The History and Mathematics of Codes and Code Breaking

Reading Questions for August 31st

In preparation for class on Tuesday, August 31st, please read the first chapter in the Simon Singh book and think about the following questions.

  1. What advantages do transposition ciphers offer over substitution ciphers?  What advantages do substitution ciphers offer over transposition ciphers?
  2. Many of the examples of cryptography in this chapter dealt with uses in political or military contexts, where the need for keeping secrets is usually clear.  What are some reasons that people today might need cryptography in other settings?
  3. On page 15, Singh writes, “Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics.”  If such a level of scholarship was required for the development of the frequency analysis approach to solving substitution ciphers, what do you make of the fact that amateur cryptanalysts today often use that approach “on their own,” so to speak, without being trained in it?
  4. On page 41, Singh writes, “The cipher of Mary Queen of Scots clearly demonstrates that a weak encryption can be worse than no encryption at all.”  What does Singh mean by this and what does it imply for those who would attempt to keep their communications secret through cryptography?

As a reminder, note that responding to these questions by leaving a comment here on the blog is one of the ways in which you can contribute to your participation grade in this course.


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Introduction: Online Discussions


  1. John Hunt

    1. Transposition ciphers are more difficult to decipher for the intended and unintended recipient of the message,so while it may offer a higher level of security, transposition ciphers are not practical unless an algorithm for deciphering the encryption is given to both parties in advance. In addition shorter messages are more easily deciphered if transposition is used simply because there are less possible combinations of the letters. Substitution ciphers are more simple to decipher for the intended and unintended recipient, so while it is easier to figure out, the actual key can be as simple as word committed to memory. Depending on the type of substitution used, a longer message can more easily be deciphered using frequency analysis.

    2. Codes today are primarily used for business transactions, in order to keep competitors and sometimes the government from knowing what the government is doing.

    3. There are two possible reasons to justify the afore mentioned statement. The first being, when Al-Kindi created frequency analysis there was very little room for guesswork. Amateur code breakers may use a method that resembles frequency analysis however few amateurs will deal with it as precisely as Al Kindi. The second possible reason is how sophisticated cultures teach and raise populations. Amateurs in today's generations raised in sophisticated countries have been taught to think a certain way, a way that was perhaps not taught in other, less sophisticated, cultures.

    4. Singh is referring to the sense of security encryptions and codes give message writers. When one writes a message in code, he or she does not intend on that code being broken, therefore the writer may say something he or she would rather keep private. For example in the case of Mary Queen of Scots she and her attempted liberators were extremely explicit in their writings for they did not intend on their encryption being broken. If they had written in plaintext there is a strong chance that they would have been careful not to say exactly what they were planning

  2. Sam Mallick

    1. Transposition ciphers are much harder to decode, offering a higher chance that a message will remain encoded and not be read by enemies or other prying eyes. The disadvantage is that it is also nearly impossible for the intended recipient to see the message. This makes the message useless because the plain text cannot be reinterpreted. Substitution ciphers can be cracked once the interceptor discovers encryption techniques. Any people who know the key can easily decode them, but the downside is that the key can be discovered through investigation.

    2. While political and militaristic messages still need to be encrypted, there is a great deal of importance in strong encryption for business or medical purposes today. With the prominence of technology, communication is much faster and contains more and more information. For instance, online banking needs the strongest encryption possible to keep peoples’ account information safe from criminals who may try to gain access. It is therefore necessary to encrypt sensitive data and protect the general public from identity theft and other “e-crimes.”

    3. Because it has been done before and is more or less common knowledge, frequency analysis can be done fairly easily without formal training. On Singh’s statement that a civilization needed sophistication to develop cryptanalysis, it is true that civilizations first needed the ability to feed their populaces, collect taxes, and keep up workable infrastructure to even have need of cryptanalysis. A civilization must be stable before it can begin to develop culture, arts and science, therefore cryptology required a stable civilization to grow. In the modern day, amateurs live in relative ease (at least in the more technologically advanced part of the world) and can pursue cryptology “at their leisure.”

