The History and Mathematics of Codes and Code Breaking

Reading Questions for November 4th

Please read Chapter 6 in the Simon Singh book and respond to the following questions before class on Thursday, November 4th. Thanks!

  1. The National Security Agency made sure that the Data Encryption Standard (DES) was weak enough that the NSA could break it if necessary.  This, however, meant that businesses were forced to rely on security that was less than optimal.  Was the NSA justified in doing this?  Why or why not?
  2. Singh writes on page 254, “[Whitfield] Diffie believed that if people then used their computers to exchange emails, they deserved the right to encrypt their messages in order to guarantee their privacy.”  Do you agree that private citizens have a right to have access to secure encryption technologies?
  3. Who invented public key cryptography-the GCHQ researchers Ellis, Cocks, and Williamson or the academic researchers Diffie, Hellman, Merkle, Rivest, Shamir, and Adleman?
  4. This chapter included discussion of several different mathematical aspects of modern cryptography.  What was one mathematical idea in this chapter that made sense to you?  What was one that didn’t make sense to you?


Class Participation Grading Scheme


Expository Essay – The Playfair Cipher #1


  1. Tanner Strickland

    1. The NSA was justified in their actions because their priority is the safety of the American people. If the public had access to encryption that the NSA could not crack, then those who intend to do harm could undermine this country’s security and it would be more difficult for the NSA to stop them. Also, the encryption that the NSA allows the public to access is still very secure and serves the purposes that the public needs it to serve because only the American government can crack the encryption.

    2. I do believe that private citizens have the right to access secure encryption because people have a right to privacy. As long as the encryption is no so strong as to stymie government attempts at national security, everyone should be able to access it.

    3. Since both groups came up with the idea separately, they both deserve recognition for coming up with public key cryptography because one group released their findings sooner, but the other group actually made the discovery first. Both groups demonstrated innovation and creativity in the field of cryptography, so they both deserved credit.

    4. The one way functions made sense to me, and they seem simple and easy to understand. The thing I had the most difficulty with was actually conceptualizing asymmetric keys in terms of mathematical functions. Asymmetric keys are easy to explain in words, but when I try to think about them mathematically, they become much more difficult for me to grasp.

  2. Preston Boyden

    1. The NSA has a tendency of being a big pain in everyone’s behind. Sure, they need to maintain national security, but they compromise so much to do it. However, in the case of the DES, the restrictions put in place by the NSA were not extreme. They allowed the data encryption to be so secure that it would be nearly impossible for any civilian, who would not have access to the same caliber computers as the NSA, to break it.

    2. I agree that people should have the ability to guarantee the privacy of their personal communications. They absolutely have the right to these technologies. As long as the encryption is strong enough to keep out criminals, it is ok. If the NSA has the power to break in, fine, but they better not use it unless there is a very good reason to.

    3. While the GCHQ researchers were the first to come up with the idea for public key cryptography, they failed to develop or implement it. The academics, on the other hand, published their findings and proceeded to make practical use of it. Therefore they deserve to be known as the true inventors of public key cryptography.

    4. Horst Feistel’s Lucifer encryption algorithm is a little difficult for me to understand. I get the basic idea, that it takes the binary code of the message and splits and folds and scrambles it, but I don’t understand the programming behind it. It seems like it almost mixes it up too much. But I guess you really can do anything with a computer program. My other confusion is how this is implemented with public key cryptography. Are the two prime numbers the key for Lucifer?
    On the other hand, I have a good grasp on the concepts of Mod and the large prime number factorability. These make sense to me.

