## Cryptography

#### The History and Mathematics of Codes and Code Breaking

In preparation for class on Tuesday, September 21st, please read pages 63 to 78 in the second chapter in the Simon Singh book and respond to the following questions.

1. Prior to the work of Babbage and Kisiki, “most cryptanalysts had given up all hope of ever breaking the Vigenère cipher.”  Given that the Vigenère cipher was well-known, what might lead a cryptanalyst of that time to give up hope in cracking it?
2. If the rows of the Vigenère square Singh uses (p. 48) were not shifts of the standard alphabet but were instead other arrangements of the standard alphabet (such as keyword cipher alphabets or keyword columnar cipher alphabet), how would that impact Babbage’s cryptanalysis technique?

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1. #### Rachel Lundberg

1. Cryptanalysts had come to rely on frequency analysis to crack ciphers, and as the Vigenere was not susceptible to traditional frequency analysis, cryptanalysts probably found themselves at a loss. The fame of the cipher was likely also a factor. They may have thought that if the Vigenere was breakable, it would have been broken already.

2. If the rows of the Vigenere square were not shifts, Babbage would not have been able to crack the cipher by determining the keyword. He would have had to employ frequency analysis on each of the different cipher alphabets used.

2. #### Sam Mallick

1. The Vigenere poses a great challenge to a cryptanalyst because it makes traditional frequency analysis impossible. One must completely rethink the process to crack a Vigenere cipher. While the solution might seem fairly obvious once explained, being the first one to figure it out was a formidable task. It required creative thinking, which had not been done in cryptanalysis for a long time, and lots of trial and error. It would be perfectly understandable for a cryptanalyst to get frustrated and give up, and if the world's best cryptanalysts all gave up, it would be a reasonable assumption that the code could not be broken.

2. If the rows were in any way scrambled, Babbage and anyone attempting to break the cipher would have to guess the length of the keyword and construct, based mostly on frequency analysis, the multiple cipher alphabets used. If a long enough passage were given, the cipher could be broken, but it would be very difficult.

3. #### Erin Baldwin

1. When faced with the task of deciphering the Vigenere cipher, cryptanalysts before Babbage were hopeless even though it had been around for a long time, because of the complexity of the cipher. The frequency analysis technique, the main tool of codebreakers up until this point, is useless against Vigenere and no one had yet found an alternative. Also, because so many different alphabets could be used, an analyst was essentially breaking codes within codes, adding to the complexity and the intimidation factor of the Vigenere cipher.
2. Babbage, after determining the length of the keyword in the Vigenere cipher, relies on frequency analysis to determine the shifts in the alphabets of the cipher. If another type of encryption technique were used instead of shifts, Babbage would no longer be able to utilize patterns in the graphs of frequency analysis to break the keyword alphabets.

4. #### Jonathan O'Hara

1. The Vigenere Cipher could not be cracked with mere standard frequency analysis, which was, at the time, the main form of code-breaking. It had not been broken before the time of Babbage, and the fact that many had tried yet none had prevailed could have led one to believe it was almost impossible and futile to even attempt.

2. If the Vigenere cipher was not made up of shifts of the standard alphabet, Babbage would've had to determine the keyword and its length. He would then have to use frequency analysis on the multiple possibilities of cipher alphabets. Basically, it would have been even HARDER.

5. #### Tyler Merrill

1) Because the Vigenere Cipher was well know, yet unbroken, many people assumed that if it could be broken, it would have already been . It remained unbroken for so long because frequency analysis was the main technique of cryptanalysts. This method alone cannot completely solve the Vigenere, so a cryptanalyst may assume it was not able to be solved.

2) If the Vigenere Square used by Singh had been composed of rows that were ciphers other than shift ciphers, the pattern of the frequency analysis of every nth letter (n represents the number of the letter in the keyword.) would not reveal the identity of the keyword. Babbage would have to do a more in-depth analysis of the letters to determine the keyword. Because of this, he would most likely decipher the code while trying to discover the keyword. This would make it much harder to crack the code, because the keyword would be unknown and you must solve n ciphers that must all fit together.

6. #### Danielle Curran

1. Because none of the existing strategies for cracking ciphers worked on the Vigenère cipher cryptanalysts gave up on deciphering the code. The same thing happened with monoalphabetic ciphers before the Arab scholars developed frequency analysis. Without a known strategy for solving a problem, most people knew of no way to go about deciphering the code.

2. If the rows of the Vigenère square were not shifts of the standard alphabet, Babbage's technique would still work, but it would be much more difficult to decipher the code. Frequency analysis would help a cryptanalyst to decipher letters such as e and t in each of the rows of cipher alphabets, but a clear pattern would not be as easily visible.

7. #### Tanner Strickland

1. The fact that the Vigenere cipher had a reputation of being unbreakable would have made cryptanalysts more likely to believe that this is the case because nobody wants to waste his or her time trying to accomplish something impossible. It is the same as if a math teacher gave students a problem and told them it was impossible to solve. The students might try to solve it for a little while, but eventually they will give up because they do not think it is possible. In the same way, cryptanalysts did not want to try to accomplish a something that was widely believed to be impossible.

2. If the rows of the Vigenere square were not standard shift ciphers, but instead other kinds monoalphabetic substitution ciphers, the level of difficulty of deciphering the plain text would increase greatly. It would become much more time-consuming to decipher because the only method to figure out each individual row of the square would be to use frequency analysis. Also, frequency analysis would be more difficult because one has a smaller total number of letters off which to base the frequency analysis, increasing the chance that the frequencies could be skewed.

8. #### Max Gillett

1. I think that most cryptanalysists of that time were familiar with concepts such as frequency analysis, and may even have had a knack for recognizing patterns, but lacked Babbage's creativity and reasoning skills. I also think it's very easy for someone (not just a cryptanalyst) to conclude that a problem is unsolvable based on the lack of others' success, and write off the challenge as impossible.

2. Babbage's method of determining the length of the keyword would not be impacted, but he would have had to apply more frequency analysis (and some more guesswork) after determining the keyword's length in order to decipher the message.