    4. The implication here is that a message sender will be more frank in his statements if he believes no one but the intended recipient can read them. If he knows his messages may be discovered, he will use vague statements or euphemisms that would be understood by the recipient but not by the interceptor. If a code can be cracked (which, history tells us, is the case with many codes that were once considered uncrackable) then it is dangerous to give sensitive information in an outright way. As the book said, saying “Jupiter” instead of saying “attack at dawn” is safer because it alerts friendly commanders of a plan but means nothing to unfriendly ears.

  3. Tanner Strickland

    1. The distinct advantage that stands out to me about transposition is that codes of this kind are extremely difficult to crack unless one knows the trick that was originally employed to create the code. Also, transposition cannot be subjected to frequency analysis because the standard alphabet is used to write the message; the letters are just scrambled. Substitution, on the other hand, is advantageous because it requires less effort to create; all that is needed is an algorithm and a key. This is easier for the recipient of the message to decipher because as long as he or she knows the key and algorithm, the recipient will have no trouble deciphering the substitution.

    2. Outside of the political and military arenas, cryptography is also necessary in many business fields. In order to protect their customers' privacy, companies that facilitate the exchange of information, like BlackBerry, used cryptography to send messages from one place to another in a state that is unreadable to anyone who doesn't know how to crack the code. Businesses may also communicate using cryptography to prevent competition from finding out any private plans.

    3. In highly developed nations of modern society, the level of scholarship is extremely high and constantly growing compared to that of Al-Kindi's society. Although the civilization in which Al-Kindi lived made a variety of advancements in numerous fields of scholarship, today many nations have long surpassed the level of scholarship that the Islamic society achieved. Because of the high level of advancement in today's world, what was once ground-breaking can now appear run-of-the-mill. Consequently, ameteur cryptanalyts can do what only a professional could once do.

    4. When Singh makes that statement about the cipher of Mary Queen of Scots, he is saying that because Mary and her cohorts believed their encryption to be secure, they spoke freely about the plans to assassinate Queen Elizabeth I. Since the encryption was actually weak and insecure, it was easily broken, and the plans about which they had spoken so clearly were made plain to the English court. If Mary and her helpers had not had so much faith in the encryption's security, they would have been more cautious about what they said, and there may not have been enough evidence to prove Mary's guilt. Therefore, Mary would've been better off had she had no encryption at all instead of a weak one. The message that Singh is trying to send is that if one wants to communicate secrets via encryption, he or she better be sure that the encryption is secure or else everything that is supposed to be kept secret may be discovered.

  4. Erin Baldwin

    1. Transposition ciphers are difficult to decipher because of the number of distinct arrangements that can be produced from a short simple sentence. While this is advantageous when trying to pass along a secret message, it also proves difficult to decipher on the other end. Substitution on the other hand is easier for the recipient to reverse back into plain text, but if intercepted is less difficult to figure out. Techniques like frequency analysis can be used on substitution ciphers.
    2. Cryptography can be used in many settings today, from passing notes in the classroom to encoding messages on a blackberry for commercial purposes. Today, the value of being able to keep information and media private is priceless, so encryption is very popular on laptops, cellular phones, and even cameras.
    3. Our culture today has a very different thought process than the civilization that the first cryptanalysts dwelled in. While every work and thought that the scholars of their era introduced was totally unique and the revolutionary, today we are well acquainted, even if not formally, with problem solving processes. From a young age we do puzzles, solve riddles, and even play intellectually stimulating videogames that ultimately prepare us to have the persistence that is required to decipher successfully. Without training the amateurs of our area will arrive with time to the proven technique of frequency analysis.
    4. Mary Queen of Scott’s encryption was worse than no encryption at all because the queen and the conspirators, working under the assumption that their correspondences were safe in their courier’s hands, wrote candidly about the assassination plot. Because the reality of the situation was that their messages were being read and deciphered by Queen Elizabeth’s men, not only were they implicated in the conspiracy, but the prosecution also had solid evidence against them, ultimately leading to Mary’s beheading. Had they not used a cipher and instead created code words that only their entourage could understand, they would have still faced charges of treason (for which they could receive no legal aid and would be likely imprisoned), but without damning and irrefutable evidence against them, they may have received lesser sentences.

