## 2 Related Work  
In the era of telematics and telemedicine, a large amount of sensitive information is being transmitted in a public network environment. To protect the information privacy of these transmissions, much information security research has proposed various solutions. These schemes include symmetric encryption [6; 7; 8; 9] and asymmetric encryption. Owing to the high maintenance cost required by the asymmetric public key method, some symmetric encryption systems have been popularly used recently [10; 11; 12]. The symmetric encryption must generate the shared key required for the conference immediately, as the zero-knowledge-based key exchange mechanism came into being. In the key exchange process, it must be ensured that the transfer messages are not tampered with or resented. Therefore, some researchers use the timestamp mechanism to ensure the security of the communication using the irreversibility of time [13; 14; 15]. However, some researchers believe that the computer's  
Figure 1: A scenario of our proposed two-phase pre-checkup and subsequent validation key agreement authentication mechanism (TCVK). timestamps cannot guarantee consistency. The computer's computing speed is very fast, and a tiny time error will cause the key agreement to fail. As a result, many scholars have started to use one-time random numbers instead of timestamps [10; 11; 12]. Traditional public key cryptosystems (TPKCs) and elliptic curve cryptosystems (ECCs) are key exchange systems commonly used by many researchers. Recently, in order to reduce the computational cost of communication preparation and the advent of the post-quantum era, many researchers have focused on lightweight and time-independent security. Therefore, key exchange mechanisms using hash functions and Exclusive-OR (XOR) operations have been proposed. Lightweight certification can achieve better execution efficiency than TPKC and ECC designs, so it has become a new design requirement. Instead of the traditional password directly input method, a more secure and unique biometric authentication method is often used for offline key verification in recent works [16; 17; 18]. Recently, the fuzzy extractor has replaced the hash function corresponding to a single result of the dynamic range, which is a biometric tool for user recognition and inspection process [19; 20; 21]. The fuzzy extractor allows users to use their biometric characteristics as keys. When users enter their biometric characteristics into the extractor, the extractor will use the generation algorithm Gen \((B_{i})=(X_{B},P_{B})\) to randomly generate a fixed string of words (Gen for generate and Rep for reproduce), where secret key \(X_{B}\) is a word string and extracts a public key \(P_{B}\) that can be stored. An example of a biometric fuzzy extractor is shown in Figure 2. Our study also uses a combination of smart cards and participant certifications. If it equipped with powerful Central Processing Unit, Random Access Memory, and Input / Output device a smart card can deal with more data processing tasks. The uniqueness of a participant's identification can be confirmed using the computing system installed in the smart cards [22]. In the algorithm design of secure information communication protocols, in order to prove that the algorithms used to exchange messages in the public network are secure, researchers usually use probabilistic assumptions and verification. In 1993, [PERSON] and [PERSON] (1993) first published a rigorous method of cryptographic proof using mathematical abstraction random oracles [23]. The main issue is to strengthen the proof using random oracles when weak password assumptions cannot be used to prove the password hash function. In contrast to the security in the standard cryptographic model, each hash function is replaced with a random oracle in the random oracle model to prove that the system is secure.