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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

Comments

vii, 57 pages: charts. Includes bibliographical references (pages 56-57).

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