The popularity of cloud computing has revolutionized Online Analytical Processing (OLAP), yet risks of privacy leakage limit the use of public clouds in security-critical scenarios, such as healthcare and finance. Fully Homomorphic Encryption (FHE) is a promising solution that enables computations on encrypted data without decryption. However, the performance overhead of FHE hinders its practical use in OLAP. Existing FHE-based OLAP systems primarily focus on single-machine optimization and lack proper co-design with OLAP characteristics, leading to suboptimal effectiveness. Our key idea is to distribute FHE-based OLAP across multiple machines, inspired by the MapReduce model, to reduce end-to-end latency. In this paper, we propose Hedas Hedas stands for Homomorphic Encryption-based Distributed Analytical System, the first distributed FHE-based OLAP system that achieves secure and efficient OLAP. Hedas effectively addresses the limitations of FHE by introducing the pre-group operation and two key stages: Secure Map (SMap) and Secure Reduce (SReduce). These stages securely and efficiently execute filtering and aggregation operations in OLAP. By leveraging the MapReduce model, Hedas effectively distributes FHE-based OLAP across multiple machines, achieving a notable reduction ( \(\sim \) \(44.1\%\) ) in end-to-end latency using four computing nodes, with further reductions as the number of computing nodes increases. Additionally, two case studies are conducted to address the optimization of the filter bottleneck within Hedas, and evaluation experiments demonstrate the efficiency and scalability of Hedas compared to the state-of-the-art single-machine FHE-based OLAP system.