The History and Mathematics of Codes and Code Breaking

Reading Questions for October 21st

In preparation for class on Thursday, October 21st, please read the fourth chapter in the Singh book and respond to the following questions.

  1. Given what you’ve now read about Bletchley Park’s role in World War Two, would you say that “Bletchley Park’s achievements were the decisive factor in the Allied victory”?
  2. Why might the Germans increase the number of scramblers and plugboard cables in their Enigma machines to make them more secure, yet also insist that the Enigma cipher could not possibly be broken by the Allies?
  3. We’ve seen that the Vigenère cipher was once though unbreakable but later broken.  Given that history, why might the Americans and French conclude that the Enigma cipher was unbreakable prior to the start of the Second World War?
  4. Singh writes on page 149 that “the creative codebreaker must ‘perforce commune daily with dark spirits to accomplish his feats of mental ju-jitsu.’”  In light of your own experiences breaking ciphers, which is more important to successful codebreaking-logic or creativity?  Or is an equal balance of both required?
  5. The Timeline: Take a look at the crpytography timeline you’ve built as a class. What insights about the history of cryptography occur to you as you examine the timeline? How could the timeline be improved to make it more useful to you, particularly as you think ahead to your “big questions” paper at the end of the course?


Essay #2 – Expository Paper


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


  1. courtneysh

    1. It’s impossible to pinpoint the victory specifically on Bletchley Park because there were so many factors involved in the outcome of the war, but Bletchley Park to be sure lent an enormous contribution to the Allied victory, mainly in the way of time awarded to the Allies by way of them knowing what their enemies were plotting and being able to react. If Bletchley park hadn’t existed, or even existed at a lesser extent, the war would have surely gone on for much longer.

    2. Perhaps it was in false confidence that they boasted of having invulnerable technology. As was seen with the supposedly unbreakable Vigenere cipher, the impossible can become possible given the right combination of inspiration and effort, and by adding these extra layers of security, the Germans were dramatically increasing the number of possible solutions, probably in hopes of delaying strokes of enemy genius for a while longer.

    3. Before the war, the Americans and the French didn’t have the technology to break the enigma. It wasn’t until the Polish invested their forces (out of fear of invasion I might add) into deciphering the enigma, and a leak was found, that the machine was considered breakable.

    4. Logic and creativity both play an active role in code-breaking, more primarily logic, because there are certain tactics that have either worked in the past or make sense to test out, so they must be tried first, but when the cryptanalyst reaches a supposed dead end, creativity becomes crucial. However, a creative mind can analyze a cipher and see it completely differently than a logical mind, noticing different patterns and cribs. The two tactics complement each other nicely as a creative mind alone would seem sporadic and arbitrary if the first few attempts were unsuccessful, and a logical mind would hit a roadblock if its systematic strategies were also unsuccessful. Since we are naturally inclined to be weighted in one direction moreso than the other, teams are often useful when deciphering.

  2. Tanner Strickland

    1. A war on the scale of WWII is never decided by just one factor, such as the advantage that the Allies had due to Bletchley Park. Therefore, nobody can pinpoint Bletchley Park as the decisive factor of the war, because there were others, such as America’s decision to become involved in the war in the first place. Bletchley Park did, however, make a large contribution to the Allied victory because it gave the Allies such a huge advantage over their enemies.

    2. The Germans probably realized that there is never any point in taking unnecessary risks during the war. In other words, although they believed their cipher could not be broken, there was no need to risk being wrong when all they had to do to make the cipher much more secure was add some scramblers and plugboard cables.

    3. One reason the Americans and French may have come to this conclusion is because they were just following the conclusion that most others had reached. Also, before WWII, the Americans and French did not have a desperate need to break the Enigma cipher because they were under no dire threat of invasion before the war, so it was easier for them just to conclude it was unbreakable. The Polish, however, realized how desperately they needed to crack the Enigma cipher because they were under threat of invasion, so they invested more resources into cracking the cipher.

    4. In my own experience, logic has played the more important role in cracking ciphers because I have cracked ciphers that have been cracked before. As a result, I have an example to follow, and using logic, I can apply the same methods used previously to crack the cipher. I believe creativity, however, would be more important in cracking a cipher that has never been cracked because this kind of cipher requires more out-of-the-box thinking.

    5. Now that the timeline is becoming more developed, I am beginning to see some relationships between what is happening during certain periods of history and the development of cryptology. For example, some of the greatest feats of cryptanalyzation have occurred during times of war. The main improvement I would like to see in the timeline is for it to be more detailed and encompass more of the history of cryptography because the more information the timeline contains, the better understanding it would provide me with issues to write about in the “big questions” paper.

