| 1. Bitcoin has no rigorous security definition. 2. Bitcoin can be "attacked" (for some vague notion of what it means to attack a system that has no security definition) in polynomial time. 3. The economics of Bitcoin are extremely suspect and based on a poorly developed economic model, supported by neither the Austrian school nor by modern monetary theory. This is probably the underlying cause of the lack of a security definition, as the security definition of a digital cash system will almost certainly be driven by the system's economic model. These issues have been covered ad nauseam by many people, and have been largely dismissed by the Bitcoin community. All the while we have seen increasing amounts of energy sunk into Bitcoin mining, we have seen a major block chain fork that left transactions in question, and we have seen wild fluctuations in the value of Bitcoin currency. |
Bitcoin is a heuristic for Byzantine concensus that requires 50% + epsilon of mining hash power to subvert.
This is not explicitly stated in the original paper, but the original paper comes very close.
I don't know what else you would want.
Regarding economics: All you need for a functioning currency is a supply of speculators who will bet on its future value and thus prop it up. That is only sustainable if the currency is the best at what it does for some meaningful niche (e.g. untrusted digital transactions). This is not part of any proir school of economics, but it's close to common sense, and is strongly supported by the success of bitcoin thus far.