## 4 ROLQ-TEE Scheme
### Detailed Construction
Meanwhile, it also supports three types of queries--reverse nearest neighbor query (RNNQ), average query (AVGQ), and maximum query (MAXQ)--to address different objectives in optimal location queries; finally, (c) the data user revocation mechanism facilitates the efficient revocation of expired users' query permissions through a simple key refresh process. Finally, the security of the ROLQ-TEE scheme is based on the discrete logarithm problem and the collision resistance of hash functions, as demonstrated in [37; 38]. Experimental evaluations of various query types confirm that the scheme is both practical and scalable. Furthermore, we plan to incorporate mechanisms such as zero-knowledge proofs or blockchain-based consensus in future research work to address the problem of collusion between entities and support batch query processing. B.L. : conceptualization, data curation, formal analysis, methodology, software, writing--original draft preparation, and writing--review and editing; F.Z. : conceptualization, funding acquisition, project administration, resources, supervision, and validation; J.X. : funding acquisition, methodology, and supervision; Q.W. : formal analysis, funding acquisition, project administration, and validation; J.L. : data curation, investigation, software, and writing--original draft preparation; D.F. : data curation, investigation, and writing--original draft preparation. All authors have read and agreed to the published version of the manuscript. We thank the anonymous reviewers for their fruitful suggestions. This work was supported in part by the National Science Foundation of China under Grant 62202090, 62173101 and 62372069, by Doctoral Scientific Research Foundation of Liaoning Province under Grant 2022-BS-077, by the Fundamental Research Funds for the Central Universities, China under Grant N2417006, and by Liaoning Collaboration Innovation Center For CSLE under Grant XTCX2024-015. Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest. ## References

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