I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was Galois theory. I am interested in doing 'my own' research, if you catch my drift. That is, I would like to apply the Galois theory I will be studying to something, and do some research. My professor mentioned some possible applications within coding-theory and cryptography. Do you have any specifics in mind? I would be happy to hear your insights.