Authentication with anonymity protection is a popular topic and there are some popular techniques for achieving customer anonymity during the authentication process. Dog  categorizes existing techniques into four categories: probabilistic encryption schemes such as the OAKley protocol , pseudonym schemes such as , hash chain-based diagrams, such as Ohkubo et al.s  and error correction schemes such as [2, 3]. It is difficult to extend to their anonymous versions key CDHP-based chord schemes such as [5-7, 13] (or ECDHP-based diagrams such as ) and reduce the modular exposure load (or the burden of multiplying points). In this article, we first formulate a modified ECDHP (MDHP) and prove its safety. Next, we propose a new bipartisan key agreement scheme authenticated with client anonymity, based on the problem of MECDHP and Ohkubo et al.s Hashing chain technique . The new scheme protects customer anonymity, effectively reduces the customer`s computational load and preserves the high security of the ECDHP. 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]. The authenticated key agreement aims to simultaneously provide authentication of communicating parties and to set up secure meeting keys. Today, it is very easy for all network operators, or even outsiders, to apprehend the behavior of users and violate their privacy when they surf the internet, when important agreements do not protect the identity of users. It is therefore essential to design important agreements that protect the identity of the customer.
These systems can protect users` privacy when they benefit from internet activities, e-commerce transactions or online commerce. 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.