Secret Code Breaker Queenie Chou Richmond District Incentive Program Floor Location : M 7 C

The project studies the simple and complex mathematical equations involved in the structuring of a Cipher in Cryptography. I researched the association between math, encryption, and decryption in a Cryptograph. This project includes a literature research based on past information on types of cryptography, and also my self-study on the simplest cipher’s mathematical equation: Caesar Cipher, and the complicated process of Enigma Machine. I also looked at several cryptography algorithms for future reference.

While researching this project, I realized that there are many different types of Ciphers. There are Poly-alphabetic Ciphers (multiple simple substitution of alphabets), and Mono-alphabetic Ciphers (single simple substitution of alphabets). Example of mono-alphabetic ciphers is Caesar Cipher and for Poly-alphabetic ciphers there are the Vigenere Cipher, and the Engima machine. Of those, the Ciphers are divided into even smaller categories. Of course, Mono-alphabetic Ciphers are much less reliable than Poly-alphabetic ones as they are easy to "break" or "crack" due to their simplicity.

All of the mono-alphabetic ciphers are used in conjunction with a key. It may involve numbering the keyword’s letters alphabetically in columns. The resulting Ciphertext is a result of a mathematical shift in the original text. Re-Numbering involves re-arranging the order of the English alphabet with a four digit number. A Bifid Cipher uses a 5 by 5 grid set up like a multiplication table. The English alphabet is then converted to numerals.

Poly-alphabetic Cryptography is involved with complex mathematics. The RSA (Rivest-Shamir-Adleman) Cipher is encrypted with the use of Logarithms, Modular Arithmetic, and the Euler Totient Function. It is almost the most secure Cipher as encryption and decryption of the text involves such advanced math. The Vigenère cipher is a repeated key Cipher whose design integrates letter frequencies with its encryption. As the Vigenère Cipher is set out in a 26 by 26 alphabetical grid (each row begins with an alphabet shift of +1), the Ciphertext that is produced has a frequency distribution that is relatively horizontal when plotted on a graph.

This project further studies the relationship of math and alphabets and how mathematic will always be the underlying basis for cryptography.