I would also strongly recommend her pursuing the quantum computing idea. When I was in high school (just a few years ago) I wrote a quantum computing algorithm that analyzed the effects quantum computing will have on hash functions. I also made modifications to a quantum simulator (written in C, run on a linux laptop) for a more "experimental" and tangible final project.
I recommend starting out with a book: "A Shortcut Through Time: The Path to the Quantum Computer" (http://www.amazon.com/gp/product/B000AXRTYM/qid=1 136705266/sr=8-8/ref=pd_bbs_8/104-0428655-4663948? n=507846&s=books&v=glance)
to think about which cryptology problems could be solved with a quantum computer.
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I would also strongly recommend her pursuing the quantum computing idea. When I was in high school (just a few years ago) I wrote a quantum computing algorithm that analyzed the effects quantum computing will have on hash functions. I also made modifications to a quantum simulator (written in C, run on a linux laptop) for a more "experimental" and tangible final project. I recommend starting out with a book: "A Shortcut Through Time: The Path to the Quantum Computer" (http://www.amazon.com/gp/product/B000AXRTYM/qid=1 136705266/sr=8-8/ref=pd_bbs_8/104-0428655-4663948? n=507846&s=books&v=glance)
to think about which cryptology problems could be solved with a quantum computer.