1. Abstract: Cryptology is a combination of the processes of keeping a message secret (cryptography) and trying to break the secrecy of that message (cryptoanalysis). Professor Lesh of the math department teaches a general education math class on cryptology, during which the first several weeks focus on classical cryptology (early techniques for encoding a message). I have created a set of web based tools that will act as an aid for the students helping them to break the codes they will see in their homework. Solving these homework problems is very time consuming but with the web based tools I have created students will be able to solve these problems faster allowing them to do more as well as having another means to study. Professor Lesh will also see theses advantages since she solves the problems for the class as well. Additionally, it will allow her to use more complicated examples since students can now backtrack more easily. Since these tools are web based it will allow students to use them without any downloading or installation. It will also make them easier to access since they can be used from almost any computer with an internet connection. By being easy to use and accessible to everyone, the tools I created should greatly benefit the students and the professor of a classical cryptology course. MonoAlphabetic Cipher: This is the next cipher students learn. The Caesar Cipher is a form of the Monoalphabetic cipher, both have a 1-1 mapping between ciphertext letters and plaintext letters. However, while knowing the decryption of one letter in the Caesar Cipher helps you decrypt the rest of the code, knowing one letter here does not help decrypt the rest. In this area of the page students can enter the plaintext value of each of the ciphertext letters. By comparing the frequency analysis of the typical English language to the frequency analysis of the ciphertext, students will have a guide to help them decrypt the code. They can see the progress of their decryptions in two places. The first is in the plaintext box located at the top, the second is located directly below that. Caesar Cipher: The first Cipher (a specific method of encoding and decoding a message) the students learn is the Caesar Cipher. In this cipher every letter is shifted some value forward or backwards. For example A with a Caesar shift of 3 would result in D. One severe downfall to this Cipher is that once you know one letter you know them all since all letters hold their relative positions. Also since there are only 26 values, this Cipher is very vulnerable to a brute force attack. For this tool, students can enter the value that they want to shift the text by. When they click shift, the result of this shift is displayed in the plaintext box. Vigenére Cipher: The Vigenére Cipher is the most complex classical cryptology cipher the students will work with. Unlike the Monoalphabetic cipher, this is not a 1-1 mapping, instead it is based on a keyword. Each letter of the keyword corresponds to a different Caesar shift (a=0, b=1…). The first part of the tool finds the repeated segments in the text. An example of this can be seen below. This is how the student finds the length of the keyword. Once they have the length of the keyword they enter it here and are given a place to input the keyword and can choose which group of letters they want to look at. By looking at the frequency analysis of a group of letters, students can figure out the keyword one letter at a time, decrypting the ciphertext. Repeated Strings: The figure to the left is what the student will see when they create the graph of repeats in the cipher text. By printing this out the student will be able to check off the factors of the distance between these segments. In order to do this as quickly as possible I used a version of a longest common sub-string algorithm. By creating a two dimensional array you can see the length of all repeats in two strings. In this case the two strings are the same. Rows are filled out one at a time. If the letter of the column matches the letter of the row the value of the upper-left cell is increased by 1, otherwise a 0 is entered (pseudo code to the right). Once the table is filled out you can examine it and find all of the repeats as well as how long it is and where it is located. This algorithm has a runtime of O(nm). Since it uses the same string it has a runtime of O(n 2 ). Here is one example below, with the string THBZTHBT. T H B Z T H B T T 1 0 0 0 1 0 0 1 H 0 2 0 0 0 2 0 0 B 0 0 3 0 0 0 3 0 Z 0 0 0 4 0 0 0 0 T 1 0 0 0 5 0 0 1 H 0 2 0 0 0 6 0 0 B 0 0 3 0 0 0 7 0 T 1 0 0 0 1 0 0 8 Future Work: If enough time is saved new Ciphers could be introduced to the class and new tools could be added accordingly. In the most extreme case a class could focus on classical cryptology and this tool could expand to accommodate that. Another feature that would be helpful if added would be the ability to encrypt as well as decrypt. This will allow students to create some examples of their own allowing them to more easily do additional studying. for(i=0; i<the length of the string; i++) { for(j=0; j<the length of the string; j++) { if (the ith letter is equal to the jth letter) cell [i, j] = cell [i-1, j-1] +1; else cell [i, j] = 0; } if (any repeated strings ended) (add the string and its locations to a binary search tree with the string as its value) } Senior Project – Computer Science – 2007 WebTools for Classical Cryptology Tristan Beeble Advisor: Chris Fernandes Typical English FrequencyCiphertext Frequency Analysis