  5. Rachel Lundberg

    1. The advantage of transposition ciphers is that someone without knowledge of the scrambling system would be faced with the impossible task of testing all of the vast number of possible arrangements of letters. The advantage of substitution ciphers is the ease of use. It's easy both to define the key and to use it.

    2. Because anything on the Internet is essentially available for every other Internet user to access, it's important for much of this data to be encrypted. From email, to bank accounts, to personal information stored on websites like eBay or FedEx, it all has to be protected to provide a secure method of transferring data.

    3. The amateur cryptanalysts today do not really use those methods "on their own," in the sense that they just "figured it out" without the knowledge of math and linguistics that early cryptanalysts had. They were able to figure it out because of how far society has developed. Despite having had no formal training, these amateurs have been exposed in various ways to the knowledge that forms the basis for their techniques.

    4. Singh is pointing out that someone who believes their message cannot be read may not be as careful about what they say. If their messages are being deciphered, their security is gone, and their encoded candor would be far more harmful than a vague message without a code. So, for those using cryptography to communicate, you can't be too careful. There's no good way to be sure that your code is secure, so it's best not to speak too freely, and to use things like code words or phrases as another level of protection.

  6. Preston Boyden

    1. Transposition ciphers can be simpler, allowing the sender and receiver to communicate with a minimum of effort exhausted learning and employing the shift or permutation of the plaintext being used. While someone using a substitution cipher would have to look up each individual symbol and rewrite the message, someone reading a transposition cipher would just have to memorize the key, then shift or rearrange the ciphered message to reveal the intended message. The disadvantage of this type of cipher is that it is not very secure. Once someone figures out the key or shift, they can then decipher any message using that particular key. In substitution ciphers, they must figure out the meaning of each different symbol, with no correlation to each other.

    2. People may need to use a cipher or code to keep a variety of things secret. For example, if a husband was meeting with a group of friends to go out gambling once a week, but his wife prohibited him from engaging in such activity, he and his friends could communicate in code. Alternatively, email is a very important means of communication that requires encoding to protect people's security and private information. If anyone were able to intercept and read everyone's emails, people would stop using emails to communicate with each other. This would apply to almost all other means of internet-driven communication.

    3. Well, first off, our culture and society is far more advanced than the early Muslim civilization. The way we educate our children significantly impacts the way they think and look at the world. We are taught to pay attention to spelling, numbers, and facts. Naturally many people would focus on the letters or symbols that recur most frequently. Then a natural progression would be to compare those recurrences to a sample of pain text.

    4.Singh means that people rely on codes and ciphers too much. When they believe their code is unbreakable, they write whatever they want, no matter how incriminating it may be, since they are confident that no one will be able to interpret the message, even if it is intercepted. When not using a code or cipher, people trying to keep a secret will be more carful in what they write down, and try not to give anything away or provide valuable information for those who may intercept the message. If this same level of precaution were taken in conjunction with a code or cipher, evidence would be extremely difficult to find.

  7. Jonathan O'Hara

    1. Transposition ciphers are more difficult than substitution ciphers to decipher as the code gets longer due to the seemingly endless amount of possible arrangements. It is extremely difficult to decrypt a transposition cipher unless the one who is decrypting the cipher is given the algorithm. However, with shorter ciphers, transposition is less effective due to the limited number of combinations and ways to rearrange letters. Substitution ciphers are easier to figure out as the code gets longer with the use of frequency analysis.

