In the dataset collected from various social networks, each user is matched with the closest target user to establish associations primarily within similar social circles, encompassing aspects such as education, family, and hobbies. It's worth noting that the utilization of social data, which may contain consumer information, can potentially expose privacy concerns. To address this, the paper presents a methodology based on the discrete logarithm, employing the Kangaroo method to compute within an arbitrary cyclic group. This method assumes the value lies within a predefined interval. Additionally, Wiener and Van Oorschot introduced a method called “linear speed-up,” which minimizes storage requirements. It can also be effectively monitored and parallelized in its corresponding design, making the Kangaroo technique a valuable tool for addressing discrete logarithm issues. The Kangaroo method, offers a robust solution for discrete logarithm problems. Parameters can be fine-tuned to optimize its performance, preventing “useless collisions.“ This paper also introduces an analysis of the potential acceleration achieved by utilizing parallel resources beyond the algorithm's initial configuration. Through this approach, the Kangaroo method is applied to cryptosystems that safeguard user privacy when dealing with social data. To maintain privacy, the propagation direction is controlled by a limited set of indicators, ensuring that each user can access consistent functions based on homomorphic attributes, while remaining unable to access another user's data due to the random number concealment. This paper demonstrates that the proposed method is designed with consideration for communication cost and computation overhead.