Definitely possible (Score 3, Insightful)

I think I'm more qualified than most to answer this, since I in fact wrote my first published paper when I was in high school, and it was on cryptography. Most of cryptography is just maths, which is actually more accessible to beginners than other subjects since you don't special lab equipment. I'd say the best way to get into it is to think of a cryptographic problem you'd like to solve, and then just work on it. The problem that got me started was how to prove that you're a member of some group without revealing your identity. There are many different solutions, with different tradeoffs -- so even if a problem is supposedly solved there is often scope for new solutions.

For an idea of where cryptography research is going these days, she should read eprint.iacr.org. A lot of those papers are pretty technical and heavy going, but it will at least give some starting points.

The biggest problem I'd see is not finding a feasible problem, but finding a teacher capable of marking it. I know none of my high school teachers could have marked my cryptography research.