The History and Mathematics of Codes and Code Breaking

Reading Questions for September 16th

In preparation for class on Thursday, September 16th, please read pages 45 to 62 in the second chapter in the Simon Singh book and think about the following questions.

  1. For some time before the development of the Vigenère cipher, “anybody sending an encrypted message had to accept that an expert enemy codebreaker might intercept and decipher their most precious secrets.” (Singh, p. 45)  How is this environment different from the one that Mary Queen of Scots experienced, where one didn’t know how likely it was that one’s encrypted message was secure?
  2. Can you think of any ways to improve the security of the Vigenère cipher?
  3. The Great Cipher used by Louis XIV remained unbroken for 200 years.  What were the factors that led to such a secure cipher?
  4. Why do you think that the advent of the telegraph motivated the use of a more secure cipher like the Vigenère cipher?

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.


Resources for September 9th - Transposition & Keyword Ciphers


Cryptography in the Movies


  1. Erin Baldwin

    1. For some time before the development of the Vingenere cipher, because the codes were so elementary, encryption was almost a secondary form of defense. It was so likely that your code would be cracked if your message fell into the wrong hands, that hiding messages and keeping correspondence away from enemies was equally important as the encryption techniques. This differs greatly from the period in which Mary Queen of Scotts lived, a period of somewhat elementary encoding, where most correspondents felt secure with their encryptions and were generally unaware that their messages had been intercepted and in some cases deciphered.
    2. The security of the Vigenere cipher could be improved by also encrypting the code word, so that even if the enemy cryptanalysts discover what the word is, they still have no idea what the word translates to in cipher text. For example, if a message relaying the fact that the keyword is “white” is intercepted and decoded, then the enemy has the upper hand and the ability to decode all your messages using the Vigenere cipher. However, if they know that the word used is “white,” but do not know what white translate to in cipher text (and the enciphered version of white is used as the keyword for the Vigenere cipher), then you maintain the upper hand. As an additional measure of security, any code can be used to encrypt the key word. Enemy code breakers essentially have to figure out two separate codes.
    3. The Great Cipher remained unbroken for such a long period of time for a variety of reasons. First of all, instead of translating individual letters in the plain text into cipher text, it transformed messages syllable by syllable. Also, some “traps” were implemented in the code that did not stand for encrypted letters, but instead deleted the letters that came before it. In addition, increase the difficulty of deciphering the message, the pattern of encoding for syllables was sometimes broken and individual letters were represented by isolated numbers. Any person trying to break the code would have to work on a word to word basis, filling in the blanks with a “cross-word like” method.
    4. The advent of the telegraph motivated the use of more secure ciphers because telegraph use required the assistance of a telegraph operator and when a private line wasn’t available, a public telegraph station. This meant that in order to communicate in a timely manner, messages were exposed to a number of individuals who would not be ideally privy to such information. To combat the effects of so many people seeing messages that were supposed to be private, secure forms of encryption became more popular. They helped to ensure that sensitive information that had to be passed through many hands before reaching its final destination remained secure.

  2. Rachel Lundberg

    1. Mary Queen of Scots and her contemporaries thought their ciphers were unbreakable, whereas those described by the quote were completely aware that a skilled cryptanalyst could crack just about any cipher they could come up with. For this reason, the latter were probably more careful about the information they transferred and more prepared to deal with the consequences of their messages being deciphered.

    2. The cryptographers could agree upon a different method of creating the Vigenere square, so that the shift numbers would be out of order. To make this work, they would use a set of numbers (between 1 and 26, or some other numbers if they decided to number their square differently) as their keyword instead of a word. That way, even if the keyword were known, the cryptanalyst would not know the cipher alphabet they were using. Further, the cryptographers could give each row several different number labels, and each time they cycled through the numbers that constituted their keyword, they could switch to referring to the next set of labels. The downside would be that the communicators would have to keep instructions somewhere for the construction of the irregular Vigenere squares.

    3. Most of the numbers of the Great Cipher represented syllables, presenting a greater number of possibilities than if they stood in for letters. It was made tougher by the fact that the cipher was not consistent--some numbers represented letters rather than syllables. Finally, the cipher included little tricks, such as numbers that removed those that came before.

    4. People who sent sensitive information by telegraph needed strong encryptions because they not only suspected, they KNEW others would be reading their messages. There was not just the threat of enemies tapping the wire, but in order to be sent, the messages had to be read by operators who could potentially be bribed for their knowledge.

