I have recently been assigned to advise a student on a senior thesis. She has taken linear algebra, introductory real analysis, and abstract algebra. Her interest is in cryptography. And she has a love of Bitcoin. The point of a senior thesis is to get a student to teach themselves a subject and learn to find and read mathematical papers. Original work that could be published would be nice, but is often untenable.

My question is whether anyone knows of any research that is/has being/been done in cryptography related to Bitcoin. Thanks.