The core idea, that a difficult to counterfeit banknote can be used for off-line Bitcoins transaction is
EXCELENT. I emphasize, IMHO it's completely fantastic.
The problem lies in the details: a banknote does not have something to hide a private key, and so prevent double-spend.
I propose a simpler solution: Using an unspendable Tx output that holds the banknote country and serial number, some BTC are associated forever with a certain banknote. (the data is described in the public script).
Every one agrees that the bill's value is now X BTC. That's it. The only party that can reliable try to cheat making a perfect counterfeit bill is a government. If governments create counterfeit bills, then they'll be terribly exposed to loss of credibility. Therefore nobody will create a perfect counterfeit bill.
To check that a bill has value, you carry a portable database of BTC-to-Bill binding outputs. Everyone agrees that to be valid, a bill binding transaction must be one day old, so everyone can carry the small database and sync it once a day. (This is the same system the
Firmcoin.com uses)
We would be actually using the government low-cost of manufacturing facilities to create difficult to counterfeit banknotes for Bitcoin. For example, a 100 USD banknote costs 10 cents to manufacture in a batch of a billion bills.
From the economic point of view, the bill's value is the maximum between the fiat previous value and the BTC value, so it's seems that some value has been created from thin air, because you could just create money by accepting the fiat value, and then selling the bill by the other BTC denomination (or vice versa). By using a very low-valued bill, for example a 1 USD bill for 1 BTC, the problem is mitigated. Nevertheless I doubt the governments put the same security features in a 1 USD bill than in a 100 USD bill.
Finally, for the system to work, everyone must agree that those BTC bills really hold the BTC value. But you can count on me: I would agree! Why not?
Now imagine people using ALL USD bills as BTC banknotes!
Since the creation of Bitcoin, I never heard a more disturbing idea for governments than that!
So let's define a standard for the creation of dollar BTCs and make it a reality!!
Thanks btcusr: one never stops getting surprised by crazy ideas...that come true... I will post about this in my blog...
Best regards,
Sergio.