There is no concept of "wallet ID" in Bitcoin transactions as transmitted over the wire. There are only input and output values in transactions (which do have an ID number).
If you know someone is connected to a given input, then you can trace them through any outputs to other parties.
So it's not quite as simple as a "wallet ID". The transactions in given Bitcoin wallet software may be connected to each other (by the mechanism I describe above), but are not necessarily connected, particularly if you generate a new address for each transaction for which you are the receiving party (and/or take additional precautionary measures). It's entirely possible to have a wallet full of untraceable transactions.
You can also use a tumbler, which is basically where you and several other people all run your coins into one wallet, and then withdraw random amounts up to the amount you put in. Obviously the issue there is someone needs to keep track of who has how much in the tumbler, but I imagine there's services out there.
That would be a bad tumbler design. A better design pays you out in bitcoins that have no connection to the bitcoins you paid in. Say you pay into wallet A and someone else pays into wallet B then you could get paid entierly out of wallet B. Then the only person who could follow the path would be the owner of wallets A and B.
If you're guaranteed to not get any BTC back you put in, then that seems like it could reveal information in itself. Perhaps a better design would be it totally randomly redistributes.
I see -- I think the above argument is that the tumbling service, i.e. owner of wallets A and B, has the evidence of laundering. Concentrated in one place it's easier to protect, and easier to attack, I guess?
No, it has nothing to do with where it's concentrated; I don't know of any tumbler designs that aren't concentrated in one place.
It has to do with that if Alice gets a Bitcoin by selling uncensored newspapers in China, transfers it to wallet A in the tumbler, and then the tumbler transfers that to Alice's Coinbase account, Alice is going to jail. The transaction record tells us that Alice's Bitcoin came from the uncensored newspaper through an intermediary. The Chinese government can then arrest Alice on suspicion of selling illegal newspapers. At that point Alice must either prove somehow that wallet A in the tumbler is owned by the person who really sold the newspapers (which will be impossible), or admit that she sold the newspapers and used a (bad) tumbler in an attempt to hide her transaction. That is to say, if there's a chain of transactions connecting Alice to the newspaper sale, the tumbler has provided Alice no anonymity.
Contrast this with a more realistic tumbler design: the tumbler owner (let's call him Troy) deposits a bitcoin from Coinbase in wallet A. Alice is the first user of the tumbler, so she gets a bitcoin selling uncensored newspapers in China and deposits it in wallet B. The tumbler owner then forwards the coin from wallet A (minus a fee) into Alice's Coinbase account. Now Bob, as the second user of the tumbler, comes along and deposits a coin he got from selling LSD on the Silk Road into wallet C. Troy then sends the coin Alice got from selling uncensored newspapers (minus a fee) to Bob's Coinbase account.
Alice now has a coin from Coinbase, Bob has a coin from Alice's sale of an uncensored newspaper in China, and Troy the tumbler operator has a coin sitting in wallet C waiting for the next person to use the tumbler. The Chinese government has no way to track the transactions to Alice. IF Bob lives in China the Chinese government could come and accuse him of selling uncensored newspapers, but the accusation would make no sense; he has alibis for some of the days newspapers were sold, he's not educated enough to write, etc., because he didn't sell the newspapers. Bob can even say he used a tumbler, but he used it because he purchased a lot of bondage pornography: embarrassing, but not illegal. But more likely than not, Bob won't even be accused of Alice's crimes, either because he lives in a different country or because the accusations won't make any sense. Both Alice and Bob's anonymity has been protected.
Great explanation, I understand it better from a technical perspective.
I assume Troy is hidden to the authorities, who only have the Blockchain ledger and no other information to go on? That's waht I meant by "concentrated" above -- how likely is it that the Chinese government would find Troy and extract the information out of him with legal threats or with a heavy wrench?
I don't think the owner of the tumbler has any motivation to keep records (after each transaction is complete). So he deletes the records and spares himself the heavy wrench.
If Troy is trustworthy, he'll delete the transaction history.
However, there area number of attacks possible from Troy's perspective. He can keep a transaction history and use it to blackmail Alice and Bob. He can simply keep coins sent to the tumbler and send out nothing. It's very important that Troy be a trusted actor.
> IF Bob lives in China the Chinese government could come and accuse him of selling uncensored newspapers [...] Bob can even say he used a tumbler, but he used it because he purchased a lot of bondage pornography: embarrassing, but not illegal.
Not relevant to the example, but this is totally illegal.
So if you want anonymity you have to be careful that no one can connect you to a wallet ID.