  3. Rachel Lundberg

    1. I would not say that Bletchley Park was the singular deciding factor. There are too many forces at work during a global conflict for any one to control the situation so completely. That aside, the work done at Bletchley was extremely valuable to the Allies and it would not be a strectch to say that it was one of several deciding factors.
    2. It doesn’t seem that the Germans had absolute confidence in the Enigma. For example, if they had been certain that it could not be broken, they would not have investigated the possibility when the nine tankers were sunk. Their sense of security was not total. Even as they were relatively sure that Enigma could not be cracked, they knew the importance of keeping their communications secret, and in a conflict with such high stakes, they likely felt that it was best to plan for contingencies.
    3. Enigma must have seemed impenetrable because it had mechanized encryption. In a way, the ciphers had been made by a machine, and this was something the cryptanalysts were not used to dealing with. It was a cipher for a new age of technology, and many may have thought that it would require a breakthrough in technology to break (which, it turns out, it did). Without their own machine to combat the Germans’ portable cipher factory, the American and French cryptanalysts must have felt outmatched.
    4. If the cipher has been cracked before, chances are that there are several useful techniques that have been developed that one can employ. In this case, the logical approach is best, trying out what has worked in the past. When this is not an option, one might have to be more creative to find a weakness in the cipher. However, I don’t think that logic and creativity can be fully separated–creativity does not mean trying haphazard ideas. Creative ideas employed in codebreaking are still based on logic. Both traits are necessary; in what relative amount they are necessary would not remain constant, but would vary according to the cipher and the faculties of the cryptanalyst.
    5. One trend I see is that there tends to be a lot of activity surrounding technological innovations such as the telegraph, the Difference Engine, and the Enigma machine. The advancement of cryptography is accelerated by the advances in other areas of science. It might be helpful if each entry included a brief mention of the results or consequences of the event. It would be easier to see then how the events might tie together.

  4. Erin Baldwin

    1. Bletchley park’s achievements were the deciding factor in the Allied victory during World War II, not in that the Allies would have lost without the code-breaking unit (though it is a real possibility), but in that their victory would not have come in the time or manner that it did. Whether they were the decisive turning point or not, the Allied powers without a doubt owe a great amount of their success to the men and women of Bletchley park.
    2. While the Germans would have liked to believe indefinitely that the Enigma machine was undecipherable, realistically they had to know, even if it was a seedling of a doubt, that their machine could not remain secure forever. With that notion, the increase in security was more than likely a “better safe than sorry” measure. It was very easy and not at all inconvenient for the German’s to introduce more cables and scramblers compared to the arduous task that the additions would bring to those trying to crack the code.
    3. Like Singh points out, “necessity is the mother of invention.” In the period before World War II, where France and the U.S. seemed relatively secure and were under no direct threat, it was easier for them to label the Enigma unbreakable than it was for them to attempt to crack it. By denouncing the possibility of ever deciphering the code, they freed themselves from devoting resources toward the endeavor.
    4. Creativity and logic both play important, yet very different roles in code-breaking. Creativity comes into play largely in the primary breaking of a code. By analyzing the cipher and plain text from different angles, an innovative mind can concoct a strategy for breaking a certain code every single time. Logic becomes very important when attempting to use a strategy to decipher text, because it is not a straight forward process. One must be able to see patterns in the text and figure out what they might mean in the context of the code. Because of this relationship between creativity and logic, I have found that in my own code-breaking work, the most important skill is logic. Perhaps, this is because I have not been forced to create new strategies or break unique codes, but instead have had to apply already developed methods.
    5. According to the timeline, big breakthroughs in cryptology seem to center around times of conflict and war, whether it is directly before, during, or after these periods. The great minds of the time are always drawn in to the important work of cryptology, which can often decide battles, even wars. A timeline that included more events would be helpful, but also one that followed up on specific events in greater details. For example instead of saying that the Enigma machine was cracked over a period of years, give the exact developments as they occur.

