## 1 Introduction  
Weareable devices are seamlessly integrated into our daily lives and capture various key-value data that span health metrics, physical activity tracking, sleep patterns, location data, biometric identifiers, and environmental conditions. For example, consider the key-value data generated from smartphone app usage, where the key represents the application name and the corresponding value indicates the time spent on each app, e.g., \"a user may spend 2 h on YouTube, 1 h on Twitter, and 0.5 h on Instagram\". In this scenario, \"app name\" serves as the key, while the respective durations constitute the values. This key-value pair not only provides a snapshot of the digital behavior of the user, but also unveils insights into their preferences and social interactions. Although such data are valuable for personalization and app optimization, they raise privacy concerns relating to tracking the online activities of individuals. The aggregation of these seemingly benign key-value pairs could enable the inference of aspects of a user's lifestyle, underscoring the need for carefully considering privacy implications. Local differential privacy (LDP) is a privacy-enhanced technique for mitigating privacy challenges. In this approach, individual users locally perturb their personal data before transmission to an untrusted server. Various LDP protocols have been introduced to address distinct data types. [PERSON] et al. proposed the LDP framework RAPPOR [1], which represents a significant advancement in privacy-preserving techniques. [PERSON] et al. presented PrivKV [2], which is an LDP scheme that is tailored for the secure collection of key-value data and is characterized by a two-dimensional structure accommodating both discrete and continuous values. The landscape of LDP protocols for key-value data has been further enriched by the introduction of several alternative schemes [3; 4], reflecting the ongoing exploration within the realm of LDP. However, the localized nature of perturbation in LDP protocols introduces a vulnerability to \"poisoning attacks\". In such attacks, malicious entities introduce fake users who transmit counterfeit data for a specific key with the intention of manipulating the analytical outcomes of the server, such as altering the frequency of particular keys or their mean reputation scores. If a fraudulent user submits the fabricated key and value data in a predetermined LDP protocol, the server cannot detect these data because of the privacy guarantee offered by LDP. [PERSON] et al. [5] studied a family of poisoning attacks on LDP schemes. Furthermore, [PERSON] et al. [6] identified three distinct types of poisoning attacks that specifically target PrivKV, demonstrating its vulnerability. They proposed defense mechanisms against these poisoning attacks; however, these defenses necessitate the prolonged observation of data collection for optimal efficacy. In this study, we investigate the vulnerability of the LDP protocol for key-value data to poisoning attacks. First, we introduce a cryptographic protocol known as oblivious transfer (OT) [7] to mitigate intentional key selection by fake users. In contrast to the conventional approach of conducting random sampling locally, our protocol involves the server collaboratively in the secure sampling process, providing proactive security, as opposed to the reactive methods that were employed in prior studies. Second, we demonstrate the vulnerability of PrivKV to poisoning attacks using its estimation algorithm. Because the reliance of estimation depends on a single frequency for a key, it is vulnerable to manipulation, particularly when dealing with a limited number of targeted keys. To address this limitation, we propose integrating an expectation maximization (EM) algorithm [8]. By iteratively estimating posterior probabilities, the EM algorithm enhances consistency across all observed values, thereby improving accuracy even in scenarios with a large user base.