Cryptography

The History and Mathematics of Codes and Code Breaking

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Secure? So you thought...

World War II was a well choreographed ballet of air raids, land advances and U-boat attacks that required coordination across nations. The element of surprise was vital for successful attacks; maintaining secrecy in communications was absolutely crucial in winning the war. Because there were so many operations all across the globe involved in one of two sides, each nation developed their own coded system of transmitting information. After traditional encryption techniques were cracked in World War I, World War II demanded a whole new system of cryptographic methods that had not yet been solved. Both the Germans and the Japanese turned to machines to meet these new standards. The Nazi used Enigma machine and the Japanese employed Purple machine were both inventions that digitalized the encryption process for the first time. While the British worked on Enigma at Bletchley Park, the American codebreakers focuses their efforts on the Pacific powers. They worked on cracking the Japanese code that came to be known as Purple. The disadvantage they faced, unlike the British who had a version of the Enigma machine, was that no one knew how the encryption machine had been constructed. The cipher text it produced, was determined by many nations to be unbreakable, but the American cryptographers prevailed and worked for months to crack the code and ultimately succeeded. In wrongfully assuming their communications were secure, the enemy provided America (and Britain) with imperative intelligence, allowing us to evade attacks and plan successful missions of our own, ultimately leading to our victory on the beaches of Normandy.

I Forgot to Tell You I Broke That Awhile Ago

Germany having no clue their ciphers were practically useless during the First World War was genius on behalf of British Intelligence. Britain, haven broken their cipher and not allowing Germany to know had turned out well for the Allies because it discouraged Germany from creating a new cipher. In my opinion, it made sense for  Winston Churchill and the British Royal Navy to release their histories of the war and specifically their knowledge of German encryption when they did. Doing so gave the British a lot of clout within the world of crypt-analysis and national intelligence as well as it gave the men who worked in Room 40 the recognition they deserved. Also, it would be pretty naive to think that if another war were to come about that Germany would use the same codes and encryption techniques they used previously. Even if the British had kept it a secret, Germany increased their military technology so much during WWII that it would not be a far stretch to believe they would incorporate something similar to the Enigma at some point. I think what mostly came out of Britain revealing they had broken Germany’s cipher in the way they did was to make Germany look like a disorganized and careless nation, practically saying, “We beat Germany because they were oblivious to their intelligence and because they were blinded by their own pride.”

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.

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