognized by the masses. Although the art form itself was advanced, the advancement was lost in history if recognition by the masses was absent.

A second factor favouring military cryptographic advancements is usability. During the early phases of the first World War, Germany had advanced into French territory. However, the French destroyed their landlines as their armies retreated so Germans were forced to use radio communication. The French did not need to use radios so there were no messages for the Germans to intercept and decrypt. Thus, the art of decryption was unusable to the Germans and they did not develop a military cryptanalytic bureau until two years after the start of the war.

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.

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