Vr-Peks: A Verifiable and Resistant to Keyword Guess Attack Public Key Encryption with Keyword Search Scheme  
[PERSON]  
State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 580025, China; [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (S.D. ); [EMAIL_ADDRESS] (T.L.) [PERSON]  
State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 580025, China; [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (S.D. ); [EMAIL_ADDRESS] (T.L.) [PERSON]  
State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 580025, China; [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); midomountain@sina. PEKS technology can effectively protect the privacy of sensitive user information. It can be applied to cloud healthcare services, enabling the sharing of electronic medical records among multiple hospitals or departments within the same hospital. When a patient visits a hospital, the hospital extracts key information, such as their name, gender, and disease name, to construct a medical record index using these keywords. The hospital then stores the index and encrypted medical records on a cloud server. When Hospital A needs to share medical records with Hospital B, it uses B's public key to encrypt the keywords and medical files and creates a medical record index. These contents are then packaged and uploaded to the cloud server for storage. B's hospital staff can generate keyword traps using a private key and send them to the cloud server for searching. Once the cloud server completes the search, it returns the matching encrypted files. After decryption by B's hospital staff, they can obtain the plaintext files of the patient's medical records. However, [PERSON] et al. [6] stated that the keyword guess attack (KGA) in the PEKS scheme is still an unresolved problem due to the low entropy property of keywords. In KGA, an attacker intercepts the keyword search trapdoor of the data receiver, encrypts guessed keywords with the receiver's public key, and matches the ciphertext with the trapdoor to obtain the keywords of interest to the user, leading to a serious privacy violation [7]. KGA can be divided into internal KGA and external KGA. External KGA means that the attacker is a malicious party unrelated to the cloud service provider, and they obtain the trap gate by eavesdropping on the public channel between the cloud server and the receiver. In internal KGA, the attacker is a semi-trusted or malicious cloud server, and they can obtain the trapdoor directly from the receiver and can execute \(Test(W,T_{W})\) to check whether the keyword matches the trapdoor. Therefore, the attack capability of the internal adversary is more powerful. Many researchers have proposed different protocols to resist KGA [8; 9; 10; 11]. Although SE can guarantee the privacy of sensitive data, risks due to hardware failures, network attacks, and the system vulnerabilities of cloud servers still exist [12; 13]. In particular, malicious cloud servers have powerful attack capabilities. As [PERSON] et al. [14] conclude, attackers with more power have no incentive to attack. Malicious cloud servers are not only capable of performing KGA, but may also perform actions such as intentionally dropping, corrupting, or tampering with cloud data, or incorrectly performing search operations. Therefore, it is necessary to introduce a verification mechanism in PEKS schemes in order to ensure the correctness of the search results and detect the dishonest or malicious behavior of cloud servers. Therefore, some scholars have begun to study verifiable keyword search schemes [15; 16; 17]. However, with the continuous development of quantum computers, the above PEKS schemes constructed based on traditional number theory and hard problem assumptions are vulnerable to quantum attacks [18].