Gedanken experiment: suppose a mighty organisation wants to take over bitcoin for whatever reason that is not financial. They want to do this in the most brutal way one can think off: make an entirely new block chain, starting with Satoshi's genesis block as it is, and distributing it, so that it will be the accepted block chain by all nodes: in other words, it should be of similar block height, and include some more PoW than the actual, current block chain.
They give themselves a year to pull off the feat.
How much $$ do they need to do so grossly ?
My rough guess is that it will be somewhat in the ballpark of the current market cap of bitcoin, but it could be in fact about 7 times higher too.
Essentially, they would need to buy/construct A LOT of hardware, and use A LOT of power to re-calculate a new chain. In what ballpark would the price of such an act range ?
Again, note that although they would, at that point, own all of bitcoin (all the addresses they would generate would be theirs of course), this would probably kill bitcoin. Their aim wouldn't be to make financial win, but another political goal, whatever it is (for instance, destroy bitcoin). How much do they need if they give themselves about one year to do so ?
And with a simple one line code change we can all upgrade to a new version of Bitcoin Core that completely ignores their "attack chain". They fail in their attempt to destroy Bitcoin, and they waste all that money on absolutely nothing.
As a realistic attack, it's foolish and wouldn't be successful.
But, if you're simply curious, there are a few things you'll have to consider first...
Where will they get their ASICs from? There aren't enough in existence right now to pull off their intended attack, so they'd first need to build their own chip foundry and then create enough ASICs to generate the needed hash power.
Where will they house all that equipment? They'll need a site with a LOT of electricity, and some significant amount of cooling equipment to prevent it from all overheating.
We'd need to predict how much the difficulty will rise over the next year, but assuming we could come up with a reasonable estimate, it shouldn't be too difficult to calculate a reasonable amount of electricity cost and hash rate. From there, you'd have to come up with your own ideas about what it would take to manufacture, house, cool, and maintain all that equipment.
Now, if they can use slave labor to manufacture everything, can steal or "confiscate" the operations facility, and can get free electricity, then I suppose the attack is just reduced to the cost of the raw materials needed.
