Given the application domains of soft set theory, such as decision-making processes, image processing, machine learning, and data mining, it is natural to consider that this theory could be utilized more effectively in encryption systems. A review of the literature reveals that soft set-based encryption systems have been explored in a limited number of studies. This study seeks to develop a new approach for soft sets in encryption systems by utilizing newly introduced algebraic and topological tools. In this system, parties will be able to generate encryption keys independently using soft sets they determine themselves rather than through prior mutual agreement. Additionally, the method of key generation and the size of the key space in the resulting encryption system provides a more secure and distinct alternative compared to existing soft set-based encryption systems.