Spatial crowdsourcing (SC) outsources tasks to a set of workers who are required to physically move to specified locations and accomplish tasks. Recently, it is emerging as a promising tool for emergency management, as it enables efficient and cost-effective collection of critical information in emergency such as earthquakes, when search and rescue survivors in potential ares are required. However in current SC systems, task locations and worker locations are all exposed in public without any privacy protection. SC systems if attacked thus have penitential risk of privacy leakage. In this paper, we propose a protocol for protecting the privacy for both workers and task requesters while maintaining the functionality of SC systems. The proposed protocol is built on partially homomorphic encryption schemes, and can efficiently realize complex operations required during task assignment over encrypted data through a well-designed computation strategy. We prove that the proposed protocol is privacy-preserving against semi-honest adversaries. Simulation on two real-world datasets shows that the proposed protocol is more effective than existing solutions and can achieve mutual privacy-preserving with acceptable computation and communication cost.