Frequency estimation of physical symptoms for peoples is the most direct way to analyze and predict infectious diseases. In Internet of medical Things (IoMT), it is efficient and convenient for users to report their physical symptoms to hospitals or disease prevention departments by various mobile devices. Unfortunately, it usually brings leakage risk of these symptoms since data receivers may be untrusted. As a strong metric for health privacy, local differential privacy (LDP) requires that users should perturb their symptoms to prevent the risk. However, the widely-used data structure called sketch for frequency estimation does not satisfy the specified requirement. In this paper, we firstly define the problem of frequency estimation of physical symptoms under LDP. Then, we propose four different protocols, i.e., CMS-LDP, FCS-LDP, CS-LDP and FAS-LDP to solve the above problem. Next, we demonstrate that the designed protocols satisfy LDP and unbiased estimation. We also present two approaches to implement the key component (i.e., universal hash functions) of protocols. Finally, we conduct experiments to evaluate four protocols on two real-world datasets, representing two different distributions of physical symptoms. The results show that CMS-LDP and CS-LDP have relatively optimal utility for frequency estimation of physical symptoms in IoMT.

对人们的身体症状进行频率估计是分析和预测传染病的最直接方法。在医疗物联网（IoMT）中，用户可以通过各种移动设备向医院或疾病预防部门报告其身体症状，既高效又方便。不幸的是，由于数据接收者可能不受信任，因此通常会带来这些症状的泄漏风险。作为保护健康隐私的一项重要指标，本地差异隐私（LDP）要求用户应扰动其症状以防止这种风险。但是，用于频率估计的称为草图的广泛使用的数据结构不能满足指定的要求。在本文中，我们首先定义了LDP下物理症状的频率估计问题。然后，我们提出了四种不同的协议，即CMS-LDP，FCS-LDP，CS-LDP和FAS-LDP解决上述问题。接下来，我们证明设计的协议满足LDP和无偏估计。我们还提出了两种方法来实现协议的关键组件（即通用哈希函数）。最后，我们进行实验以评估两个真实世界数据集上的四种协议，它们代表了两种不同的身体症状分布。结果表明，CMS-LDP和CS-LDP对IoMT的物理症状频率估计具有相对最佳的效用。