This paper presents a video surveillance-based face image security system that utilizes post-quantum cryptography algorithm for enhanced security. The system accurately extracts face images from the surveillance video using the multi-task cascaded convolutional neural network (MTCNN) and subsequently encrypts them using the ring learning with errors (ring-LWE) algorithm. The encrypted facial images are then transmitted to a remote server for secure storage. The proposed system is implemented on a central processing unit (CPU) platform and its operations are accelerated using a graphics processing unit (GPU). The evaluation results on an NVIDIA GeForce RTX 3090 Ti GPU for videos from the standard reference database of National Institute of Science and Technology (NIST) show that the proposed system can perform face image encryption and decryption as fast as 1.33 ms and 0.51 ms on GPU platform for parameter set n = 256 and q = 7681, respectively. Moreover, the analysis of security parameters such as histogram, correlation coefficients, and entropy proves that the proposed system outperforms its predecessors in terms of confidentiality. The proposed system is also assessed using various security parameter sets to showcase its compatibility with diverse computational resources.