Next-generation wireless networks, including edge intelligence and wireless distributed learning systems, confront two main obstacles: protecting privacy and communication efficiency. This work addresses these challenges within a distributed learning framework by leveraging the inherent privacy advantages of quantization. We utilize a Laplace mechanism based on random quantization that simultaneously ensures communication efficiency and robust privacy protection. Unlike existing Gaussian mechanisms, which do not account for decoder or server-level privacy, our approach safeguards against an honest-but-curious server attempting to decode data using dither signals. This mechanism guarantees privacy not only for the database and downstream processes but also at the server level. Through extensive evaluation in a distributed learning setup, we validate the effectiveness of the Laplace mechanism on datasets such as MNIST and CIFAR-10. Our results demonstrate improved accuracy compared to the Gaussian mechanism while simultaneously ensuring communication efficiency and privacy protection to both the decoder (server) and database through precise realization of the Laplace distribution, which is often a challenge while simultaneously achieving communication efficiency and privacy protection with the help of quantization. This highlights the potential of random quantization in achieving both privacy and utility in distributed systems.