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?
I guess there is no consensus among researchers and academics on the security of Bitcoin protocol. Thanks to Stack Exchange Network, The following links should help you to answer some of your questions:

1- Bitcoin research at Cryptography StackExchange

2- How secure is the Bitcoin protocol? at Cryptography StackExchange

3- Are there any fundamental security vulnerabilities in Bitcoin? at Bitcoin Stackexchange

Here is a comprehensive list of research publications at Bitcoin wiki that include research and analysis of Bitcoin.