Multi-party access control has been proposed to enable collaborative decision making for the protection of co-owned resources. In particular, multi-party access control aims to reconcile conflicts arising from the evaluation of policies authored by different stakeholders for jointly-managed resources, thus determining whether access to those resources should be granted or not. While providing effective solutions for the protection of co-owned resources, existing approaches do not address the protection of policies themselves, whose disclosure can leak sensitive information about, e.g., the relationships of co-owners with other parties. In this paper, we propose a privacy-preserving multi-party access control mechanism, which preserves the confidentiality of user policies. In particular, we propose secure computation protocols for the evaluation of multi-party policies, based on two privacy-preserving techniques, namely homomorphic encryption and secure function evaluation. An experimental evaluation of our approach shows its practical feasibility in terms of both computation and communication costs.