  3. Sam Mallick

    1. The time before the widespread use of the Vigenère was characterized by a much greater fear that a ciphered message would be read. This meant that the governments of Europe put a much higher priority on employing skillful cryptographers. Fear led to caution because governments knew their codes could be cracked and were also confident that they could break codes of other nations. Occasionally, a particularly effective cipher would go uncracked, but on the whole codes had to be viewed as a temporary deterrent from prying eyes.
    2. The Vigenère relies on multiple rows of potential cipher alphabets. Typically, there are 26 rows, each beginning with a different letter of the alphabet shifted over one from the preceding row. By scrambling the order of these rows, using less predictable patterns within the rows (or, better still, no patterns at all), or even using more than 26 rows (symbols and numbers could be used in the keyword), the cryptographer can complicate and randomize an already complex cipher system that would be very difficult to crack.
    3. Typically, ciphers rely on replacing individual letters with something representative of individual letters. By using numbers to represent entire syllables, the Rossignols had a much more complicated cipher alphabet that is counter-intuitive to Western reading (Japanese uses a syllabic alphabet, but most Western languages combine letters to make whole syllables). In addition, further complications and traps within the cipher meant that frequency analysis would be somewhat difficult.
    4. With the advent of the telegraph, messages were sent in a much more public way. When before an individual letter carried by an individual messenger had to be specifically acquired, of which the sender and/or the intended recipient would probably be aware, the telegraph made the interception of messages easier and more discreet. Messages could be tapped or stolen by bribed telegraph transmitters. It was therefore necessary to introduce more secure encryption techniques.

  4. Aubrey

    1. This is creates a different environment, because correspondents are aware that their message may be intercepted and decrypted. Because of this, they will probably not send messages that were to risqué. However, this also means that it is much more difficult to relay important messages with confidentiality.

    2.The Vigenère cipher could be more secured by using more than 26 different rows of letters. There could be more rows where the letters are not in alphabetical order, making it harder for a foe to decrypt.

    3.The Great Cipher was an original idea. This meant that cryptanalysts could not use standard procedure to decrypt the cipher. The Great Cipher also used phonetics instead of writing, which made it much harder to decrypt. Encoding syllables had not been exploited during the time of the cipher, so it was not known to check for this. The nulls and fake symbols heightened the security

    4.In order to send a telegram, the message one wanted delivered went through a number of operators before reaching its destination. Because of this, the message was not strictly private. Anyone wanting to send a confidential message would have to encrypt it in order for it to remain a secret. Operators were frequently bribed to divulge information sent in telegrams.

  5. Tanner Strickland

    1. In the time between that of Mary Queen of Scots and the creation of the Vigenere cipher, cryptanalysists had the upper hand on cryptographers. Since the cryptanalysts were able to decipher the monoalphabetic substitution ciphers used by cryptographers, this time period was characterized by a sense of insecurity felt by anyone sending an incrypted message. Nobody could be certain that his or her message would not fall into the wrong hands and be read by enemies, so at this time, people were probably very cautious with what they said in any message they sent. As a result, it is very likely that few people included anything in their encrypted messages that could incriminate them, like Mary Queen of Scots did.

    2. Although the Vigenere cipher is already extremely difficult to crack, certain letter combinations could be initially set as nulls, so when those letter combinations appeared in the cipher text, only the reader would know to ignore them. Anyone trying to crack the code, however, would be further confused by this addition.

    3. One major factor that led to the security of the Great Cipher was the fact that the people who made it thought outside the methods used by most cryptographers. They were creative and unprecedented, forcing others to have to cast almost blindly for a way to crack the cipher because they had no model to work off of. The Great Cipher was something cryptanalysts had never encountered before, so they had to try to crack the cipher through trial and error. Also, the addition of traps within the cipher that did not follow its pattern of creation made it even more difficult to crack.

    4. One reason why people began to use ciphers that were more difficult to crack, like the Vigenere cipher, after the advent of the telegraph was because there was very little privacy involved in telegraphs. Numerous people saw them, such as the telegraph operators and anyone who was tapping the telegraph wires. Since access to messages was so easy, a cipher that was more difficult to crack than a monoalphabetic substitution cipher was necessary. Also, many of the messages sent by telegraph did not need to be deciphered at the speed of messages sent earlier during times of war, so people could begin using more complex ciphers that were harder to crack. Finally, technology had moved forward greatly since the time when the Vigenere cipher was largely ignored, so people had more resourses to encipher and decipher text at a faster rate.

  6. courtneysh

    1. Since cryptography was becoming more standard, it could be assumed that a weak encryption was a risk. More people were using codes and because of it, more people had the skills to break codes. In Mary Queen of Scots experience, she was the only person she knew who used codes to communicate, causing her to be careless in her technique. Cryptography had become a newsworthy topic, and the new attention it was getting seemed to inspire people to be more careful.

