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Publication Date
2023-01-17
First Advisor
Geremias Polanco
Document Type
Honors Project
Degree Name
Bachelor of Arts
Department
Mathematics and Statistics
Keywords
Blockchain, cryptography, digital signatures, hash algorithms, consensus mechanisms, encryption schemes, cryptocurrency
Abstract
This thesis is an exploration of the mathematical concepts employed in modern encryption schemes, with a focus on their use in blockchain technologies. The goal is to provide an introduction to the operation of blockchain and to use it as a frame for investigating common information security algorithms in use today and the underlying hard math problems that make them possible. The algorithms discussed include the Secure Hash Algorithm family, the Digital Signature Algorithm, and the Elliptic Curve Digital Signature Algorithm. This paper examines the underlying mathematical problems employed by each of these algorithms, which include the discrete logarithm problem, the problem of finding eth roots modulo N, factoring large numbers, and the elliptic curve discrete logarithm problem, and their relative complexity to demonstrate their ability to provide information security.
Rights
©2023 Lucy Groves. Access limited to the Smith College community and other researchers while on campus. Smith College community members also may access from off-campus using a Smith College log-in. Other off-campus researchers may request a copy through Interlibrary Loan for personal use.
Language
English
Recommended Citation
Groves, Lucy, "Mathematics Underlying Cryptographic Protocols with Application to Blockchain" (2023). Honors Project, Smith College, Northampton, MA.
https://scholarworks.smith.edu/theses/2557
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Comments
vii, 57 pages: charts. Includes bibliographical references (pages 56-57).