Consider Bitcoin. It’s infamous as the currency of choice for dark markets — but it’s also, “in a sense, the least anonymous money that has ever existed, since every transaction is observable by anyone with a bitcoin account,” to quote economist David Friedman. Just ask alleged Silk Road kingpin Ross Ulbricht, who had 700,000 bitcoin on his laptop directly traceable to Silk Road’s accounts.
You can’t ask for payment in unmarked bitcoin; there’s no such thing. Claims that “Large European companies may eye Bitcoin as an option for securing their data and keeping it private from the United States” are currently comical. Sure, you can “tumble” your bitcoin payments, ie have them mixed and mingled with those of strangers, or perhaps use a service like Dark Wallet (which is essentially a distributed tumbler) — but then you have to implicitly trust that service to protect your anonymity…and not keep your money.
But you underestimate today’s mathematicians and cryptographers at your peril. I give you Zerocoin, a way to perform genuinely anonymous cryptocurrency transactions. It was intended as an extension to bitcoin, but is also fully workable as a separate and independent “zerocoin” cryptocurrency.
A Few Thoughts on Cryptographic Engineering: Zero Knowledge Proofs: An illustrated primer http://bit.ly/1A17Ht8