Traceability in Permissioned Blockchain

In this paper, we propose the traceability of assets in a permissioned blockchain connected with a permissionless blockchain. We make traceability of assets in the permissioned blockchain be defined and be expressed as a hidden Markov model. There exists no dishonest increase and decrease of assets in this model. The condition is called balance. As we encrypt this model with fully homomorphic encryption and apply the zero knowledge proof of plaintext knowledge, we show that the traceability and balance of the permissioned blockchain are able to be proved in zero knowledge to the permissionless blockchain with concealing the asset allocation of the permissioned blockchain.