with his answer but let me try to clarify.
Point 1: Attack vectors
There are currently two perceived attack vectors for people wanting to kill Bitcoin. One is called a 51% attack (gaining more computing power than the network), which is what haze is talking about. The other involves using a quantum computer to break Bitcoin's cryptography.
The 51% attack is indeed possible (especially early on) but it couldn't kill Bitcoin. The goal of such an attack would be to undermine confidence in Bitcoin, thereby dropping the exchange rate. However, nothing would "break" with bitcoin. Think of it, in the worst case, like the stock market crashing. Does that mean people never get involved with stocks again? Gold prices can plummet too for different reasons. Really there is no such thing as any 100% guaranteed money system. It's believed that at some point so many people will use bitcoin the cost to overcome the network computing power would be infeasible to anyone to try. I recommend holding the majority of your wealth in gold and convert as much to bitcoins as you need/feel comfortable with at a time. I predict a majority of the world will eventually use Bitcoin because it's a superior money system.
As for quantum computing breaking the algorithm all such discussion is theoretical and not currently perceived to be a threat.
Point 2: Anonymity
There are ways to use the Internet anonymously, including use of the Tor network which Bitcoin supports. People anonymously buy drugs using bitcoins on the site Silk Road, and have done so for well over a year now.
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