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We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We show that two classes of Maximum Mean Discrepancy (MMD) based tests attain this optimality on Rd, while the quadratictime Kernel Stein Discrepancy (KSD) based tests achieve the maximum exponential decay rate under a relaxed level constraint. Under the same performance metric, we proceed to show that the quadratic-time MMD based two-sample tests are also optimal for general two-sample problems, provided that kernels are bounded continuous and characteristic. Key to our approach are Sanov’s theorem from large deviation theory and the weak metrizable properties of the MMD and KSD. 

In this paper, we propose a secure lightweight and thing-centered IoT communication system based on MQTT, SecT, in which a device/thing authenticates users. Compared with a server-centered IoT system in which a cloud server authenticates users, a thing-centered system preserves user privacy since the cloud server is primarily a relay between things and users and does not store or see user data in plaintext. The contributions of this work are three-fold. First, we explicitly identify critical functionalities in bootstrapping a thing and design secure pairing and binding strategies. Second, we design a strategy of end-to-end encrypted communication between users and things for the sake of user privacy and even the server cannot see the communication content in plaintext. Third, we design a strong authentication system that can defeat known device scanning attack, brute force attack and device spoofing attack against IoT. We implemented a prototype of SecT on a $10 Raspberry Pi Zero W and performed extensive experiments to validate its performance. The experiment results show that SecT is both cost-effective and practical. Although we design SecT for the smart home application, it can be easily extended to other IoT application domains.