Require that everyone take all of their existing US currency to a bank within the next 30 days (or forego the value of the currency).  Have the bank scan the currency for its serial number, associate that serial number with its owners SSN or EIN, and then have the bank post-it to a block-chain ledger so there is no dispute over ownership of the currency.  Every retailer would then obtain modified debit/credit card scanning devices which can also scan the serial numbers of US currency.  If you want the ham sandwich at Subway, you're $20 bill must be scanned by Subway and now becomes the property of Subway's EIN on the block-chain ledger.  Currency that was not scanned at the bank has no value.

Certainly, it's not perfect.  But give me more than a weekend to think about it and I'm sure we can do away with the CTA.