The History and Mathematics of Codes and Code Breaking

Reading Questions for October 12th

In preparation for class on Tuesday, October 12th, please read the third chapter in the Singh book and respond to the following questions.

  1. When the Zimmerman telegram was deciphered by the cryptanalysts of Britain’s Room 40, Admiral William Hall decided not to tell American President Woodrow Wilson about its contents because doing so might let the Germans know that Britain was capable of breaking their codes.  Given the danger posed to America by the unrestricted U-boat warfare indicated in the telegram, was this ethical of Admiral Hall? (For those of you who responded to this question in your first essay, please don’t cut-and-paste your essay here…)
  2. Germany learned that Britain had broken their codes from histories of the First World War written by Winston Churchill and the British Royal Navy.  Given that this knowledge prompted Germany to invest in the Enigma machine technology prior to the Second World War, should these histories have been published?  What might have motivated Britain to make their code-breaking success known in this fashion?
  3. Given the various incidents recounted in this chapter, what are some conditions that seem favorable to the advancement of military cryptography?
  4. Singh’s examples of breaking difficult codes (such as the example beginning on page 116 about a keyword as long as the plaintext) seem to make breaking such codes (relatively) straightforward.  Why are these codes so much more difficult to break in practice, as you’ve seen on recent problem sets?


Essay #1 Revisions


Essay #2 – Expository Paper


  1. Tyler Huber

    1. This was a tough decision, but I think it was an ethical one. The ability to break the codes was a major advantage for the British, and a key factor in winning the war, so I believe the possible lives given up by not telling President Wilson are less numerous than the lives that would have been given up if Germany had found out the British could break their codes.
    2. I think that Britain published this information both because they did not expect to be in the same situation with Germany a second time, and also wanted to show their citizens how far ahead they (the British) were in the war. However I think they should’ve kept this information secret for longer, until they were positive that such methods of encryption were no longer in use.
    3. War is definitely a situation that helps advance military cryptography. This is because during wartime the exchange of information is that much more important. Militaries are constantly both trying to break enemy codes and making sure theirs are not broken. This is what spurs on the advancement of cryptography in the military.
    4. In Singh’s examples, he knows exactly what he’s looking for in each step, so breaking the cipher is very systematic. In practice, however, the text does not always have the same frequencies or patterns it’s supposed to, and breaking the cipher takes much more trial and error, and at times some creativity. This makes breaking the cipher much more timely and difficult. Oh and frustrating.

  2. Tanner Strickland

    1. Yes, Admiral Hall’s decision was ethical because he used discretion in order to save as many lives as possible. His decision to keep the cracked cipher a secret ultimately helped the Allies to win the war because it gave them such an advantage over the Central Powers. Therefore, the loss of Ally life was minimized.

    2. In hindsight, I do not think it was the best idea for Britain to release the fact that they had cracked the German’s code in World War I because if this information had been kept secret, German codes in World War II would’ve probably been less developed and easier to crack. Britain had no way of knowing, however, that World War II would occur. Britain’s main motivation in revealing their superior knowledge was to appear to the world as if they had control of the war the entire time; I think Churchill released the information because of pride in his country’s accomplishment.

    3. The desperation caused by wartime is one condition that history has proved as ideal for the advancement of military cryptography because it is of the utmost importance for armies to keep their messages secret during this time. Also, improvements in technology that decrease the privacy of sending messages lead to an increase in the general advancement of cryptography, which leads to the advancement of military cryptography as well.

    4. First of all, Singh already knows where to insert the arbitrary “the’s” because he knows his own cipher. We as students would not known where to put these “the’s” so easily. Second, breaking a cipher with such a long keyword requires large amounts of trial and error, which Singh avoided once again due to the fact that he knows his own cipher. This saves hours of time just guessing and checking different possible solutions.

  3. Danielle Curran

    1. I think that it was an ethical decision because America found out about the unrestricted U-boat warfare without Britain’s help, and when America still did not enter the war Admiral William Hall found another way to get the message to the United States without letting the Germans know that they could decrypt their messages.
    2. A history of the war had to be published sometime, so that future generations would know what happened and so that history could be accurately recounted. Britain probably wanted the world to know how valuable their code-breaking successes were to the war, and since the war was over they most likely did not see any problem with publishing their account of what happened. When they published the histories they also did not know that a second world war was coming. Perhaps the timing was not optimal, but I think that no matter when these histories were published it would have had a similar effect on Germany’s actions afterwards.
    3. The greates advancement of military cryptography seems to occur during times of increased warfare. This is most likely due to the fact that governments are willing to pay high prices for both advanced encryption and for good teams of cryptanalysts. Thus the incentive to create better codes and code-breaking techniques is higher.
    4. The methods Singh is suggesting take much more time in reality than they do in his examples because they rely on a lot of guess and check work that takes a lot of time and effort to go through, whereas he already knows the answer so he can use the correct answer as his first or second guess and skip all of the trial and error that those of us who do not know the answer would be forced to go through.

