Keypoint detector and descriptor are two main components of point cloud registration. Previous learning-based keypoint detectors rely on saliency estimation for each point or farthest point sample (FPS) for candidate points selection, which are inefficient and not applicable in large scale scenes. This paper proposes Random Sample-based Keypoint Detector and Descriptor Network (RSKDD-Net) for large scale point cloud registration. The key idea is using random sampling to efficiently select candidate points and using a learning-based method to jointly generate keypoints and corresponding descriptors. To tackle the information loss of random sampling, we exploit a novel random dilation cluster strategy to enlarge the receptive field of each sampled point and an attention mechanism to aggregate the positions and features of neighbor points. Furthermore, we propose a matching loss to train the descriptor in a weakly supervised manner. Extensive experiments on two large scale outdoor LiDAR datasets show that the proposed RSKDD-Net achieves state-of-the-art performance with more than 15 times faster than existing methods. Our code is available at https://github.com/ispc-lab/RSKDD-Net.