A substantial number of passengers in Europe rely on trains for transportation, facilitated by a network of high-speed international trains. However, the coordination of train schedules across multiple networks often poses challenges due to incompatible timings. The scheduling of multiple train networks shares similarities with multi-processor task scheduling and airline scheduling but is distinguished by its cooperative nature rather than a competitive one. Cooperative scheduling necessitates the sharing of private information. This information, 'demand', is commercial sensitive information, since it can reveal demographic information like incomes and tax returns. Privacy-preserving protocols can enable the computation of statistics without revealing this demands (in railway systems) to unauthorized parties. Despite the critical role of privacy in multi-party scheduling, research in this domain remains limited due to domain specific constraints. A model supporting such privacy considerations could significantly help Europe achieve its carbon-neutral goals while improving cross-border services. In this research, we propose a system designed to facilitate joint service scheduling, ensuring confidentiality, integrity, and authenticity. We use partial and fully homomorphic encryption techniques that mimic the outcomes achievable with a trusted third party. We conduct a comparative analysis of online and offline approaches, emphasizing how they achieve confidentiality, collusion-resistance, traceability and non-repudiation. Theoretical and experimental evaluations demonstrate the feasibility of the system for real-world applications by creating schedules for upto four parties. Our solution for scheduling seven slots takes approximately three hours, which is a feasible duration to solve a problem of this size.