Opinion on a Possible Senior Design 1 Project?

Question

I have two senior design classes and right now I'm prepping for the first one in the fall semester. I was thinking about implementing an RSA Stream Cipher using shift registers. Is this too easy?

Answer 1

I've implemented RSA in Mathematica and Python. It wasn't terribly difficult, and was a lot of fun.

p = large prime
q = large prime
n = p*q
phi = totient(n) = (p-1)*(q-1)
public = 65537
private = (1+k*phi)/public
where k is the first integer that makes private a whole number.
Encrypting:
y = mod(x^public,n)
Decrypting:
x = mod(y^private,n)

I have no idea how to implement it using shift registers, though. Are shift registers capable of calculating VERY large exponents? Sounds like a good project to me, though I wouldn't count on being able to achieve good security. The security standard these days is a modulus of 1024 to 2048 bits!