Since the number of facial images has grown in social networks, such as Facebook and Instagram, face recognition has been recognized as one of the important branches of image processing research area, and large databases of face images have been created. As a result, the response time of the face recognition system is recognized as a challenge. Fortunately, dimension reduction techniques help to reduce the number of computations significantly, which directly effects on system response time. As many facial features do not include important information, which is required for getting a better result from the face recognition systems, these techniques are applicable for facial images, as well. Local Feature Hashing (LFH) is a hash-based algorithm that has been used for face recognition. It has shown notable computational improvements over naive search and can overcome some challenges, including recognition of pose, facial expression, illumination, and partial occlusion parameters. With the aim of improving the time that it takes to run the LFH algorithm, we have tested several versions of Locality-Sensitive Hashing (LSH) algorithm. The results showed that some of these algorithms improve the response time of the LFH algorithm. In comparison with the previously conducted research, the number of input images has been increased in our tests. Besides, the number of extracted key-point vectors have been decreased, and the accuracy has not been decreased. In addition, our algorithm is able to overcome the challenge of the existence of foreign objects, such as glass. Among all different hash versions that for the first time used for face recognition, some of them are not recommended for these systems and several functions can provide minimum response time, rather than previous hash-based algorithms.