The History and Mathematics of Codes and Code Breaking

Reading Questions for October 26th

In preparation for class on Tuesday, October 26th, please read through page 201 in Chapter 5 of the Singh book and respond to the following questions.

  1. As we end our reading on military cryptography, what do you now say to the question of the importance of cryptography in World War Two?  To what extent was cryptography the decisive element of military victories?  Bear in mind Admiral Chester Nimitz’s quote on page 191 and Major General Howard Conner’s quote on page 200.
  2. Given the United States’ poor treatment of Native Americans over the years, what might motivate young Navajo men to join the Marines during World War Two?  What social challenges do you think they faced while serving in the Marines?
  3. Why have we not read much thus far about contributions of women to cryptography? Why does Singh limit his discussion of women at Bletchley Park to one sentence on page 161?
  4. What examples have you seen thus far of the work of cryptographers and cryptanalysts not getting the credit it was perhaps due? Is it important to give accurate credit to groundbreaking work in cryptography, mathematics, or science? Why?


Resources from October 12th and 19th – Zimmerman Telegram, Enigma Machine


Problem Set 5


  1. Sam Mallick

    1. Cryptography was certainly one of the most important factors in the Second World War. I would not go so far as to say it was the one most important factor because WWII was incredibly complicated and no one field can be isolated from any other. Cryptography was, however, among the top deciding factors in the war because the Allies utilized it incredibly effectively while the Axis’s cryptology efforts were actually self-destructive.
    2. There was no doubt a certain pride in the American-ness of Navajos–they fought because they saw themselves as American or because they wanted others to see them as American. In WWII, there was an incredible opportunity for young Navajo men to prove themselves and their nation. As for treatment by other soldiers, I’m sure there was some discrimination in the beginning, but Singh speaks of the military’s praise of the Navajo, both as code talkers and as soldiers. Any discrimination that existed in the beginning soon faded into respect for what the Navajo did for the War effort.
    3. With the exception of a few women such as Ada Lovelace, women before the 20th Century were not in a position to be prominent cryptographers because there was less education and social opportunity at their disposal. Singh’s discussion of women is so limited because it was mostly men doing the actual cryptography; women did contribute to the effort, transcribing messages and working radios, but given their handicapped social and educational position, they were not able to take a center-stage part in codebreaking. Certainly into the future, though, that will change.
    4. When we discussed plagiarism, we talked about how it was important to give proper recognition when it was due. The same holds true in the “real world” beyond academia. By all means people who make discoveries or important innovations deserve credit for their work because their efforts resulted in a contribution to society for which they should be recognized and remembered. On occasion, however, there is need to delay such recognition. We saw how Britain’s recognition of WWI cryptographers ultimately led to Germany developing stronger encryption. Even if it is long after the fact, however, credit should eventually be given.

  2. Erin Baldwin

    1. Cryptology was indisputably very important in World War II. Many important victories would not have happened as they did, if it were not for the successful use of code to relay important information and the impressive work of code breakers who were able to decode the messages of the enemy. However, without downplaying the extraordinary accomplishments of the cryptographers and cryptanalysts during the war, I would still maintain that a similar outcome may have been reached without their achievements, albeit the means of reaching the same end would have been drastically different. The allies may not have won the same battles or taken the same strategic positions without such advanced cryptology, but that is not to say that they would not have still won the war.
    2. The Navajo men were motivated, as Singh points out, by the spirit of nationalism that was rampant at the time. On the reservations, it was an especially strong feeling of the original Americans wanting to join the war effort , which was considered a very American thing to do. Those that did join though often faced discrimination and other hardships because of the cultural barriers between the Navajos and the rest of the troops. Many of the Navajo had grown up on reservations and were raised according to tradition. It was very easy for the troops to misunderstand the Navajo culture and to see them as outsiders because of the differences between their upbringings and beliefs.
    3. The contribution of women in cryptography has thus not received much attention because many women in the time periods discussed did not have the same opportunities as the men of their generations. Without the education and the job availability that was open to men, women were not in positions that were conducive to becoming cryptographers or cryptanalysts. That being said, some women like Lovelace did break through the gender barriers and others worked in the background of agencies like Bletchley Park, though for a woman to be star in a field so dominated by men, such as cryptology, was unheard of, even frowned upon.
    4. The common theme with successful codes and the breaking of great codes is that those who should receive credit for the work are often denied their glory until a long time after the fact (Alan Turing, Navajo code talkers, etc.) There of course are practical reasons for this, maybe governments do not want to release sensitive information just so an employee can be acclaimed for his work or perhaps the code/broken codes are still in use. However, when the time comes that the confidential information can be released it is important the individuals receive credit for their contributions as would their peers who had made strides in non-classified parts of the field. In addition, those who contribute to cryptology through “groundbreaking” work that others then build on should also receive credit. This would include those like Rejewski, on whose research the code-breakers at Bletchley Park relied on to break the German Enigma machine.

