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    Hamming Codes and the McEliece Cryptosystem

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    DillBthesis_2011_Final.pdf (549.4Kb)
    Author
    Dill, Ben
    Advisor
    Phil Rose; Holly Zullo; Grant Hokit
    Date of Issue
    2011-04-01
    Subject Keywords
    Algorithm; Binary system (Mathematics); Coding theory; Data transmission systems -- Design and construction; Redundancy (Engineering) -- Data processing
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    URI
    https://scholars.carroll.edu/handle/20.500.12647/3408
    Title
    Hamming Codes and the McEliece Cryptosystem
    Type
    thesis
    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.
    Degree Awarded
    Bachelor's
    Semester
    Spring
    Department
    Mathematics, Engineering & Computer Science
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