An attacker that controls more than 50% of the network’s computing power can, for the time that he is in control, exclude and modify the ordering of transactions. This allows him to:
- Reverse transactions that he sends while he’s in control. This has the potential to double-spend transactions that previously had already been seen in the block chain.
- Prevent some or all transactions from gaining any confirmations
- Prevent some or all other miners from mining any valid blocks
via Weaknesses – Bitcoin.
With less than 50%, the same kind of attacks are possible, but with less than 100% rate of success. For example, someone with only 40% of the network computing power can overcome a 6-deep confirmed transaction with a 50% success rate.