Andes, to have control of 50% of the network you need to deploy 101% processing power (you´ll end up having 50,5%)
But, why thinking there will only be 1 dishonest entity? If there is one, there could be more, each one of them would have their own self-interest on controlling the network. If a lot of "dishonest" entities with great processing power try to control the network, they would make the 51% attack less probable themselves.
Manuel, lets address the scenario where several powerful groups want to
destroy bitcoin (not simply manipulate it one way or another).
Under this scenario, the goal of all groups is the same, so the "
the enemy of my enemy is my friend" principle would apply. Why compete if we can cooperate? It does not matter if there is one or many powerful groups that want to destroy bitcoin, the result would be the same, as long as they have enough combined power.
...Which takes us to the obvious conclusion: bitcoin cannot survive in its current configuration without the support (implicit or explicit) from a decent percentage of the worlds economic powers (establishment).
Why? Because a successful attack on bitcoin cannot be prevented if the attacker (or attackers) have enough economic resources.
Why? Because the whole paradigm of the integrity of the system is based on brute force hashing. I.e. mine is bigger than yours paradigm.
As long as successful attacks can be carried out simply by the means of brute force, Bitcoins will never deliver the promise to subvert the current economic powers.So for one; to all anarcho capitalists out there, bitcoin is not the answer to your prayers. Bitcoin is not a resilient decentralized system per-se, and probably never will in its current incarnation, until the brute force paradigm is replaced for something else, that is really resilient to attacks by the means of force.
This is the greatest misconception in bitcoin right now, as I see it. It is sold as being the solution for the corruption of the banks and governments, which it is not. Banks and governments can render bitcoin unusable at their whim any time, if they ever perceive bitcoin as a real threat.
Better wake up.