Digitally Signed Money

Public key digital signatures provide a means of verifying the integrity and authenticity of a document - that it came from who it says it came from, and hasn't been altered since. These signatures work by creating a summary (hash) of the document and encrypting it with a private key. The recipient then uses a published public key to verify that the hash is correct.

This could be applied to currency as a means to prevent counterfeiting. Essentially, a bill's mint, value, and serial number would be concatenated and digitally signed, then printed on the note. To verify that it is a legitimate bill, the issuing mint's public key would be downloaded and the signature checked.

As each signature is unique, the whole bill would have to be replicated in order to counterfeit it. In this case, the serial number could be blacklisted, as they are now.

While someone with significant motivation could duplicate the design of a note, cryptographical algorithms make this virtually impossible. Massive amounts of computing power is required to perform prime factorization to produce the private key. To date, the longest number to be factorized was 576 bits (174 digits) long. According to the RSA, a 1620 bit number would require 8.0 x 10^14 GHz with 1.92 x 10^17 terabytes of RAM running for one year. In contrast, private keys are typically 4096 bytes long. And while there's nothing close to that today, the only group which might ever be able to do it is already part of the federal government.