Traditionally, key convention schemes transfer the identities of participants in the clear. Since data protection has been a major concern in many applications, it is desirable to protect the identity of participants during the key agreement process. These types of key convention schemas are called authenticated key convention schemas, with a client anomaly (or simply an anonymously authenticated key agreement). Chien  classified four types of key two-party convention systems based on protecting the anonymity of participants. type 1: the privacy of the identities of two communicating parties is not protected; This type corresponds to the classic two-party key agreement systems. Type 2: The identity of the client is protected against strangers, but not the identity of the server. Type 3: The identity of the client is protected from outsiders, but the anonymity of the server is protected against unregistered entities. Scenarios of such a type are such; In a mission-driven ad hoc network, clients and servers want to protect their identity from the outside, while all pre-declared clients know the IP address or MAC address of the servers. Type 4: Client identity and server identity are protected from outsiders.
Type 2 is most popular for authenticated key convention schemes that protect the anonymity of the participant, as it corresponds to cases where customers want to protect their anonymity from the outside. In this document, we focus on key authenticated two-party agreements for Type 2 cases and aim to improve the customer`s computational efficiency. We present the model and discuss the security requirements of the D-H key agreement system authenticated with Customer Anonymity as follows. Our model consists of three types of entities: clients, servers and external. Customers want to create secure session keys with servers through key convention schemes and their identity must not be established by outsiders. A stranger can actively manipulate the communication by reading, modifying or intercepting. In this section, we first propose the MECDHP and prove its safety. Next, we introduce the model and discuss the security requirements of an authenticated key agreement scheme with the client anomaly. Authentication with anonymity protection is a popular topic, and there are a few popular techniques to obtain customer anonymity during the authentication process.