  3. Sam Mallick

    1. We Americans love our freedom, so we’re up in arms when organizations like the NSA want to pry (i.e. by giving us inferior encryption). While this does make it easier for the “bad guys” to access our information, it also makes it easier for the NSA to find the bad guys. Ultimately, I believe we have to trust the NSA to do their jobs well and protect us even if it does mean some loss of our privacy.
    2. With the amount of information being transferred via technology today and the ease with which it can be encrypted, I believe that ordinary citizens should have the right to secure data encryption. While some information, such as what books I buy from Amazon, is not sensitive, other information, such as the credit card number I use to purchase said books, is very sensitive and should absolutely be encrypted to protect me and prevent crime.
    3. Who invented calculus: Newton or Leibniz? Who broke the Vigenère: Babbage or Kasiski? The only truthful answer is both. While the blokes at GCHQ did it first, the academics came to the same conclusions independently. While it was unfortunate for GCHQ that their system was no longer secret after Diffie and co. published their discovery, it was fortunate for the Brits that it was not independently discovered, kept secret, and used by people with malicious intent. Credit should be, and to some extent has been, given to both parties.
    4. In reading about Public Key Cryptography for my post to the timeline, I feel like I developed a fairly good understanding of how it basically works. The introduction of modular arithmetic, however, threw me for a loop.

  4. John Zeleznak

    1. I think that the NSA was justified in doing this. Even though this in turn created a monopoly of sorts, which is generally frowned upon, overall I think it was for the best. A lot of times, people are happy to receive information and do not question where it came from. The same principle applies here. If the NSA discovers something important because they were able to break an encryption because of its lack of extreme difficultly, I highly doubt anyone would question the means if the information was used for the betterment of society. Whether this is ethical or not isn’t really the point. The fact of the matter is that as long as interests are being protected, most people don’t really care about the method employed in protecting it.
    2. I agree with Singh’s statement because giving citizen’s the right to privacy is a way of the government saying that it trusts the people in the country and through this trust, the government also asserts that some things are fundamental and cannot be taken away from an individual. This puts forth a certain morality that defines a ruling body more than any other action it could produce.
    3. The researchers from both parties deserve the credit that goes along with this find. The simultaneous developments show how easy it is for multiple groups of people to come to the same conclusion. Just because one team implemented their findings more extensively does not lessen the accomplishments achieved by the other party. All of the information is sound and therefore, joint-credit should be given.
    4. None of the mathematic principles in this chapter were necessarily over my head, but some of the examples that implemented the principles on a higher level were a little more challenging for me to comprehend. However, after a couple of reads, I understood the examples.

  5. Erin Baldwin

    1. The NSA was not justified in doing this. In trying to keep the DES low enough for them to be able to break; they effectively created a monopoly on all the information being sent. Also it leaves information vulnerable to decipherment, because the NSA is surely not the only organization capable of breaking it. Instead of going about national security by being able to break the DES, the NSA should have to acquire warrants to view specific information or should be given access to codes used by suspect organizations.
    2. Citizens should have a right to secure encryption technology. The right to privacy is a very basic idea and even in the age of the Internet and open sharing, it should not be ignored. Private citizens should be able to encrypt messages, should they chose to, in order to feel secure about communications. At the same time however, the need to encrypt a message means that information is being sent that is above a normal standard of secrecy. Individuals that utilize heavy amounts of encryption could be flagged by government organizations and a multitude of these messages could be cause for investigation, a non-intrusive inquiry into the individual’s business dealings to decide the nature of their business. Instead of denying the use of encryption to all individuals, which is a denial of the right to privacy.
    3. The British researchers invented public key cryptography. Although both ideas were developed independently, it was the GCHQ team that came up with the idea and the way of achieving it first. However, because each team spent so much time on the discovery and truly came up with the systems without knowing of the other’s work, I think they should both receive credit.
    4. I understood the binary digits representing letters idea. The idea of a function that cannot be reversed was challenging to comprehend. Also, it didn’t register with me how it could take all the computers in the world longer than the history of the universe to calculate some prime numbers. Although I understand that this is a difficult task, it seems that one computer should be able to handle it.

  6. courtneysh

    1. Yes, the NSA was justified in doing this because the interest of the country’s safety was at stake. The businesses using these encryption tactics were exposed to the NSA, the only organization with materials to decrypt their messages, but since the NSA’s primary task is to ensure the country’s safety, there was no inherent danger in such exposure.

