Task assignment is a critical issue in mobile crowdsensing (MCS), an emerging sensing paradigm applied to realize various sensing applications for smart cities. Existing task assignment schemes mostly require the exact location information of tasks and workers for optimization, which inevitably brings the issue of location privacy leakage. Therefore, researchers have started investigating privacy-preserving task assignment schemes. However, most of these works either make inaccurate assignments or only concentrate on workers' privacy. In this article, we propose a novel bilateral privacy-preserving and accurate task assignment framework in fog-assisted MCS, called BRAKE. Specifically, we utilize the multisecret sharing scheme to preserve location privacy in the MCS task assignment, where tasks and workers only need to provide the secret shares of their real location information to fog nodes. Moreover, we consider distance-oriented and time-oriented tasks for assignment optimization and propose an adaptive top-k worker selection algorithm to accurately select the most suitable workers. The security analysis proves that BRAKE can resist collusion attacks, and the extensive evaluation results demonstrate the efficiency and accuracy of BRAKE.