#### Individual Presentation or Panel Title

Strengthening Cryptological Attacks: Applications of Frequency Analysis on the Hill Cipher

#### Abstract

The Hill Cipher is a cryptological method that uses 2x2 matrices to replace pairs of letters in a plaintext message with other pairs of letters to create a ciphertext message. Many aspects of number theory and linear algebra are involved in this technique of enciphering and deciphering a plaintext message. The purpose of this project is to investigate the relationship between the Hill Cipher and frequency analysis algorithms, which count how many times letters (or blocks of letters) appear in a plaintext or ciphertext message. Frequency analysis is typically used in monoalphabetic substitution schemes, which involve replacing one letter with another letter during the enciphering process. This project will apply frequency analysis to a polyalphabetic scheme. In this situation, an additional complication arises as the frequency analysis relies heavily on the position of the letter pairs. As such, it is not always a reliable method to find the deciphering matrix, unless the Maple code used to analyze the ciphertext message is augmented to take position of the 2-letter blocks into consideration. The goal of this project is to show how two cryptological methods that are not typically used together may be altered slightly to produce a reliable method of recovering the deciphering scheme.

#### Location

Glass Dining Room

#### Start Date

20-4-2013 3:30 PM

#### End Date

20-4-2013 4:20 PM

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Strengthening Cryptological Attacks: Applications of Frequency Analysis on the Hill Cipher

Glass Dining Room

The Hill Cipher is a cryptological method that uses 2x2 matrices to replace pairs of letters in a plaintext message with other pairs of letters to create a ciphertext message. Many aspects of number theory and linear algebra are involved in this technique of enciphering and deciphering a plaintext message. The purpose of this project is to investigate the relationship between the Hill Cipher and frequency analysis algorithms, which count how many times letters (or blocks of letters) appear in a plaintext or ciphertext message. Frequency analysis is typically used in monoalphabetic substitution schemes, which involve replacing one letter with another letter during the enciphering process. This project will apply frequency analysis to a polyalphabetic scheme. In this situation, an additional complication arises as the frequency analysis relies heavily on the position of the letter pairs. As such, it is not always a reliable method to find the deciphering matrix, unless the Maple code used to analyze the ciphertext message is augmented to take position of the 2-letter blocks into consideration. The goal of this project is to show how two cryptological methods that are not typically used together may be altered slightly to produce a reliable method of recovering the deciphering scheme.