What is expected from a mathematics student bachelor's thesis?

Well, I like maths, I like studying it and applying it. But I always feared the moment when I'd actually have to do a thesis. I'm in my third year of bachelor's studies. What I was wondering about is what kind of topic should I be looking for, for my thesis? It just is hard to me to see how I could actually research and contribute something to the field as a bachelor's student, as in something not trivial and that no one with much more education has come up with before.

From merely passing courses to coming up with something of mine is a huge leap for me, and I can't see how I can do something meaningful with the limited education I have. I'm feeling a bit like in maths, before say a phd there would be nothing new for me to come up with. I am interested in cryptography, so I was given by one of my teachers a paper on elliptic cryptography that seemed interesting and a nice starting point. But now I realise I don't know where to head.