The barely reproducible key in the smart card

 I need a simple algorithm to explain the analog key concpt.

Consider one party has the analog, uniquer key,  Input a number and read out a unique code. But this machine is analog, one direction.  There is no way to write an output and read an input.

But, the owner of this key can characterize its reverse as a power series, say 100 elements long.  That is, the owner of the analog key sends another party the reverse coefficients so the sending party can simulate the inverse using a few hundred instruction.  

The send selects a word to send, say 16 bits.  It will run the encoder backwards and get the coded value, which it send.

The receiving part, having the encode and the machine can simply input all possible values until the proper code appears on output.  Each execution of the machine in the normal flow takes one clock cycle, enough to sle the analog logic settle.

The attacker does not have the machine, but it has the reverse script.  However, running the reverse scrip requires a few hundred instruction times 2^16, a few hundred times the work required by the proper receiver.

But the message is sent by the time the attacker can decode, and once sent in finance the destination will already have the data under a different key. The attacker may get some information, but the ability to steal is minimal.

This is the basic idea.  Encoding a short message requires some work, decoding without the machine is nearly impossible.

Such a unique analog system can be easily imprinted on a chip, and the card on set up can go through discovery to recover the reversing set of coefficients.  It really cannot be reverse engineered because the analog effect is below the gate level, it is in atomic distribution which has random variations. 

It seems a bit laborious for the decoder, but it need be done only once, to share a secret digital key then public encryption can handle the rest. The share key need not be reused so it has no value to the attacker except informational.

Something like this works, well enough certainly for a smart card with a consumer credit limit.