Provable Security - Recent research has shown that hackers can efficiently infer sensitive user activities only by observing the network traffic of smart home devices. To protect users’ privacy, researchers have designed several traffic obfuscation methods. However, existing methods usually consume high bandwidth or provide weak privacy protection. In this paper, we conduct thorough research on smart home traffic obfuscation. We first propose a fixed-value obfuscation scheme and prove that it is perfectly secure by showing the indistinguishability of user activities. Yet, fixed-value obfuscation has high bandwidth consumption. To further reduce the bandwidth consumption, we propose combining fixed-value obfuscation with Multipath TCP transmission. The security and performance of the proposed multipath fixed-value obfuscation method are theoretically analyzed. We have implemented the proposed methods and tested them on public packet traces and simulated smart home networks. The experimental results match well with the theoretical analysis.