A collection of research efforts I made to satisfy various requirements as an undergrad. Below is a brief summary of each paper found in the repository.
Honors Thesis - A Robust Numerical Method for a Singularly Perturbed Nonlinear Initial Value Problem:
I propose a numerical method for approximating the solutions to differential equations that has applicable contributions to the
field of mathematics. This paper was defended at a conference against several graduate level mathematicians.
Validation of Secure Network Traffic and the Convergence to Quantum Mechanics:
This paper presents research on various encryption schemes and their applications in securing
data. Specifically, I discuss their vulnerabilities, implementations (both logically and mathematically), and briefly
mention their durability against cryptanalysis attacks. I also present their mathematical properties, and theories that
are assumed to hold within a security parameter. In particularly, I focus my attention on the RSA (Rivest, Shamir,
and Adelman) Encryption Algorithm and AES (Advanced Encryption Standard) Algorithm in CBC mode (Cipher
Block Chaining) against chosen-plaintext attacks1 due to their popularity. I also introduce BB84 (Benett and
Brassard 1984) and its relation to the one-time pad encryption scheme. Finally, by analyzing the pros and cons of all
of the algorithms, I explain why the use of the one-time pad and BB84 key exchange are inherently superior to what
is used today.
Applications of Abstract Algebraic Structures in Semantically Secure Encryption Extending to Network Security:
I present research on various encryption schemes and their applications in securing data. To do
this, I discuss their vulnerabilities, implementations (both logically and mathematically), and briefly mention their
durability against cryptanalysis attacks. I will discuss their mathematical properties, and theories that are assumed to
hold within a security parameter. Namely the RSA (Rivest, Shamir, and Adelman) Encryption Algorithm and AES
(Advanced Encryption Standard) Algorithm in CBC mode (Cipher Block Chaining) against chosen-plaintext
attacks1. Finally, I will explain why all cryptography will eventually converge to a field of quantum mechanics.