# Is bitcoin cryptographically secure

I am trying to understand the bitcoin protocol in the context of computational cryptographic security.

The question is a reference request to foundations of cryptography articles on bitcoin.

My first question is what abstract cryptographic protocol bitcoin is trying to implement? Do we have a definition of electronic money/digital currency in cryptography that captures bitcoin? What are the security requirements for a secure electronic money?

If the answer is yes, companies like eBay provide a centralized mean of electronic money transfer. Does considering a decentralized electronic money changes the definition of abstract cryptographic protocol for electronic money? Or is it just the same concept but in a model where there is no trusted third party?

Can the adversary break the protocol if it has more computational power than the combined computational power of other (honest) parties?

Assume that we have $n$ parties $P_i$ for $1 \leq i \leq n$ plus an adversary $A$ networked and the adversary wants to break the bitcoin protocol. For simplicity let's assume that the network graph is $K_{n+1}$ and adversary does not control the network and simply is a party like others. What would be the exact mathematical claim about the security of the protocol in this simple case?

• Have you read the original bitcoin paper? S. Nakamoto, Bitcoin: A peer-to-peer electronic cash system – Max Mar 15 '13 at 11:24
• I doubt that there is a formalised understanding of what it means for a complex system like the Bitcoin to be secure. There is some work on notions of aspects of Bitcoin, e.g. regarding the security of time-stamping systems (e.g. "On Provably Secure Time-Stamping Schemes" by Buldas and Saarepera from a few years ago, or Lipmaa's dissertation "Secure And Efficient Time-stamping Systems"), but I'm not sure how close this is to Bitcoin's time-stamping. – Martin Berger Mar 15 '13 at 12:51
• There is a new paper on arxiv that claims it is not. Ittay Eyal and Emin Gun Sirer, Majority is not Enough: Bitcoin Mining is Vulnerable. – user18275 Nov 6 '13 at 0:29
• Here is a related cstheory question that might be of interest. There is also a whole bitcoin SE, but it tends to not be very critical or questioning of the technology and is more for practical questions about using bitcoins. However, it might still be useful to search there. – Artem Kaznatcheev Nov 6 '13 at 17:05