  3. Tanner Strickland

    1. Singh makes it very obvious that cryptography played a vital role during WWII. The ability to communicate with troops or allies in a fashion that the enemy cannot understand is an enormous advantage and proved to be a vital factor in many wartime victories. Cryptography alone did not win the war, however. If the Allies had not been as industrialized or advanced as they were, no amount of secure ciphers would have won a battle. As a result, I believe that cryptography was one important factor of the war, along with many others, such as technology and resources.

    2. The Navajos were some of the first Americans, so they probably participated in the war because of the powerful loyalty they felt, not towards the American people, but to their geographical home. Also, in Native American culture, warriors earned great respect, so WWII was an opportunity for these Navajos to prove themselves and earn respect. I would think that their biggest social challenge in the military would be to earn the trust of other soldiers because most soldiers probably did not consider the Navajos to be Americans in the same way they considered themselves Americans.

    3. Women in cryptography have not been discussed much up to this point because until fairly recently, they have not had access to the same education and resourses that men have. Cryptography is like most other academic fields with regard to the fact that women were not given the opportunity to contribute their own thoughts and discoveries for centuries. As a result, the influential discoveries of women in cryptography are probably closer to the present, which is a time period that Singh has not discussed yet.

    4. Groundbreaking discoveries in cryptology often occur in times of need, like during a war. Wartime also necessitates secrecy, so people like the Navajo code talkers do not get credit for what they have done at the time. Due to national security, this secrecy takes precedence over the recognition of those who have made great discoveries. These people do, however, deserve recognition when there is no more risk by sharing the information with the public. Just like any other scientist, inventor, or even author, every person should be accredited his or her contributions to society.

  4. Tyler Merrill

    1. I still feel like the success of Allied cryptographers was the main factor of the Allied victory. Key victories were due to the information gained by cryptanalysts. Nimitz credits the victory at Midway to intelligence and Conner credits the victory at Iwo Jima to the Navajo code talkers. Because these decisive battles were seriously affected by cryptography, cryptanalyst were the main factor that resulted in the Allied victory.

    2. Navajo men may choose to enlist as code talkers to gain the respect they had been denied for so long. They wanted to prove that they were dedicated to the country and could help the efforts in the war. While in service, they could face ridicule from white soldiers. Segregation was still present in America, so the anti-minority sentiment would most likely be prevalent in the military.

    3. During the time most of this book takes place women were considered intellectually inferior. They were left to do the monotonous jobs such as watching bombes. Singh limits his discussion of women to one sentence because they were confined to tedious jobs that did not contribute anything creative to the field of cryptography. This is not because women did not have the capacity to be cryptanalysts, but because they were not allowed to.

    4. Turing, Babbage, and Rejewski did not receive credit for their discoveries until years later. Turing and Rejewski were not given credit to keep their discoveries secret from enemies. Babbage did not receive credit because he did not publish his findings. It is important to acknowledge the success of cryptanalysts. If the British knew of the brilliance of Rejewski, they could have used him at Bletchley Park instead of a satellite location. It could have possibly saved Turing’s life. If authorities knew of his genius and contribution to the war effort, they may have ignored his homosexuality, saving his embarrassment.

  5. courtneysh

    1. Cryptography was crucial in WWII. Without cryptography, the war would have lasted much longer, and many military victories can be directly attributed to successes in cryptanalysis. For example, the decipherment of purple, the Japanese code, led to the assassination of Yamamoto. Major General Howard Conner points out a time when advances in cryptography failed to save the day, but as with all things, there is room for error and in this case, there simply wasn’t time enough to act. If it was the sole factor of the war effort, the allies would likely have not won the war, but coupled with military strategy, cryptography allowed the allies to be very successful.