  5. Sam Mallick

    1. The work done at Bletchley Park was no doubt key to the timing and decisiveness of the Allied victory, but all the other factors that went into the victory must be taken into account. Also, the work done by Polish cryptographers in the “Biuro” must not be ignored. The groundbreaking cryptanalysis done by Rejewski laid the foundation for the work of Bletchley Park.
    2. A theme that I’ve noticed in this course is that the cryptographers develop an “unbreakable cipher” which the cryptanalysts proceed to break. Then an attempt to create a new “unbreakable cipher” begins. Perhaps after the publication of cipher breaking information by the British after WWI made the Germans more aware of that fact, leading them to seek extra security. As for the claim that Enigma could not be broken, pride may have been involved, or perhaps the high command wanted to assure German officers of security and boos their morale; it is very likely that they also wanted to intimidate the enemy into not trying to break the cipher.
    3. It’s been said that “rules are made to be broken.” While that may not be true, history seems to tell us that ciphers are made to be broken. Still, no matter how many new ciphers are broken, people still claim new ciphers to be unbreakable. They seem to think “well, the last one was breakable, but this time it won’t be because people are smarter and technology’s better.” While cryptographers do get smarter and technology becomes more helpful, cryptanalysts also become more adept and also have better technology (as in the case of the bombes). The Vigenère was “unbreakable” until it was broken. Then it was merely “difficult to break.” The same was true with the ADFGVX Cipher and Enigma.
    4. It takes creative thinking for a person to find ways to effectively use logic. As in all problem solving, creativity without logic is wishful thinking and logic without creativity is a computer.
    5. I find it interesting to see how many categories we have. Cryptography is a subject that touches many others, which is something that some people don’t think about. Also, I’m fascinated (and also a bit disturbed) that there are numerous events categorized as “military” while the only ones categorized under “unsolved” are in no way related to the military. Perhaps there is a lack of necessity to solve them, which is why they remain unsolved. Or perhaps these are ciphers that are so strong they have stood the test of time longer than the toughest ciphers the armies of the world have come up with. Maybe we will have to wait until they are cracked to know for sure…

  6. Tyler Merrill

    1. The achievements of the cryptanalysts at Bletchley Park undoubtedly had a profound impact on the success of the Allies. Without the intel gained from cryptanalysis the Allies would have lost many more lives and possibly the war. Before the Enigma was cracked, German U-Boats were sinking many ships of the Allies. The Germans were also advancing on land. They had the element of surprise and the advantage in war. The allies began to have success when they cracked the Enigma. Because of this, the efforts of the people at Bletchley park were necessary to the Allies success.
    2. They clearly had some idea that the Allies were making progress on deciphering the enigma, but still wanted to give an image of power and control. They wanted the public to think they were in control, so that they could maintain support. The Germans altered the Enigma because they realized that it could be broken, but would not say it publicly to maintain power.
    3. The Enigma may have been considered unbreakable because it was the first time encryption was mechanized. It was also considered unbreakable by the French and American because they did not have a reason to break the code. There was no pressing reason for them to work on the code, so they just left it as unbreakable.
    4. Logic is required to understand the basic methods of cryptography, but I believe that creativity is more important to crack new codes. The methods used to crack the enigma machine begin with a creative spark, then logic takes over. The idea of how to begin to crack a code is creative, not logical. The creative idea comes, then logic is used to explain it to others. In my experience, finding something to start from is most difficult. After I find out where to start, logic and understanding of codebreaking methods takes over.
    5. The timeline shows the exponential advancement of cryptography. Between the first example of cryptography (2000 bc) and 1500 AD we have 5-10 events. So over 3500 years we have found 5-10 advancements. That means that we have found at least 30 events that occurred in the past 500 years. The renaissance, development of communication, and technology have led to significant advances in cryptography.

  7. John Zeleznak

    1.I would absolutely agree with this statement. Having the knowledge of where German attacks and stations were combated the overwhelming advantages Nazi Germany had at the beginning of the war: controlling a large portion of Europe and basically singling out Great Britain as the only power against them. So much of the early war was not actually fought on land and because Britain relied so heavily on naval domination, knowledge of where and when German U-Boats would be stationed help them keep supply lines open and remain superior in the one of the few areas that the Third Reich had yet to dominate.
    2.After reading the British Royal Navy’s accounts of the First World War, Germany would surely realize that just because you aren’t aware of your codes being deciphered doesn’t mean they aren’t being cracked. The increased precaution came so that Germany did not make the same assumptions they did during the previous war. I believe that they couldn’t have been so naïve as to assume that the Enigma was truly unbreakable. These assurances are most likely just a way to demoralize cryptanalysts that, despite a large amount of time, could still not effectively decode the Enigma messages.
    3.Part of the reason that the Vigenere cipher was considered unbreakable was because the techniques/technology had not been developed. The cipher was not comparable to anything cryptanalysts had encountered. The same goes with the Enigma. The level of technological advancement was so astounding for the French and Americans that the only thing they could conclude was that the Enigma was unbreakable.
    4.In my experience, logic and creativity coincide. Both logic and creativity look for the same trends that indicate how a code could be cracked. By logically using creativity, you happen upon things that conceptually make sense. However, you would not be able to make use of these discoveries without thinking outside of the box and anticipating how other people would encipher something. By finding a balance between the two, you ensure that you’re not randomly guessing nor putting yourself through a painstakingly repetitious cycle with no foreseeable results.
    5.This timeline shows how all aspects of cryptography have been evident throughout history. Codes have been used in many different aspects of society. I think that if keywords were used during the posting process of timeline events (similar to the Delicious feed), it would be a lot easier to find corresponding events without having to scroll through the entire timeline. The color-coding is really helpful in seeing what aspects the event affected, but the keywords would be able to narrow it down even more.

