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I installed the wallet from Bitcoin's official website on 4 computers each running Microsoft Windows 7.

Moreover on each of the 4 PCs, I installed OpenVPN client, meaning each of the computers access the internet via VPN.

Suppose I do not use an online Bitcoin mixer to further anonymize my transactions.

Instead I transfer my Bitcoins from one computer to another, all the while making sure that the VPN gateway/exit node is located in a different country.

Question: can my transactions be traced back to me?

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Well, that depends. First, never reuse addresses if you are doing this.

Second, if you are not mixing, the transactions will, with no exception, be traceable. Would there be someone focused on you, he would see the bitcoins move around, and so most probably think they are spent. But if he is really interested in you, he will probably keep track of the coins and whenever you really spend one of them, he will probably notice and try to track the owner of that address to see what you did with them.

He will probably only stop keeping track of those coins if he sees them being spent by someone that cannot be you, or if he cannot track them anymore as they are split up and combined with many other coins.

You must be quite paranoid considering your few questions here. I can maybe advise you to buy bitcoins for cash like via localbitcoins.com. Apart from the guy you trade with, no one will know you bought coins.

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Well, if there would be people tracking you, they probably aint stupid and know that you could be doing that. Furthermore, when you would f.e. add the coins to a web wallet or an exchange, they would also travel across the globe and they will also keep an eye on those coins. Someone seriously wanting to find you would probably keep track on everything until it is no longer possible and only when he found something he will consider the odds of it still being you. That's what I would do though. –  Steven Roose Jun 17 '13 at 8:17
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Well, yes. When you put coins in a mixer, they will be split up in many small parts and you will receive many small parts from many different other users. That's what a smart mixer might do. So mostly none of your own coins come back to you, meaning that it is a real dead end. The only thing one could do to track across mixers is when he sees your transaction of 100 BTC being split up in 10,000 parts, look for another transaction that combines little parts to 100 BTC. But I would consider smart mixers to have some latency and maybe sent the 100 BTC in small parts to different addresses. –  Steven Roose Jun 17 '13 at 8:20
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Yes, that's correct. –  Steven Roose Jun 17 '13 at 16:38
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@user5556: When you're tracing bitcoins, you totally ignore intermediary hops that have no known identities or other transactions. So if you see bitcoins go from A to B to C to D, if you have no information about B or C, and they were only used as intermediaries between A and D, you ignore them. The very first, most obvious step someone tracing your bitcoins would do would make this pointless. –  David Schwartz Jun 21 '13 at 10:49
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@StevenRoose: Right. That's the difference between a mixer and what the question is asking about. –  David Schwartz Jun 22 '13 at 21:06
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