With the rapid development of sixth-generation (6G) communication technology, global communication networks are moving towards the goal of comprehensive and seamless coverage. In particular, low earth orbit (LEO) satellites have become a critical component of satellite communication networks. The emergence of LEO satellites has brought about new computational resources known as the \textit{LEO satellite edge}, enabling ground users (GU) to offload computing tasks to the resource-rich LEO satellite edge. However, existing LEO satellite computational offloading solutions primarily focus on optimizing system performance, neglecting the potential issue of malicious satellite attacks during task offloading. In this paper, we propose the deployment of LEO satellite edge in an integrated satellite-terrestrial networks (ISTN) structure to support \textit{security-sensitive computing task offloading}. We model the task allocation and offloading order problem as a joint optimization problem to minimize task offloading delay, energy consumption, and the number of attacks while satisfying reliability constraints. To achieve this objective, we model the task offloading process as a Markov decision process (MDP) and propose a security-sensitive task offloading strategy optimization algorithm based on proximal policy optimization (PPO). Experimental results demonstrate that our algorithm significantly outperforms other benchmark methods in terms of performance.