    2. The Navajos saw themselves as the first American people, and fostered a great sense of patriotism. It was this that inspired them to support the war effort, but the government was offering them jobs that were likely much better paying than their other options. The Navajos were surely discriminated against in the marines, many of their men could not even distinguish between them and the japanese, which also likely inclined their white peers to see them as enemies despite their allegiance to America. Furthermore, the Navajos had differing cultural standards from the average American, and it was difficult for them to acclimate to the culture while at the same time acclimating to a war. Specifically, it was very hard for them to witness the casualties because Navajo tradition commanded ritualistic ceremonies to honor the dead, but there simply wasn’t the time or resources to do so during the war.

    3. Women were not allowed the same job opportunities as men until the 1980’s, and during the period we have read about, the norm was for women to stay at home and keep house. There were of course women who got into the field, as we have seen examples dotted throughout, but it was probably also considered improper for women to hold unknown government jobs. Still, during wartime, so many men were absent from the home front as they were serving their duty as soldiers, that women were needed to supplement the jobs that the soldiers would have held. Thus, either there must have been women that just don’t get much credit, or they were all in the factory making rivets.

    4. All of the achievements we have read about are incredibly impressive and definitely deserve praise. Alan Turing is a great example, and many of his peers at Bletchley Park, specifically the man who was identified as his former headmaster as “lame” for not volunteering to serve in the army. It is understandable, however, that the government is cautious about publicizing their knowledge because it could either still be in use or clue foreign countries into their own weaknesses. Still, the cryptanalysts did the work, and they deserve credit for it, even if the general public might not have been aware of the work as it was going on.

  6. Rachel Lundberg

    1. Doubtless, cryptography played a vastly important role during WWII. The fact that it was so instrumental in such key events as the Battle of Midway and D-Day, which were in turn so important to the outcome of the war, demonstrates this. I think it is very fair to say that if it did not itself control the outcome, it at least shortened the war and saved numerous lives on both sides. I still hold that in a conflict like WWII that takes place in so many different arenas, it is impossible to say that one factor, such as cryptography, was the single most influential.
    2. While the Navajo may not have been in complete support of the American government, the United States was still their ancestral home, and their desire to protect it was no different than that of other Americans. They likely faced prejudice from the other Marines because their culture was so different–they did not share the same religion, customs, or even the same native language. For this reason, they would have had to gain the trust of the other soldiers, rather than just being accepted as the white Americans were.
    3. Though this was beginning to change in the period prior to WWII, the lives of men and women, from the standpoint of what was socially acceptable, were different. Even when women did gain access to opportunities for higher learning, it was still uncommon for them to go into the math and science fields. In the time of Bletchley Park, the tradition of the assumed intellectual superiority of men had lessened, but it had not been eradicated, and the men still had the advantage of education. Singh’s single sentence illustrates that, though progress was being made, the groups of cryptographers who actually worked with the ciphers–and were therefore responsible for the breakthroughs–were still made up of men.
    4. Cryptographers have often been denied credit, at least until long after the fact, for fear that revealing their accomplishments might give away an advantage, usually a nation’s military advantage. This has been the case with the Room 40 cryptanalysts, Alan Turing and Bletchley Park, the Navajo code talkers, and others. Most people like to be recognized for their achievements, and they should be allowed that right. However, in some cases this recognition must be sacrificed (at least temporarily) for the sake of security. It is unfortunate when someone dies before their contributions are made known, but one person’s fame cannot be put above the lives of others.

