Bitcoin Research 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.
 A: Added: There are financial aspects of bitcoin too.
With Bitcoin At $60k, Satoshi Nakamoto Is Now One Of The 20 Richest People On The Planet on March 13, 2021.
Satoshi Nakamoto is the anonymous "entity" who created bitcoin.

Two papers with real world monetary implications:
Two Bitcoins at the Price of One? Double-Spending Attacks on Fast Payments in Bitcoin
Don't know if this is fixed in the current implementation.
An Analysis of Anonymity in the Bitcoin System
Quote:

At the time of theft, the stolen Bitcoins had a market value of approximately half a million U.S. dollars. We chose this case study to illustrate the potential risks to the anonymity of a user (the thief) who has good reason to remain anonymous.

Added
Bitcoin related news from popular media.
http://www.theregister.co.uk/2014/03/03/mtgox_to_customers_your_call_is_important_to_us_not/

MtGox declared bankruptcy last week, taking more than $US400m worth of Bitcoin with it.

http://www.theregister.co.uk/2014/03/04/bitcoin_bank_flexcoin_shuts_down_after_hackers_strike/

Bitcoin bank Flexcoin pulls plug after cyber-robbers nick $610,000
Your money is gone. Kthxbye

A: there is a nice preprint server, widely used by cryptographic researchers: http://eprint.iacr.org
If you do a search, there are some papers talking more or less about bitcoin. I guess "Decentralized anonymous credentials" is a good begin for your student. This is indeed a well known area of research, and is the main point of bitcoins (with mining).
You may take a look at Google Scholar http://scholar.google.com/scholar?hl=en&q=bitcoin&btnG=&lr= there are many references dealing with bitcoins, probably some mathematical with a large interest.
