In this paper, we study the privacy-preserving task assignment in spatial crowdsourcing, where the locations of both workers and tasks, prior to their release to the server, are perturbed with Geo-Indistinguishability (a differential privacy notion for location-based systems). Different from the previously studied online setting, where each task is assigned immediately upon arrival, we target the batch-based setting, where the server maximizes the number of successfully assigned tasks after a batch of tasks arrive. To achieve this goal, we propose the k-Switch solution, which first divides the workers into small groups based on the perturbed distance between workers/tasks, and then utilizes Homomorphic Encryption (HE) based secure computation to enhance the task assignment. Furthermore, we expedite HE-based computation by limiting the size of the small groups under k. Extensive experiments demonstrate that, in terms of the number of successfully assigned tasks, the k-Switch solution improves batch-based baselines by 5.9X and the existing online solution by 1.74X, with no privacy leak.