In this work, we leverage the pure skin color patch from the face image as the additional information to train an auxiliary skin color feature extractor and face recognition model in parallel to improve performance of state-of-the-art (SOTA) privacy-preserving face recognition (PPFR) systems. Our solution is robust against black-box attacking and well-established generative adversarial network (GAN) based image restoration. We analyze the potential risk in previous work, where the proposed cosine similarity computation might directly leak the protected precomputed embedding stored on the server side. We propose a Function Secret Sharing (FSS) based face embedding comparison protocol without any intermediate result leakage. In addition, we show in experiments that the proposed protocol is more efficient compared to the Secret Sharing (SS) based protocol.