The remainder of this article is organized as follows. The related works is introduced in section 2. In Section 3 we provide a detailed description of the BB84 protocol. In Section 4 we give a simple presentation of the technique of model checking and we show why this technique is desired to analyze protocols of quantum key distribution. In section 5 we present our analysis of BB84’s security by introducing parameters of the channel and the eavesdropper in order to study the property of eavesdropping detection. Section 6 concludes our work by giving the main results.