Nowadays, the availability of parking spaces is far behind the quick rising number of cars. Rather than building more lots, a better way is to share private-owned parking spaces. However, this faces the challenge that users are not willing to expose their privacy to the public. To solve this problem, we propose a new architecture for parking space sharing, integrating homomorphic cryptography into the design of a secure protocol for parking space searching and booking. The proposed privacy-preserving matching scheme (PPMS) is constructed in an untrusted third-party service system including two independent entities, namely, a server and an intermediary platform. Via the participant comparison protocol (PCP), a driver can choose from the matching result and be navigated to the parking space near his destination, without knowing any information of the provider and vice versa. In the meanwhile, in order to further improve the efficiency of matching, we also propose a block algorithm based on the longitude and latitude (BABLL), which utilizes a novel partitioning scheme. The feasibility of the architecture is validated through the detailed theoretical analysis and extensive performance evaluations, including the assessment of the resilience to attacks.