Proposal for Undergraduate Math Research
My proposed research would consist largely of programming to support a new undergraduate mathematics course in cryptography. Cryptography is, of course, strongly tied to both computer science and mathematics, and draws from elements of both. There are numerous different cryptographic algorithms that are implemented in software, and I will be programming a variety of them for sample purposes.
Some of the types of programming I will be doing include programs that demonstrate classical cryptographic algorithms (shift, Vignere, AES and others) and public key encryption systems ((RSA and Diffie-Hellman). I will also be writing supplementary programs that serve as tools for understanding and attempting to decrypt the various encryption schemes, such as modular arithmetic and exponentiation, the Euclidean algorithm, frequency counts, and correlations. Finally, I will write a paper detailing the various programs that I wrote, and comparing and constrasting the different encryption schemes.