This document formulated a new problem called MDHDHP and demonstrated that its safety was consistent with traditional ECDHP. Based on MDHP, we have proposed a new authenticated D-H key agreement scheme that protects customer anonymity and significantly improves customer computing efficiency. Based on the 160-bit ECC key and 1024-bit RSA key (or 1024 bit-D-H-20), the client in our scheme needs only 1/20 of the time complexity of its RSA counterparts [10-12, 14] and needs only a 1/2 temporal complexity of the diagram based on Wang et al.. Security analysis shows that the system reaches a semi-lateral secret: it reaches the secret of the front when the server`s private key is compromised, but the session keys of a compromised client are disclosed. We find here that this only applies to the keys to meeting compromised clients. These excellent performance make our system very attractive to slim customers who need anonymity protection. An interesting question is whether we can improve the computational efficiency of existing authenticated D-H key chord models while preserving the secret of the perfect front. Usually, important agreement patterns convey the identities of the participants in plain language. Given that privacy 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 agreements are called key agreement schemes authenticated with the client`s anonymity (or simply an anonymous authenticated key agreement). Dog  ranked four types of key bipartisan agreements, in accordance with the protection of the anonymity of participants. Type 1: The privacy of the identities of two parties who communicate is not protected; this type corresponds to traditional two-party key agreements.
Type 2: The identity of the client is protected from outsiders, but the identity of the server is not protected. Type 3: The client`s identity is protected from outsiders, but the anonymity of the server is protected from unregistered entities. Scenarios of this type are such; In a mission-oriented ad hoc network, customers and servers want to protect their identity from outsiders, while all pre-reported customers know the IP or MAC address of the servers. Type 4: The identity of the client and the identity of the server are protected from outsiders. Type 2 is the most popular for authenticated key agreement schemes that protect the anonymity of participants, as it corresponds to cases where clients wish to protect their anonymity from outside. In this article, we focus on key bipartisan authenticated agreements for Type 2 cases and aim to improve client computing efficiency. Authentication is an essential guarantee; However, many existing authentication schemes did not provide a key agreement during authentication [1-3], customer privacy is not protected  or many expensive modular exposures required [4-16].