A brief noteWhen the construction method producing automata with inboundedly large inverses was discovered, it was beleived it could form the foundation of public key cryptosystem.
To date attempts to construct a workable system around it have failed.
Our early attempt is visible here.
This system fails because the proposed method of combining the two automata is not one way - and typically may be fairly easily reversed.
We have now located a detailed description of the original Chinese system. It bears little relationship to the system we proposed. See the bibliography for more details.
FAPKC BibliographyThose references to the original work we know of are listed here.