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The power Internet of Things(PIoT) is a smart service system that offers full-state awareness, efficient information processing, and convenient and flexible applications to users. However, these services also pose a risk of privacy leakage. The existing research on privacy protection of power data mainly concentrates on secure aggregation, but seldom addresses the core technology of many basic services, such as KNN query. Unlike traditional relational data, the PIoT collects flowing data of user electricity consumption, and the various power parameters exhibit dynamic correlations. Attackers can use data mining and other methods to infer future trends in data changes. Therefore, this paper proposed a privacy-preserving KNN query method. Firstly, it proposed a similarity measurement model based on bucket distance, and proved the upper and lower bounds of the error between the similarity measurement model based on bucket distance and the similarity measurement model based on Euclidean distance. Through this model, the similarity measurement could be transformed into set intersection operations. Then, it constructed a privacy-preserving function, which could generate different data privacy-preserving functions and query privacy-preserving functions for various smart terminals by substituting different parameters. Based on this, it proposed a data encoding scheme based on bucket partitioning and random number allocation. After being encrypted by the privacy-preserving function, the encoded data possessed the characteristic of ciphertext indistinguishability, and could effectively resist various attacks such as chosen plaintext attacks, data mining attacks, statistical analysis attacks, ICA attacks, and inference prediction attacks. Analysis and simulation demonstrate that the proposed secure KNN query method not only has high security but also has low overhead. [ABSTRACT FROM AUTHOR]

针对保参数方向构造过渡曲线曲面方法的不足，构造了任意参数曲线曲面间既保持参数方向又具有形状可调性的C1 与C2 连续过渡曲线曲面。首先，基于2 类带1 个自由参数的调配函数，分别构造满足C1 与C2 连续的过渡曲线，并讨论基于能量优化模型的最佳过渡曲线构造问题； 然后，将所提出的方法推广到过渡曲面的构造。实例结果表明，2 被过渡曲线曲面为任意参数曲线曲面时，利用该方法构造的过渡曲线曲面不仅与2 被过渡曲线曲面的参数方向保持一致，而且可利用所带的自由参数对其形状进行调整。通过能量优化模型确定自由参数的取值，可获得尽可能光顺的过渡曲线曲面。所提方法弥补了保参数方向构造过渡曲线曲面方法的不足，是一种实用的过渡曲线曲面构造方法。

当数据点给定时，三次Cardinal 样条的张力参数和边界条件均为自由变量，因此可对这些自由变量进行优化，以得到满足某种特定要求的最佳三次Cardinal 样条。讨论了如何通过优化张力参数与边界条件使得构造的平面三次Cardinal 样条尽可能光顺。首先，分析了三次Cardinal 参数样条曲线形状的影响因素；然后，利用曲率变化能极小对三次Cardinal 参数样条曲线的张力参数与边界条件进行优化，获得张力参数与边界条件的唯一解； 最后，给出了对应三次Cardinal 样条函数的张力参数与边界条件的优化方法。实例表明，经曲率变化极小优化张力参数与边界条件后的三次Cardinal 样条比三次Catmull-Rom 样条更为光顺，插值效果更好。

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Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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