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.
Library of Congress Subject Headings
Continued fractions; Diophantine equations; Cryptography
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
Recommended Citation
Kaufer, Aaron H., "Applications of Continued Fractions in Cryptography and Diophantine Equations" (2009). Thesis. Rochester Institute of Technology. Accessed from
https://repository.rit.edu/theses/9085
Campus
RIT – Main Campus
Plan Codes
ACMTH-MS
