The paper contains the overview and analysis of modern cryptographic primitives which have a significant potential for the application in privacy-preserving cloud systems. We analyze the primitives for anonymous routing, the group signature schemes, the attribute authentication schemes and homomorphic encryption schemes. All these cryptographic constructions have appeared quite recently, most of them in the last decade. We show where these theoretic constructions can be used in practical systems. Furthermore, we show the architecture of an ideal privacy-preserving cloud system. In such a system, the users are protected against attacks on their data as well as on their digital identity and privacy. Using the privacy-preserving cloud system, the electronic services can be provided more securely and without unauthorized private data leaks. At the same time, the cloud service providers keep complete control over their assets and the accounting of services provided.