    2. Yes, I think private citizens have a right to privacy, but they surrender some of that privacy when they decide to use the internet. The internet has made the modern world much more public, and part of the trade off of having these new technologies is that we sacrifice some privacy, but when given the chance to gain some of it back, I see no harm in doing so. However, we must acknowledge that there are people who will u the technology for less than savory purposes.

    3. Public key cryptography cannot be attributed to a single person or even to a single team of researchers, because so many people contributed ideas and innovations that led to the eventual breakthrough.

    4. The modular number theory makes more sense after reading the chapter especially since we briefly discussed it in class a few weeks ago. Where initially I had to break down all of the steps of finding the mod number, I can now more easily see what the product of the function should be. Alternatively, the concept of an asymetric key was difficult to wrap my mind around.

  7. Danielle Curran

    1. The NSA was justified in their actions because they were the world’s greatest computing resource and even they only just had a strong enough computer to break into messages using the restricted cipher. If the greatest computing resource barely has the power to break the cipher, then it is difficult to imagine any company having trouble with security problems.
    2. Private citizens should have access to secure encryption technologies because they have information that needs to be protected and because they have the right to privacy. The government might have the right to limit the security of encryption, but only as long as the encryption is still strong enough to protect information from the majority of security threats.
    3. Although the GCHQ team deserves credit for inventing public key cryptography first, because the other group came up with the same invention separately and without any knowledge of the original discovery, they deserve just as much credit for the invention.
    4. I understand how the key in public key cryptography is created and how it is so difficult to figure out the two original prime numbers used to make the public number, but I have trouble understanding how these numbers are used to encrypt and decrypt messages.

  8. Max Gillett

    1. I think the NSA was justified in doing this. If one does make an argument against the NSA’s actions, it has to involve the legality of the government ignoring privacy laws. The reality of the situation at the time is that no entity, individual or business, had the resources to crack this suboptimal security other than the NSA.

    2. Personally, I feel that private citizens should have access to advanced encryption methods, regardless of the NSA’s ability to decrypt such methods. However, I recognize that terrorists can take advantage of such technology and make a private citizen’s perceived privacy seem trivial in comparison to their ability to successfully carry out an attack on our country. Some sort of balance has to be attained.

    3. I think both groups can be equally credited with inventing public key cryptography. Neither group used the others’ work to advance their own and both groups came to the same conclusions (and went through the same thought processes) in a relatively short span of time. I don’t think that time should matter in situations like these.

    4. Surprisingly, I had no issue understanding everything that was discussed in this chapter. I think that attending a lecture on public key cryptography and writing a paper on the Hill Cipher (which involved a lot of linear algebra) helped a lot.

  9. Aubrey

    1.) Though it seems unconstitutional at first for the NSA to leave DES vulnerable to decryption, it was in the best interest of Americans and the U.S. to do so. Having a totally secure encryption method gives businesses secure communication, but also gives criminals secure communication. Also, DES was extremely secure, making it challenging for even the NSA to crack it. This gave businesses highly secure encryption.

    2.) It is the right of the citizen to have access to secure encryption methods. Citizens should have the right to communicate privately. Having said that, the cost of having perfectly secure encryption methods can be high, due to the prevalence of terrorists plotting attacks using long-distance communication. Citizens should give up some of their freedom- allowing a slightly flawed encryption system, in order to protect the U.S. from terrorist attacks.

    3.) I think that there were two, independent inventions of public key cryptography. Both the GCHQ researchers and the researchers merit credit for their work. However, I think the GCHQ researchers deserve more credit, because they came up with the idea of public key encryption first. This is impressive because technology was not as developed when Clifford Cocks came up with the idea. However, because it was not released until two decades later, the academic researchers are given the most credit.

    4.) The idea of an assymetric keys, one separate key for encrypting and one for decrypting, is awfully mind boggling. I understand that it’s possible, I just don’t have a thorough understanding of how this actually works. Modular arithmetic was somewhat easy to understand from having studied it and attended a lecture on it

Leave a Reply

Your email address will not be published. Required fields are marked *

Powered by WordPress & Theme by Anders Norén