    2. Cryptography can be used to protect sensitive information and data for businesses. It can also be used for digital security, from everything to credit card information to personal info these days.

    3. In a day and age where world news can be accessed in a matter of milliseconds with the click of a button, one could say that we have reached an incredibly impressive level of scholarship and intuition. People are now able to access information so quickly online and through other resources that one can learn a bit of general cryptography by just reading articles online. The world we live in now (at least in the United States) has reached a high level of scholarship and societal development that people are now able to pursue interests such as cryptography in relatively easier ways.

    4. Singh is referring to the fact that Mary and Babington both were extremely straightforward in their communications, leaving no room for possible speculation as to whether she was behind the conspiritors to murder Elizabeth. Singh is implying that being vague in an encoded message is better than being extremely candid. If for some reason the code was deciphered, there could be a lot more at stake if the message was blatant as opposed to indirect.

  8. Tyler Merrill

    1) Transposition ciphers involve the rearrangement of the letters in a message. This means that longer transposition ciphers offer numerous rearrangements that could not possibly be checked by hand. With a long message, transposition ciphers offer more possible keys than substitution resulting in a higher security level. While the higher security level provides protection from cryptanalysts, it also makes it harder for the intended recipient to decode the message. To be useful, a transposition cipher must have a previously agreed upon key. Because the key is more complex in transposition ciphers, it must be recorded by both sender and receiver. This poses a security risk that is not present with substitution ciphers. Substitution cipher keys usually shift the alphabet a certain number of letters down or employ a key word or phrase that can be easily memorized.

    2) Encryption is used in many areas other than politics and military strategy. Commercial and private banking could be one area. Encryption could be used to protect confidential financial information. Cryptography could also be used to protect the identity and information of clients stored on business servers. Information passed on the internet for online purchases could also be encrypted to protect the clients.

    3) Because modern society has achieved scholarship surpassing that of society more than one thousand years prior, amateur cryptanalysts have the knowledge of professionals from centuries ago. This knowledge allows amateurs to effectively use frequency analysis without specific training in cryptography.

    4) Singh is saying that easily broken ciphers explicitly describing details of plans can reveal more information than vague plaintext. He implies that even when using a cipher, the sender should write expecting the enemy to break the code. Babington would have written more cautiously and not named conspirators if he knew his nomenclator could be cracked. His weak cipher lulled him into a fabricated sense of safety that led to him revealing the entire plot and his accomplices.

  9. Max Gillett

    1. Transposition ciphers, while easy to crack once the reader recognizes the pattern, are easier to remember than substitution ciphers. The end user need only remember the numerical displacement of the letters or a certain key phrase. Substitution ciphers make decryption more difficult, but require either more memorization or the use of a “cheat sheet” to recall what each character stands for.

    2. In today’s society, more and more information is digitized and distributed electronically through the internet. Encryption is now widely used to prevent eavesdropping and unauthorized access to information. Businesses and consumers store sensitive information on their hard drives that, if stolen or lost, could have serious financial consequences for either themselves or their customers. E-commerce sites also rely on encryption to maintain secure channels of communication.

    3. Not only is there a daily demand for critical thinking in today’s society , but people as a whole are vastly better educated than they were a couple centuries ago. What were considered breakthrough achievements in mathematics and statistics several hundred years ago are now taught in today’s elementary and middle schools.

    4. Using weak encryption can lull the user into a false sense of security. Those who rely on the use of encryption should be wary of the fact that their information has the possibility of being intercepted and decrypted, and utilize additional security mechanisms if at all possible.

    • Max Gillett

      I just realized that I misunderstood the terms for question one. Here's my new response:

      Transposition ciphers (rearrangements of the actual characters in the message) offer stronger encryption (especially with longer messages), but both parties must know the method of rearrangement for the encryption to be effective. Substitution ciphers (where symbols or characters are substituted for plain text letters), while less secure, are often easier to remember. The end user need only remember the number of letters everything is shifted or a certain key phrase.

