This technical note proposes an algorithm to assess the safety of the cyber-physical system (CPS) in the presence of cyber attacks, which can be designed intelligently to avoid the detection. The main idea is based on the reachability analysis that computes the reachable set of CPS states possibly reached by all potential cyber attacks regardless of their detection. The reachable set computation typically demands a large computation cost and has mostly relied on the (over) approximation techniques. However, our algorithm analytically derives the exact reachable set solution and further establishes a recursive computation structure that can perform in the real-time CPS operation. This can significantly enhance the quality of the online safety assessment, enabling more reliable, less conservative, and computationally efficient process.