Hamming Codes and the McEliece Cryptosystem

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Authors
Dill, Ben
Advisor
Phil Rose
Holly Zullo
Grant Hokit
Editor
Date of Issue
2011-04-01
Subject Keywords
Algorithm , Binary system (Mathematics) , Coding theory , Data transmission systems -- Design and construction , Redundancy (Engineering) -- Data processing
Publisher
Citation
Series/Report No.
item.page.identifier
Title
Hamming Codes and the McEliece Cryptosystem
Other Titles
Type
thesis
Description
Abstract
In this paper, we seek to understand some basic principles of coding theory. Specifically, we define and explore binary codes, Hamming codes, and a special application of coding theory known as the McEliece cryptosystem. We describe the meaning and usage of generator matrices and parity check matrices and present bounds on the number of codewords in codes of a given minimum distance and length. We present and prove several known results about Hamming codes, including the fact that they are necessarily perfect codes. We show how to construct a cryptosystem using any linear code and discuss the strength of the McEliece cryptosystem in a future where quantum computers are a reality. Finally, we present one program which automatically decodes strings encoded with a Hamming code and another which encrypts and decrypts messages using the McEliece cryptosystem.
Sponsors
Degree Awarded
Bachelor's
Semester
Spring
Department
Mathematics, Engineering & Computer Science