This was a tricky subject to handle.
Just as the U.S. federal gov't stated that only it, and not any of the states, had the right to print money, I had the Imperium force everyone to use the Imperial credit. Local currency was only permitted when the local technology could not handle the Imperial banking system.
My Imperium was cashless. Everyone who ever opened a banking account received a card which contained all of the account owner's banking information. This information included the amount of "money" in the person's account as well as personal details like fingerprints, retina scan, and DNA sample (and any other biometric data I hadn't thought of).
Any attempts made to change the contents of the data on the card by an unauthorized device resulted in the card's immediate self-corruption.
In order to conduct a transaction, a person needed to have an authorized transaction device. The device was about the size of 2 cd jewel cases stacked on top of one another. There were two slots: 1 for the seller's card and 1 for the buyer's card. There was a LCD display, alphanumeric pad, and biometric data input ports. I made the device intelligent enough to distinguish between a severed thumb and one connected to a living being.
When transactions were made, the cards were updated with the new account values. If the account reached zero, the card failed to permit the transaction. The transaction device also kept a log of all transactions.
Credit cards still exist. They operated on similar principles.
Only banks had the ability to distribute authorized transaction devices. And the banks were closely monitored by agents of the Imperial Banking System (IBS). Transaction devices had to be brought in every year to the bank that issued the device. It didn't have to be the exact branch. It just had to be the same banking company. All transactions were downloaded into the bank's computers. The information was then sent out to all of the other bank branches via the xboat network or other data couriers. The data was also sent to the IBS, who in turn sent the data to the other banking companies who had clientele involved in transactions with that particular device.
The devices didn't stop the trade of illegal goods and services. The nature of the transaction was never recorded. I left it in there as something that privacy rights champions successfully fought for.
I'm sure that someone can figure out a way to beat this system. However, my players gave up a while ago and haven't tried in years to think of some way around it. I also might not have remembered to write out all my other safeguards. It's late and I'm tired.