Smart agriculture Internet of Things (IoT) is a typical application of IoT and has become popular due to its advantages in automatic irrigation and fertilization, crop growth monitoring, pest and disease detection, etc. To reduce resource waste, minimize environmental impact, and maximize crop yield, most smart agricultural applications require to collect and process agricultural data in real-time. However, the computational and storage resources of the agricultural IoT devices are limited. To alleviate the computational and storage pressure on agriculture IoT devices and timely process the collected data collected by IoT devices, the fog node is usually placed at the edge of the agricultural IoT. Nevertheless, the fog node may not be completely trusted. The agricultural IoT devices’ data stored in the fog node will face the potential risk of privacy leakage. In this paper, to preserve the privacy of agricultural IoT devices’ data and user query’s result in the fog-based smart agriculture IoT, we first build the K²-treap, which is used for storing the data collected by agriculture IoT devices and support efficient range-max query and dynamic update of the data. Then, we design a data encryption and comparison algorithm based on BGN homomorphic encryption technique and present an efficient and privacy-preserving range-max query in the fog-based smart agriculture IoT, which can not only securely compare two data based on their ciphertexts but also support the incremental update directly over ciphertexts. Notably, our comparison technique and range-max queries are run by the fog node, so there are no interactions between the agricultural IoT devices and the fog node during the comparison and query. Finally, we conduct a detailed security analysis and performance evaluation. The results show that our proposed scheme can indeed protect the privacy of the agricultural IoT devices’ data and query results, and the experimental test results prove that our proposed scheme is efficient.

智能农业物联网（IoT）是IoT的典型应用，并因其在自动灌溉和施肥，作物生长监测，病虫害检测等方面的优势而广受欢迎。作物产量方面，大多数智能农业应用都需要实时收集和处理农业数据。但是，农业物联网设备的计算和存储资源有限。为了缓解农业物联网设备的计算和存储压力并及时处理物联网设备收集的数据，雾节点通常位于农业物联网的边缘。但是，雾节点可能不会被完全信任。雾节点中存储的农业物联网设备数据将面临隐私泄露的潜在风险。在本文中，为了在基于雾的智能农业物联网中保护农业物联网设备数据和用户查询结果的隐私，我们首先构建了K^2个-treap，用于存储农业物联网设备收集的数据，并支持有效的最大范围查询和数据的动态更新。然后，我们设计了一种基于BGN同态加密技术的数据加密和比较算法，并在基于雾的智能农业物联网中提出了一种高效且隐私保护的范围最大查询，该查询不仅可以安全地基于密文对两个数据进行比较，而且可以安全地比较两个数据。还支持直接在密文上进行增量更新。值得注意的是，我们的比较技术和范围最大查询由雾节点运行，因此在比较和查询过程中，农业物联网设备与雾节点之间没有交互。最后，我们进行了详细的安全性分析和性能评估。