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Can anyone with enough computing power, take over the network ? This is following from a previous comment where I was asking :

... how can that be possible (to control the network) if mining tend asintotically to 21M ( alias the end of mining ) ? The only control is on early production of coins, not on the allover crypto-economy IMO.

where I'd been answered like the following :

Blocks do give miners coins, but that's not their purpose. Their purpose is to keep an ordered list of transactions. By using 51% of the mining power, they can prevent transactions from getting on that list indefinitely.

What do you say ?

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There is no question as to whether or not someone with 51% of the hashing capacity can "control" the network (i.e., decide which transactions get mined, and receive 100% of bitcoins newly issued in each block).

In fact, that happened on March 12th, 2013 following the "hard fork", when a friendly 51% attack occurred so that blocks mined on the pre-v0.8 clients would become the longest chain, rather than continuing to extend the blocks created by the v0.8 client which hadn't followed a previously unrecognized limitation of the Bitcoin protocol.

What the party with 51% hashing capacity cannot do is more important.

They cannot change the rate of issuance, for example. There are only the current 25 BTC issued per-block until block 420,000 when that will drop further, per the algorithm. The "attacker" can double spend transactions that the attacker had made (e.g., deposit bitcoins to an exchange then withdraw some other coins before double spending against the original deposit.)

So with very little economic incentive to "control" the network, there is little concern that one will happen (or if it does that it will be of much significance.)

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