  8. Aubrey

    1.) Though Bletchley Park’s achievements certainly gave the Allied powers a leg up, they can not be credited as the deciding factor of World War II. World War II, which lasted six years had a hoard of factors that determined the outcome. Because of this, the achievements of Bletchley Park cannot be cited as the sole determinant of the outcome of the war. However, the importance of Bletchley Park’s accomplishments cannot be overlooked.

    2.) It is apparent the Germans doubted the security of the Enigma machine, because they took extra steps to amp up its complexity. The Germans wanted to brag about their brainchild. However, it must be noted that cryptography is a constantly evolving science. Because of this, it makes sense that the Germans would upgrade their cryptography methods to fend off the codebreakers.

    3.) The Enigma was unlike any form of cryptography that had been used up until this point. The new form of cryptography relied on a machine, which could be perceived as more intelligent than a human codemaker. The Enigma was an enormous leap in the complexity of cryptography that it seemed impossible to break at the time.

    4.) While creativity plays a role in successful codebreaking, logic is more important. Creativity can help get the ball rolling when attempting to break a code, but breaking the code comes down to logic. Frequency analysis and the ability to see patterns are logic skills that are key to breaking a code. I have found that many times solving a code comes down the ability to deduce the possibilities of a code that can and cannot exist.
    5.) From looking at the timeline, I noted that there are waves of development in cryptography. There are periods where little to no advancements are made and other periods where several groundbreaking advancements take place. Most of the time this takes place during war time, when cryptography is a skill that is vital to life and victory. The timeline would be more helpful if entries explained more about what spurned this advancement to take place.

  9. Max Gillett

    1. I’m not sure I would go so far as to say that they were the deciding factor in ensuring an allied victory, but their breakthroughs definitely helped to not only turn the tide of the war, but drastically reduce its duration. Part of the problem with the decryption of the enigma machine, was that the Germans had to remain absolutely certain that their encryption technique had not been broken. As a result, a lot of the information that was collected was not fully taken advantage of, and too many large consecutive victories may cause the Germans to change their enciphering methods.

    2. The Germans had to assume that some efforts were being made to crack the machines and that certain editions of the machine had been stolen, so they might have reasoned that complicating the machines would further confound these efforts.

    3. This was essentially the first time that encryption was mechanized – being handled completely by a machine. Like the Vigenere cipher, the enigma cipher was unlike anything before its time. The entire process of decryption had to be rethought and reinvented.

    4. I feel that the initial decipherment – cracking the code for the first time – requires a great deal of creativity, but I also think that the two don’t have to be mutually exclusive. Using creativity to solve a problem sometimes requires making logical connections in ways that wouldn’t normally be apparent.

    5. It seems that more cryptographic achievements are being made more rapidly over time, and that most breakthroughs occur in times of necessity. I think the timeline could be improved by citing various sources about the event within the entry.

  10. Preston Boyden

    1.Just from reading Singh’s book, yes I would say so. But this is only one perspective, and while I don’t doubt the importance of Bletchley Park, Singh didn’t care to elaborate on many of the other factors that may have contributed to the Allied victory. Therefore, I believe Bletchley Park’s achievements were critical, but not necessarily the deciding factor in Allied victory.

    2.The Germans most likely felt a slight worry that their machines could indeed be broken, but didn’t want to let that fear show, as to encourage their enemies. If they learned anything from World War I, it was that they needed to be extremely careful about assuming security of their communications.

    3. All previous ciphers had at some point been broken, but Enigma was different. It was the first cipher to utilize electrical technology, and at first seemed completely unconquerable. But, this led to the advent of more machines, capable of deciphering texts much faster than people could.

    4. In breaking codes, it is clear that some skill and experience is necessary. But creativity, and luck, are the only ways one can come up with new and better ways to crack codes. If the codes aren’t changing, logic is enough, but when they are continually adapting and changing, creativity must enter into the mix in order to keep up.

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