  7. Danielle Curran

    1. Cryptography was essential to the Allied victory in World War Two. The ability to know the plans of the enemy and the ability to keep their own plans secret was essential to the American victory against the Japanese. The American cryptanalysts took away the Japanese’s element of surprise and the Navajo code talkers kept the Japanese from gaining access to U.S. intelligence.
    2. American land belonged to the Navajo before it became the United States and they have as much reason to protect it as any American citizen. The Navajo were exposed to a completely different world and culture and had to learn to adapt quickly in the wartime environment. They were often in danger of being mistaken as Japanese soldiers because of their similarities in appearance and they also had to deal with their belief that they would be haunted by spirits if they did not properly perform ceremonial rites on the dead.
    3. I think Singh’s limited reference to the contributions of women to cryptography reflects the views of the time. At this point in time it was very rare for women to hold important positions or for them to achieve the level of education in mathematics that was essential to advances in cryptography.
    4. The Navajo code talkers were not given credit or recognition for their role in World War Two until long after the war was over. I think it is important to give accurate credit to any advances in cryptography, mathematics, or science but I do not think it is necessary to give credit immediately if giving credit would cause security issues. It is important to give credit where credit is due because these people worked hard to make these advances and they should be recognized for their achievements.

  8. John Zeleznak

    1. I believe that it was even more essential than what we had hypothesized in class. It clearly gave the Americans the advantage they needed to counter an aggressive Japan. Without it, many more lives would’ve been lost in the Pacific campaign and the U.S. could have possibly had to pull resources from Europe in order to defeat Japan. This could have dramatically shifted the European theater’s result as well. Overall, it seems that the ability to have the upper hand in cryptography during World War II was pivotal in winning the war.
    2. I was very surprised that so many Navajo men joined. They must have been hoping that through their participation, the poor treatment of their people might have been alleviated. They were taking steps to ensure a better relationship between the United States and Native Americans. While in the Marines, they were undoubtedly discriminated against based on their ethnicity. Standard stereotypes probably led to mistrust as well.
    3. During this time period, female participation in the workforce was beginning to gain speed. However, because it was a gradual process that moved painstakingly slow at some points, it seems that credit was withheld from many behind-the-scenes workers. Seeing that credit was not given to many essential Bletchley Park cryptanalysts for many years, it is not surprising that the women who were not necessarily permitted to join the more comprehensive parts of the process were altogether ignored when praise was being handed out. The limited discussion could be due to the fact that many of the female occupations in the field of cryptography were simply not as interesting as the cracking of the Enigma, though this does not undermine the value of their contributions at all.
    4. We have encountered many examples of code-breakers who have not been given the credit they deserve. Bletchley Park was ignored for decades, the Navajo Code Talkers was not made public until over twenty years after the fact, and the work of Marian Rejewski seems to be consistently over-shadowed by Turing’s accomplishments which might not have been possible without Rejewski’s headway on the Enigma. Giving accurate credit is absolutely essential because the past is what we build ourselves upon. It shapes what kind of people we choose to be. In relation to knowledge, we consistently learn new things by studying the works of the great minds that came before us. If a new finding is not properly cited, the author is denying other people an opportunity to learn more about a particular subject. This could lead to the loss of important new developments in subject matter that other minds might have made.

  9. Aubrey

    1. Cryptography played a pivotal role in many of World War Two’s most important battles, such as Midway. It was often cryptography that gave one side a leg up and therefore victory. Cryptography was a decisive element in many individual military victories, however, it cannot be pinpointed as the sole reason fro the Allied powers victory.

    2. Firstly, Native Americans were the first Americans, so the Navajo men had an innate desire to see their motherland remain free and prosper. Additionally, the Navajo men saw their participation as a way to garner respect of Americans and prove to them that they were beneficial to the U.S. The Navajo men were most likely subject to racial prejudices when they first joined the military effort, however, this probably vanished after they showed their intelligence and importance to the military’s success.

    3. Due to the social constructs of the time, many women did not attend university, and if they did they shied away from subjects related to defense. This prevented many women from having the opportunity to play important roles in the development of cryptography. Many women were given menial jobs in the field, such as transcribing messages and were not given the opportunity to do some actual codebreaking. It is likely that women’s achievements in cryptography were not documented at the time of their accomplishment and are now forgotten.

    4. Throughout the history of cryptography, many cryptanalysts have gone decades without praise for their contributions to the field. For example, the Navajo code talkers, Whitfield-Diffie public key encryption, were not recognized until after their contributions. It is important many times that cryptographers not receive credit for their work, because it could reveal the secrecy of it, causing it to become obsolete or used to the advantage of others.

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