On the other hand, with the appropriate knowledge, precautions, and effort bitcoin can provide the tools necessary for near complete anonymity against an entity regardless of their resources.
That is indeed the case I am interested in. I really don't care if the government can find out if Mr. X is buying a sexual toy, but rather if they can find out who is funding paramilitary organization Y with millions of dollars even though I would expect such a person to use the best privacy methods. Specifically, I am looking into graph analysis and what it enables us to know even when used with strong privacy measures.
Well, this makes for a fun scenario. To discuss it we'll have to make some assumptions.
Lets start by assuming that the paramilitary organization is not covert. The government knows of its existence and its actions. Furthermore, lets assume that the paramilitary organization has publicly published a bitcoin address for receiving bitcoin donations towards its activities. This means that by monitoring the paramilitary organization's address they can determine exactly how much bitcoin the organization is receiving and from which addresses they are receiving that bitcoin.
This means that if we're going to donate to the organization, we need to ensure that the government is not able to connect our identity to the address from which we send.
Since the total daily transaction volume of bitcoin right now is about 2.85 million bitcoin, it is probably going to be difficult to acquire millions of dollars worth of bitcoin anonymously.
Lets assume though that through anonymous communication methods (TOR Chat?) we happen to find someone who owns 91,076.92 BTC that they want to cash out. we make arrangements for a dead drop of $1 million in cash that we've somehow anonymously acquired and stored, and they transfer the coins to an address that we've created offline.
So, assuming that we managed to remain anonymous in our acquisition of the $1 million in cash, and in our communications, there is now no way to identify who owns the 91,076.92 bitcoin.
We now must connect a client to the network in such a way that the government cannot trace our connection back to our ip address. This means we will need either a trusted or hacked chain of proxies. If TOR is as good as obscuring our ip as it claims to be, then we can use TOR for our chain of proxies. We use the connected client to sign a transaction transferring the 91076.92 BTC to the paramilitary organization's bitcoin address and then shutdown our client and TOR. We then destroy the hard drive that was used for the transaction as will as any other copy of the address or private key that we used for our transfer.
At this point, the government can probably tie the donation back to the person who has our $1 million, but they are unable to identify us as the "middle-man" who enabled the transfer. It is up to the person with $1 million to convince the government that they are not responsible for the donation to the paramilitary organization. Even if they do manage to convince the government that they didn't know where the BTC was going, the government probably won't look very kindly on their decision to engage in a completely anonymous $1 million transaction.
You can see from this description one of the biggest issues that you have to overcome in moving such a large volume of bitcoin anonymously. You need to find someone who is willing to supply you with bitcoin in a completely anonymous manner. This either means finding a single person who is willing to do that, or putting a LOT of work into finding many people who each are willing to supply a smaller amount. Once you find these people, they either need to transfer the bitcoin trusting that you'll drop the cash at the dead drop location, or you need to provide them with the drop location trusting that they will send the bitcoin once they have the cash.
