Thanks! There are related structures in electronic circuits called physical unclonable functions (PUFs) that find uses in cryptography - you might find them interesting: https://en.wikipedia.org/wiki/Physical_unclonable_function
Examples (aha, including a teaser to an upcoming product called “Verifibre”!) can be seen here:
Instead of a lookup table, that number could be signed and the signature printed onto the bank note itself. It would be impractical to either deduce the signing key or duplicate the pattern of fibers in a way that the signature was still valid.
I don’t know if there’s a signature algorithm though that is resilient to lossy and unreliable input data and which can also produce short enough output that could be printed on the face of a bank note.