  4. Jonathan O'Hara

    1. I think this was an ethical decision on Admiral Hall’s part even though a seemingly dangerous one. By not revealing the British ability to break German codes to anyone, Admiral Hall was attempting to maintain the upper hand over the central powers. Their ability to intercept and decipher German codes was a key factor in helping them win the war, which seemingly ultimately resulted in the reduction of the amount of casualties that could’ve possibly resulted had the Germans learned of the deciphering capabilities of the British.

    2. The British, it seems, published the fact that they had broken Germany’s codes as a sign of national power and strength. But it also seems like this publication was motivated by British hubris. They could have never known that they would fight another war against Germany; however, they should have never revealed the fact that they had an advantage over Germany in the first place because it put BRITAIN at the disadvantage.

    3. Wartime creates a sense of anxiety (coupled with a sense of national pride) in the general public. This sense of anxiety lends to a sense of urgency within the government to being able to decipher tough codes and encipher difficult ciphertext. There is a lot at stake during wars, which gives more of an incentive and more of a necessity to advance military cryptography.

    4. These codes are much harder to break in real life for many reasons. One is that Singh places “the” arbitrarily throughout as possible plaintext and comes up with a result immediately, which is simply unrealistic. Also, “YPT” is an uncommon set of 3 letters, leaving little choice for what the possible plaintext could be. The keyword/keyphrase isn’t always going to be a list of some sort. Basically, everything about his examples is oversimplified and takes A LOT longer and is MUCH harder, but hey, he couldn’t make a ridiculous example that would take 100 pages to explain either!

  5. Erin Baldwin

    1. The decision to not immediately inform the Americans of the unrestricted u-boat warfare was an ethical decision on the part of Admiral Hall. Although he jeopardized the lives of many American sailors by not warning them of the imminent danger that they faced, in the long run he saved the lives of many more soldiers by keeping the knowledge that the code was broken secret. The British could continue to intercept German messages uninterrupted and help end the war more quickly by anticipating the movements of the German military.
    2. The histories should have been published as they were. Whether the Germans became aware that their codes were broken before the start of WWII or during it, the nature of cryptology is that it is always evolving. Sooner or later the Germans were going to adopt a more advanced system, the histories only made it happen sooner. It some ways it was an advantage, because the cryptanalysts had more time to attempt to crack the code and to strategize about how to beat the Enigma machine. It may have been a strategic move on Britain’s part to give their cryptanalysts more maneuverability.
    3. Military cryptography seems to see the most advancement after a time of intense usage, such as a Great War or conflict. After each world war great strides were made in the field of cryptology. This probably has a lot to do with the fact that the most prolific use of encrypted messages occurs during crisis and at the same time, cryptanalysis is most urgent. After these times of urgency comes times of “catch-up” where both sides try to improve their techniques for the next intense rounds of battle.
    4. In practice, codes are not always “textbook examples” so to speak. In real life, there are more complications and nuances involved with a code than a book could ever prepare you for. The ability to see patterns and to be creative with your codebreaking, as well as the patience to process a code again and again with various strategies all make a difference when breaking a code. Also, Singh uses relatively short encrypted messages. “attack the valley at dawn” is significantly different than deciphering an entire article or even a paragraph.

