Encrypting the messages exchanged in a protocol is not enough to guarantee the confidentiality of the data exchanged. Indeed, a man in the middle can fool the rules of the protocol to know what they are not entitled to. An appropriate method of analyzing protocols must be used. There are several effective methods such as the witness functions method developed at LSI of Laval University. We will talk about the theory of witness functions in the analysis of cryptographic protocols and the excellent results that have been achieved with these functions regarding their security.