    2.The Vigenere cipher was a vast improvement from the monoalphabetic ciphers that had dominated the past, but codes are only good as long as they have not been cracked, and the Vigenere cipher would inevitably be broken at some point even if it would take some time. To further encypt the Vigenere cipher, nulls could have been added, some words could have been assigned separate symbols, or perhaps longer, more obscure code words could have been used, but there comes a point where the code is so complex that even the intended recipients have trouble decoding it or it takes so much time to decode that the message becomes outdated. The Vigenere cipher was very advanced and worked well for a time. Once it became less effective, perhaps it would be a better idea to start with a new code altogether.

    3. The Great Cipher was unique in its composition in that it used traps against the unintended recipient. The Rossignols, the father and son duo who created the cipher, assigned numbers to syllabic sounds rather than individual letters. The numbers were varying in their amount of digits, and some numbers existed that deleted the number preceding it. The Rossignols ensured that the Great Cipher would not be cracked, going through layers of encryption to make it so, and indeed when they died the secrets of the code went with them. It wasn't until two centuries later that messages encrypted with the Great Cipher could be read again.

    4. The telegraph was the first step in closing the distances between cities. If a man committed a crime in Paris and fled to London, his description could be telegraphed to the London police before he arrived. With this kind of speed, more complex ciphers, like the Vigenere, were considered a safer option since at least its layers would buy time for the criminal.

  7. Max Gillett

    1. During the time of Mary Queen of Scots, cryptanalysis was still in its infancy. There were few dedicated centers of cryptanalysis within countries, and only a limited number of types of ciphers existed. Before the development of the Vigenere cipher, but after the time of Mary Queen of Scots, cryptanalysis was at a far more advanced stage, and more countries employed a staff dedicated to decrypting enemy communications. As such, the actual transfer of the message (how it got from point A to point B) was just as important as the encryption of the message itself.

    2. The addition of a null row determined by the sum of the letters in the keyword (or some variation) and a mathematical formula to determine the order of each row in the Vigenere square could both enhance the security of the cipher.

    3. Most expert cryptanalysts were aware of monoalphabetic substitution ciphers, transposition ciphers, homophonic ciphers, and the Vigenere cipher, and were accustomed to looking for evidence of these in the ciphers they obtained. Whenever an innovative and more reliable method of encryption was conceived of, news of its discovery usually spread to other cryptanalysts and the new technique was effectively incorporated into their “toolbox.” Knowledge of The Great Cipher’s inner workings was kept closely guarded, and the cipher was not based on traditional letter substitution, but rather a syllabic substitution system. While traps such as nulls were implemented, these were the key factors that guaranteed the cipher security for such a long duration.

    4. I think that those who sent their communications via telegraph recognized that their transmissions were now relayed out in the open, open to interception, and that their messages now passed through several hands before reaching their intended recipient. The employment of a more complex cipher was only logical.

  8. Danielle Curran

    1. In this environment the people sending encoded messages were probably more careful with how much information they disclosed in their messages even though they were encrypted because they knew there was the possibility that their code might be broken. The environment that Mary Queen of Scots experienced was very different because the possibility that someone might decipher her messages did not occur to Mary Queen of Scots and thus she was very open in her letters.
    2. Instead of having each cipher alphabet in alphabetical order, a keyword cipher could be used to create the basic cipher alphabet and then this alphabet could be shifted again and again to create a new Vigenère square.
    3. Every number represented a French syllable instead of an individual letter, although some numbers actually did represent letters. Also there was a number that deleted the number in front of it and other "traps."
    4. It is much easier to intercept telegraph messages than letters because all messages went through operators who could be bribed.

  9. Tyler Merrill

    1) Due to the development of frequency analysis, monoalphabetic substitution ciphers could be cracked by enemy code breakers. Before the Vigenere cipher was created, people had to assume that if the message was intercepted, it would be deciphered. This meant that protecting the message was the primary means of safety while encryption simply gave the user more time before the enemy knew the secret message. This is different from the time of Mary Queen of Scots because during this time, people assumed that their code could not be broken. This led to people giving away their secrets without being aware of the possibility of it.

    2) The Vigenere Cipher could be strengthened by using more sophisticated ciphers down the table. If a few caesar shifts were replaced with other ciphers like keyword ciphers, the complexity is greatly increases. Also, increasing the length of the keyword would increase the security. If a keyword uses letters from different areas of the alphabet, then the security will also be increased.

    3) The Great Cipher was so secure because the elements of the cipher text did not represent individual letters, but syllables. This means that the cipher text contains many more elements than a cipher that replaces each letter with another. (There were 587 different numbers in the Great Cipher.) Also, the cipher contained many traps. One specific trap was that one number coded for the deletion of the previous number. This added security to an already complex cipher.

    4) The telegraph enabled communication at an amazing speed compared to prior methods, however, it also made many other people privy to the message being sent. The message had to be sent by the telegraph operator, who could be bribed to relay information. The telegraph wires could also be tapped by enemies who could then see the message being sent. This required more secure codes to protect information.

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