  6. Sam Mallick

    1. The decision was not ethical because Hall endangered human life through his silence. However, it would have been less ethical to alert the Germans to the presence of Room 40 because that could result in even more loss of life. War is by nature unethical but sometimes rendered necessary if there is no other way to halt a greater evil. Hall was placed in a difficult position, but in the end I believe he chose the lesser of two evils by keeping Room 40 a secret.
    2. It is questionable to whether the development of the Enigma helped or hindered Germany in the Second World War. We have discussed several times the idea that weak encryption is worse than no encryption at all, and once the Enigma was broken, it became weak encryption. It was probably not the best decision for the British to release the information about the broken codes, and pride was certainly a factor that led them to do so. Germany was a defeated and weak country after the Great War and were not seen as a legitimate threat until Hitler took power, and Churchill was no doubt proud of his government and was never known for his subtlety.
    3. Perhaps the two most motivating circumstances for the development of military encryption have been necessity and failure. When a war broke out, governments were reminded once again of the need for strong encryption, leading to development of stronger ciphers. They then proceeded to believe that these new encryption techniques were infallible until someone broke their code, meaning a new one needed to be developed.
    4. Singh’s examples serve as effective teaching tools because they are simple enough to be accessible to the beginner. In the real world (and to some extent on our problem sets) the cipher is less calculated and more likely (or, in the case of the problem sets, to test) the cryptanalyst through more randomness. A plaintext sample in a real cipher may include very few occurrences of the word “the” or the more common letters in the English language, which would undermine the way we’ve traditionally approached problems. We saw in our most recent cipher a lower frequency of “e”s and a keyword with the letters “m” and “y” in it. These unexpected complications are manageable on a small scale, but as the keyphrase gets longer, there are more difficulties to deal with.

  7. Max Gillett

    1. I think Admiral Hall’s decision was ethical. While a good deal of lives were put in danger by not giving the United States a heads-up, letting the Germans know that the British were capable of decrypting their messages would naturally have prevented the British from decryption future wartime communications. The lives lost in a single case of unrestricted submarine warfare pale in comparison to those lost in a surprise military attack.

    2. In retrospect, these books detailing Britain’s code-breaking success should not have been published, as the Germans would never have been interested in the Enigma machine if they believed their codes were still secure. I think national pride and the urge to demonstrate Britain’s superior intelligence gathering were the primary factors that accounted for these successes being released. However, the British may have believed that Germany would not be in another position to fight a war, and wanted to accurately document the events of World War 1.

    3. I think the heightened anxiety during wartime definitely encourages the advancement of military cryptography, but the true advancements occur when the country realizes that its encryption has been broken.

    4. I think that the process of breaking a code can be compared to that used to solve a math problem or show a proof. In a completed math problem or proof, the individual steps in logic are easy to understand, and it seems obvious to the reader that the answer is what is given. Solving the problem with no assistance is difficult however, as the leaps in logic have to be arrived at by one’s own creativity and intellect. Code breaking is no different.

  8. Rachel Lundberg

    1. It’s difficult to say whether or not this decision was the correct one because the potential benefits and losses on either side cannot be quantified. That aside, I think it was ethical because Hall believed that he was saving lives in the long run by keeping the information secret and allowing Room 40 to continue their work.
    2. The reports probably should not have been published, because from a military standpoint, they did not stand to do much good. The information would have come out eventually, but the fact that it was published when it was became a factor in the advances Germany made before WWII, giving them an advantage over the Allies. Those involved certainly felt pride for their achievements, and naturally would want recognition. Churchill may have also hoped that a recount of the nation’s less known successes would instill some patriotism in the average Briton.
    3. New technology and methods of communication seem to have a direct correlation with breakthroughs in cryptography. New methods (such as the radio) may be more convenient, but may also be less secure. The need for cryptography is also increased during wartime, for obvious reasons. The huge volume of weighty messages, and often the high change of interception, result in a need for secure encryption.
    4. The ciphers Singh uses are meant to be used as examples, and so are designed to be particularly susceptible to the methods Singh is demonstrating. Not all messages behave in such a convenient manner, and Singh’s techniques will not always produce obvious results.

  9. Aubrey

    1.) Though at first it does wrong for Admiral Hall to keep this a secret from President Wilson, I think he was acting in the best interest of Americans. Over the long run, the benefit of keeping the messages contents secret outweighed the costs. Having the ability to decrypt German communication would give the Allied powers a leg up in winning the war.
    2.) Britain’s hubris was in a way its tragic downfall in the area of cryptography during World War II. Britain was arrogant for not holding onto its secrets. Nothing was accomplished by sharing these methods other than giving the British an ounce of pride. Though it is understnadable that the entire history of World War I should be recorded, the British should have waited until the cryptography methods detailed were obsolete.
    3.) The high stakes of war foster advancement of military cryptography. It is vital that all communication cannot be intercepted and decrypted in order to protect the future of one’s nation and citizens. Additionally, the time constraint of military action makes secure encryption a pressing matter, which could lead to developments.
    4.) For the sake of simplicity of demonstration, Singh jumps to conclusions quickly that would otherwise take a lot longer to come to. Because he has created the cipher, it is harder for him to take a look at it from the perspective of someone who hasn’t seen the code before. Singh’s examples are elementary for the sake of teaching the reader.

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