Abstract

The theory of continued fractions has applications in cryptographic problems and in solution methods for Diophantine equations. We will first examine the basic properties of continued fractions such as convergents and approximations to real numbers. Then we will discuss a computationally efficient attack on the RSA cryptosystem (Wiener's attack) based on continued fractions. Finally, using continued fractions and solutions of Pell's equation, we will show that the Diophantine equation

x^4-kx^2y^2+y^4 = 2^j (k,j are natural numbers)

has no nontrivial solutions for j=9,10,11 given that k > 2 and k is not a perfect square.

Publication Date

5-8-2009

Document Type

Thesis

Student Type

Graduate

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Anurag Agarwal

Advisor/Committee Member

David S. Barth-Hart

Advisor/Committee Member

Manuel A. Lopez

Campus

RIT – Main Campus

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