Edge computing reduces latency and optimizes resource allocation by moving data processing to the network’s edge, ideal for tasks like post-quantum encryption. Lattice cryptography, particularly discrete Gaussian distribution, is crucial in this field. The mainstream approach for discrete Gaussian sampling involves generation trees, which require storing table information, leading to unnecessary memory usage. Balancing computational and memory loads while ensuring time consistency is crucial for post-quantum blockchain applications. Additionally, ensuring consistent sampling times for binary trees of different depths is also challenging. Accordingly, we propose a generative model that builds upon Generative Adversarial Networks (GAN) by incorporating rigorous privacy guarantees and parameter obfuscation, fully utilizing the advantages of having a fixed structure for generative models and allowing them to retain constant time. Through extensive experiments, including comparison with Falcon, which is a NIST Round-3 finalist for the post-quantum digital signature standard. Simulation results indicate that the proposed method can achieve enhanced security in the signature process while keeping computational overhead within manageable limits.