Multi-agent planning using MA-STRIPS-related models is often motivated by the preservation of private information. Such motivation is not only natural for multi-agent systems, but it is one of the main reasons, why multi-agent planning (MAP) problems cannot be solved centrally. In this paper, we analyze privacy-preserving multi-agent planning (PP-MAP) from the perspective of secure multiparty computation (MPC). We discuss the concept of strong privacy and its implications and present two variants of a novel planner, provably strong privacy-preserving in general. As the main contribution, we formulate the limits of strong privacy-preserving planning in the terms of privacy, completeness and efficiency and show that, for a wide class of planning algorithms, all three properties are not achievable at once. Moreover, we provide a restricted variant of strong privacy based on equivalence classes of planning problems and show that an efficient, complete and strong privacy-preserving planner exists for such restriction.