This key memorandum of understanding allows Alice and Bob to exchange values for public keys and securely calculate a common K key from those values and knowledge of their own corresponding private keys, allowing them to continue communicating securely. Because only the exchanged values of the public key are known, a listener cannot calculate the released key. 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. This document formulated a new problem called MECDHP and proved that its safety complies with traditional ECDHP. Based on the MECDHP, we have proposed a new authenticated D-H key agreement scheme that protects the customer`s anonymity and significantly improves the customer`s computational efficiency. Based on the digits of the 160-bit ECC key and the 1024-bit RSA key (or the 1024-bit D-H algorithm), the client of our schema only needs a 1/20 time complexity of its RSA equivalents [10-12, 14] and takes only 1/2 of the temporal complexity of the WANG et al. schema based on the ECC . Security analysis shows that the schema reaches a forward half-secret: it reaches a forward secret when the server`s private key is compromised, but the session keys of a compromised client are leaked. Here we find that this only concerns the session keys of the compromised clients. This excellent performance makes our system very attractive to Thin customers who need anonymity protection.
An interesting outstanding question is whether we can improve the computational efficiency of existing authenticated key D-H tuning systems while maintaining perfect forward security. Once the common secret is in place, the Diffie Hellman public key, private key, and settings are no longer useful. The key convention algorithm Diffie Hellman is reached. Traditionally, the Diffie-Hellman calculator problem above the Galis field (called CDHP) and the same problem on elliptic curves (called ECDHP) are, because of their hardness, the most popular elements for many authenticated key tuning schemes [4-8, 10-19]. However, modular exposure calculations on the Galis field or point multiplications by elliptic curves are a significant computational load for customers whose computing capacities or batteries are limited. Such clients are referred to as thin clients in the rest of this document. Even a Key Native D-H scheme (without authentication of the communicating parts) used by the CDHP requires two modular exposures from each part, and the corresponding version on elliptic curves would require each part to have two multiplications of points. In general, an authenticated version of the D-H key schema or an advanced version of the D-H key schema, which protects the anonymity of the client, would require more modular exposures or more multiplication of points [9-12, 14-16, 20]. It is therefore important to reduce the number of exponentiation/multitition point calculations for these thin clients. In 2014, Chien  formulated the modified D-H computational problem (MCDHP) and proposed an authenticated D-H key tuning scheme using MCDHP. The scheme  did indeed reduce the number of modular exhibitions, but did not protect the client`s anonymity. If Alice and Bob share a password, they can use a password-certified key agreement (PK) form of Diffie-Hellman to prevent man-in-the-middle attacks.
A simple scheme is to compare the chained hash with the password calculated independently of each other at both ends of the channel. One of the features of these schemes is that an attacker can only test a particular password at each iteration with the other party, which ensures good security with relatively weak passwords. This approach is described in ITU-T Recommendation X.1035, used by the G.hn home network standard. . . .