With the emergence of mobile social networks, users can make friends or negotiate projects at any time and anywhere in social communities through their mobile devices (such as smartphones, iPads). The two sides of making friends or cooperation want to know the comparison results between each other in many aspects. Aiming at the requirements of these interactive applications in social networks and considering the limited-resource setting of mobile users, in this paper, we propose a cloud-aided privacy-preserving multi-dimensional data comparison protocol. We introduce a novel comparison method for two multi-dimensional data. Because of the blinded processing trick in our comparison method and the Paillier encryption, the proposed protocol can realize our comparison method without revealing users’ data and the comparison results. Besides, a fog device and a cloud server conduct most of the computations. Furthermore, users pack their multi-dimensional data into one data using Horner Rule, making finishing the comparison of two multi-dimensional data through one-round system communication. Therefore, the presented protocol can significantly lower the computation and communication costs of the system, especially that of the user-side. Security analysis is inducted to validate security properties. Moreover, performance evaluations illustrate the computation and communication efficiency of the proposed protocol.