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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.

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Try to ask on crypto.stackexchange.com . –  Zsbán Ambrus Sep 5 '12 at 16:57
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But first, look at all the existing questions in the bitcoin tag to ensure it's not a dupe: crypto.stackexchange.com/questions/tagged/bitcoin . –  Zsbán Ambrus Sep 5 '12 at 16:58
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Hmm, turns out there's already a stackexchange site specifically about bitcoins, in beta stage: bitcoin.stackexchange.com –  Zsbán Ambrus Sep 5 '12 at 17:05
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Bitcoin uses elliptic curves for digital signatures, you could start there. –  Felipe Voloch Sep 5 '12 at 17:21
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If she had a love of Bitcoin in September of her senior year, I guess she got a nice graduation present because the value has gone up over 1000% since then. –  Nate Eldredge Oct 29 '13 at 20:56
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2 Answers

up vote 13 down vote accepted

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

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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.

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I imagine the student has finished her senior thesis by now, but this answer may yet be helpful to others interested in bitcoins. –  Gerry Myerson Oct 29 '13 at 22:36
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