Analysis of the Composition of Non-Deducibility in Cyber-Physical Systems

Cyber-Physical Systems (CPSs) are integrations of computation and physical processes. Now researchers are confronted with the difficulty in the analysis and verification of information confidentiality in complex CPSs owing to physically observable behavior and physical components appended to cyber systems. This problem can be solved effectively by using some simple or small systems to compose the complex CPSs while achieving the confidentiality of the composite system by preserving that of small systems. Firstly, the paper introduces the definition of non-deducibility and the definition and operation of Petri net and four compositions (sequence, iteration, parallel and alternative composition) for non-deducibility (ND). Secondly, this paper analyzes the ND security model, which is extremely attractive since the physical actions of CPSs are inherently observable, in the abstract cyber-physical natural gas pipeline system based on Petri net. Finally, this paper gives the conditions in which the ND security property will not be changed after the four representative compositions, the proofs of which are provided. The contribution of this study is providing a formal method and laying a foundation for exploring the confidentiality and information security in CPSs.