SamuelA:
You could wash them several times through several third parties. Let’s suppose that the bitcoin had been used to pay for the assassination of a government official, and thus it’s extremely hot. The assassin could still use many washing systems and even if some of them are lying and keeping records of which coins went where, just a single server out there (you can build an automated bitcoin wash relatively easily) that doesn’t store records, and the trail is broken.
Building a tumbler that will obfuscate the source of coins at the moment is probably a reasonable engineering problem.
Building a tumbler that will resist all future attempts to untangle is not something I would want to base a bunch of illegal actions on, but hey, I’m sure that will work out great.
Balthisar:
It’s not really untraceable, though. Not if you want to liquidate it, though. Every bitcoin has a unique fingerprint, and you can see when that bitcoin was born, what wallets is passes through, and ultimately where it ends up. The bitcoins I bought last year? There’s an electronic trail from BTC China to whatever company I transferred them to, to Coinbase. If I sell them, the capital gains can be traced back to at least BTC China. I could “wash” them in some type of bitcoin trade agreement, I guess, but that involves a lot of trust. If I spend them, they’ve been tied to at least three accounts that have my personal identifying information, so they’re not anonymous.
For people who are serious it’s not difficult setting up numerous bank accounts in false names in any number of countries.