# The Null Set

Philip Durham, Nick Garbis, Parav Patel, Leba Tolpin

The first step in creating our code was changing all of the words into its phonetic sounds. Using a dictionary, we changed all of the words into the sounds, and we ended up having more than one symbol for each vowel. Each vowel had its hard and soft sound, plus other variations. The way that eis pronounced in sea and the way it is pronounced in yes are different, so it will have a different symbol in each word. Because each vowel can have many different sounds, the letter frequency was disrupted. Each vowel became divided into different categories, so it was as if the letter did not appear as much as anticipated. The encoding into phonetic sounds causes an unexpected change in the spelling of the word . The word boy would be changed to boi. After the first step was completed, we then substituted the letters into numbers. We used a 6 by 6 block and them randomly assigned letters and sounds to the spaces. . Each sound was then replaced by a two digit number. We still had one extra sound that was not covered in the block, so we made a row 7, but it was only used in the number 57 There were 3 blank spaces that were also used in the text. They were used to separate each word. The final step was to replace each digit with a symbol. We used simple substitution for that, each digit being represented by a different symbol.

When trying to break Enigmaís code, we first divided the clusters into two digit numbers. Using the first paragraph, we tried to establish a frequency of numbers. In that method, the numbers 19, 03, 22, 70, and 08 were the most frequent. We then assigned each number a letter based on its frequency, and tried to substitute these letters into the cipher text. We substituted 7 letters to see if any possible words came up. We tried reading both horizontally and vertically. Only a few words appeared, like the and to. We then thought that the five number blocks differentiated between words. If the word was less than five letters, than fillers would be used. If it was more, it would go into the next blocks until fillers were needed to end the word. A word like computer would take up one whole block and three digits of the next block. The final two digits would just be filler. We didnít know how to distinguish when fillers were used and when they were not. Transposition seemed unlikely because it would have been hard to transpose and then put the words into the five number blocks. We would have not known where the words ended or began. We may have had the wrong letter frequencies because the methods seemed to work in some cases but not in most. One possibility was that a frequently occurring number was a space, but we used it as a letter.

For The Cryptsís code, we thought that they used the mixed cipher system. Since the words seemed to be kept in there original format, we thought that the cipher text involved substitution. We decided that the code did not involve the numerical encryption like ours did. Therefore, we assumed that it was the only group that did not change the set up of the plain text. When we looked at the single letter words, we assumed that they were either a or Im or e in the code. However, both m and e were used at the end of some two letter words. The usual two letter words do not end in an a or i. The mixed cipher system distorts letter frequency because a letter could be substituted for more than one letter in the plain text. If the letter z is frequent, it could be because it represents the letters band g. Then there might be an assumption that it is a more frequent letter, like e. However, we also thought that the code also involved transposition. A two letter word may not end in i or a, but it can start with them. The possibility of transposition made the decipherment much more difficult.

For the Kryptoniteís code, we originally thought that the single stars separated words. We also thought that they used a mixed cipher. The @ and ! were so frequent that they may have been used to represent more than one letter. When we used the single stars to separate words, there were a lot of two and three letter words, which seems normal. However, there were also a lot of words that were over ten letters long. At one point there was a word that was 17 symbols long. These words are not very common in text, so we abandoned out idea. We had no way of dividing the code up into possible words like we had in the other codes. We thought that they did not use transposition because there would be no way to tell when the word ended and another began. Just figuring out the letter frequency would not be enough to break the code. Without a way to divide the symbols up into smaller, parts, we had no direction. In all of the previous codes that we looked at, the cipher text was already broken up, like in the Cryptsís code, or we figured out a way to break it up, like in Enigmaís code. The smaller pieces were easier to work with and we could rule out some possibilities when there was a structure. The only piece of structure that we saw in this code was the division into paragraphs.

Since all of the codes seemed to use multiple layers, we could not break the cipher text. We could not get past the first step in any of the codes, which ruled out the possibilities of breaking the next steps.

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