  10. Aubrey T

    1. Transposition ciphers, which are simply rearrangements of the letters in a message, can be very safe and strong, depending upon the length of the message encrypted. A message consisting of just a sentence or two can have an inordinate number of arrangements, thus making it extremely difficult and tedious to be decrypted by an unintended recipient. On the other hand, substitution ciphers do not offer as many different rearrangements and therefore, not as much security. In addition, substitution ciphers are subject to frequency analysis. While transposition ciphers are more secure, they can be difficult for even the intended recipient to decrypt. A substitution cipher sacrifices some security for quick, easy decryption for the recipient.

    2. Encryption is still prevalent today in realm beyond politics and the military. Businesses rely on encryption to protect their plans, ideas, and strategy. Additionally, the cyber world relies on encryption to protect vital information such as passwords, credit card information, social security numbers, and private records.

    3. Today’s society is much more literate than in the days of early civilization. Learning a language is now second hand and not only limited to scholars. Because of this familiarity with a language, it is much easier for people to use frequency analysis without having training or experience

    4. A weak encryption can have devastating effects. A weak encryption can give the sender and recipient a false sense of security. The correspondents may transmit sensitive information that could incriminate them if someone else interpreted it. Singh therefore implies that encryption isn’t always reliable.

  11. courtneysh

    1. Substitution ciphers seem to be easier to decipher, whether through frequency analysis or common words like a, i, or the like we noticed in class whereas transposition ciphers can be very difficult to decipher, but it varies on the length of the message. Short transposition ciphers can be very simple (ie woc = cow), but longer ones absolutely require a key.

    2. Technology has created a much broader realm of information than people ever had, and as much as the government's goal is to protect its citizens it is becoming much harder for them to analyze every risk and keep individuals secure, so many resort to private forms of security (like home alarm systems). With encryption technology available, many would feel more secure buying into it, but there are also those, like terrorist cells, whose motives for encryption are less than kosher.

    3. Amateur cryptanalysis seems to indicate that we are a relatively sophisticated civilization where a person has access to the tools and knowledge (especially the internet) to decipher codes without proper training.

    4. If Mary Queen of Scots had communicated with her contemporaries in plaintext, she (and they) would have been more careful (and subtle) about their plans, however since they felt secure (falsely), they spoke explicitly about the details of their conspiracy. Not only did the interceptors have access to the details, but they were also able to forge a note to Mary (in the code, ergo giving nothing away) to get even more information.

  12. courtneysh

    4. (cont'd) The implications of Mary's unfortunate lesson warn us that codes are only useful as long as they are secure. Since there is no surefire way to know that a code has not been broken by an enemy, it is generally a good idea to change the code periodically.

  13. Tyler Huber

    1. Transposition ciphers have the advantage over substitution ciphers that they are harder to decipher and therefore have a higher level of security. However they lack the ease of ciphering and deciphering for writer and recipient that is prevalent in the substitution cipher.
    2. Large businesses that deal with confidential information over the internet have a present day need for cryptography. However due to the level of security of messages over the internet, the average person may or may not have a use of at least some form of cryptography over the internet.
    3. I think that the fact that the present day amateur can take on a level of cryptography that took hundreds of years for experts not because the average human has become more intelligent, but instead because he has been trained by society to think about and solve the kinds of problems that one encounters in low-level cryptography. Even as low as lower school children are taught different forms of lateral thinking. Another example is that puzzles such as crosswords are abundant in today's society whereas when frequency analysis was first introduced the average person would never encounter such problems and would therefore have no experience in lateral thinking.
    4. Singh means that if one had no cryptography on a message he would be more careful to make sure the message reached its destination without being read. However if one has weak cryptography that he thinks is sufficient he might be more careless about whose hands the message falls into, which would make it more probable for someone who wasn't supposed to read the message to intercept and then decipher it. This means that the person who is encrypting the message must be sure that his form of encryption will not be able to be broken by someone who might want the information.

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