The Theory of Witness-Functions

Cryptographic protocols are distributed programs that ensure security in all communications. They guarantee agents authentication, data confidentiality, data integrity, atomicity of goods and money, non-repudiation, etc. They are used in all areas: e-commerce, military fields, electronic voting, etc. The use of cryptography is essential to ensure protocols’ security, however, it is not sufficient. Indeed, in the literature, a significant number of cryptographic protocols have long been considered safe, but they were shown faulty many years after their use. Saying that a protocol is correct or not is an undecidable problem in general. However, several methods (logic-based methods, Model-Checking-based methods, typing-based methods, etc.) have emerged to answer this hard question under restrictive assumptions and led to varying results. Here, we present a new formal method to analyze cryptographic protocols statically for the property of secrecy. It consists in inspecting the level of security of every component of exchanged messages in the protocol by new metrics, called witness-functions, and making sure that it does not diminish during its life cycle. If yes, we declare that the protocol keeps its secret inputs. We analyze here an amended version of the Woo-Lam protocol using the witness-functions’ theory.