I'm looking for a process to create a material which has some easy to measure properties. These properties should be consistent over a long period. It should be very hard (expensive) to predict/reproduce a material which results in the same measurable properties. Every material product should generate an unique measurement result and impossible (or very expensive) to product a second product with the same measurement result.
What process, material and/or measurement could be used?
Some context: The goal would be block-chain backed physical cash currency. The process should result in a 'coin' (material product). The 'coin' can be 'read' (measurement of some over time consistent material properties) resulting in a 'coin-id' (measurement). The producer of the 'coin' reads the coin-id and adds a block to the chain which contains the 'coin-id' and his signature of the 'coin-id' and spends some (crypto) currency value. The physical coin represents the spend (crypto) currency value. For ease of use the signature could be attached to the coin (bar or qr-code). The blockchain also contains the certificates of the coin producers. The coins can be exchanged in the physical world without changes on the blockchain. A receiver of a coin can read (measure) the unique coin-id and scan the signature. A receiver knows the certificates of the coin producers. A receiver can check the veracity by checking if the coin-id is signed by a known coin producer certificate.
Addendum
Let the cost to produce a coin be c. Let the probability of a duplicate measurement be p. Let the value represented by the coin be v.
Because the represented value should be a lot bigger than the cost of a coin. The value should be a factor f bigger than the cost.
$v=cf$
The minimal value to make forgery too expensive:
$v=\frac{c}{p}$
The maximal p should be:
$p=\frac{c}{v}$
So given a $c=0.1$\$ and $v=100$\$
then the maximum $p=\frac{0.1}{100}=0.001$
Or put otherway around: given a more realistic forgery probability of $p=10^{-10}$
Maximum $f=\frac{1}{p}$, $f=10^{10}$
So a coin given $c=0.1$\$ could have a maximum value of $v=0.1*10^{10}=1.000.000.000$\$