Katherine Morrison

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Whether it is online commerce, international relations, or simply through email communication, the encryption and decryption of data is essential to the inner workings of everyday life. To encrypt and decrypt efficiently, it is important that there is some structure behind the process rather than just a random procedure. The purpose of this research is to analyze different encryption schemes and their structure, with a focus on schemes that apply algebraic coding theory to cryptography. Cryptosystems based in algebraic coding theory are particularly important to the future of cryptography, as they are resistant to attacks by quantum computers, unlike many currently employed cryptosystems. Specifically, we examine the McEliece cryptosystem and its variations, in particular the use of Reed-Solomon codes. The goal is to understand the algebraic structure underlying the McEliece cryptosystem as well as to understand its shortcomings and variations that may strengthen it. The current results show that the original Goppa codes that are used in the McEliece systems are stronger and more secure than the proposed Reed-Solomon code alternative.

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